2018052723484407_bus340_opsmgt__1_.pptx2018052723485304_bus340_opsmgt.pptx2018052723483908_bus340_opsmgt.pptx2018052723484806_bus340_opsmgt.pptx
Write a 3.5-page to 4.5-page paper that highlights your reflections about relevant operations lessons from the Boeing tour and our course time studying Lean. The paper should address what you observed and learned at Boeing, and tie that to what you read in All I Need to Know About Manufacturing I Learned in Joe’s Garage, what we discussed in class and you read in the course textbook and other readings regarding Lean concepts, and your experience in the various in-class simulations pertaining to Lean. The paper should not merely report what happened but should display critical thinking and personal insight.
here’s some more details:
Lean Reflection Paper(10%). Each student will write a 4-page paper that highlights his/her reflections about relevant operations lessons from the Boeing tour and our course time studying Lean. The paper should address what you observed and learned at Boeing, and tie that to what you read in All I Need to Know About Manufacturing I Learned in Joe’s Garage, what we discussed in class and you read in the course textbook and other readings regarding Lean concepts, and your experience in the various in-class simulations pertaining to Lean. The paper should not merely report what happened but should display critical thinking and personal insight. Additional details for this assignment will be posted on Canvas.
NOTE:THE ATTACHED video shows you what I similarly experience in Boeing tour but please do not mention anything about Toyota
VIDEO:
https://youtu.be/k4-eJsFdxaU
Operations and Project Management
ELCBUS 340
16 April 2018
1
Today’s Agenda
Class Administration – Littlefield Launch, Team Projects
Quality
Types of Variation
Control Charting
Process Capability Ratio (Cp)
Process Capability Index (Cpk)
Statistical Process Control
Continuous
Discrete
Process Capability Studies
2
50,000 Feet Overview of OPM
Managing Processes
Process Strategy
Process Performance
& Quality
Constraint Management
Process Layout
Lean Systems
Process Analysis
Using Operations
to Compete
Operations As a
Competitive Weapon
Operations Strategy
Project Management
Managing Value Chains
Supply Chain Strategy
Inventory Management
Location
Forecasting
Sales & Operations
Planning
Scheduling
Resource Planning
Process Analysis
3
Service vs. Manufacturing
Small vs. Medium vs. Large Firms
Industry type: hightech, healthcare, aerospace, IT, etc ….
Quality
A term used by customers to describe their general satisfaction with a service or product.
Costs of Quality
Four major categories:
Prevention Costs
Appraisal Costs
Internal Failure Costs
External Failure Costs
Many companies spend significant time, effort, and expense on systems, training, and organizational changes to improve quality and performance of their processes. It is estimated that COQ ranges from 20 to 30 percent of gross sales.
Costs of Quality
Prevention Costs are associated with preventing defects before they happen
Appraisal Costs are incurred when a firm assesses the level of performance of its processes
Internal Failure Costs result from defects that are discovered during the production of a service or product
External Failure Costs arise when a defect is discovered after the customer receives the product or service
Ethical Failure Costs are the societal and monetary costs associated with passing defective services or products to customers
TQM & Six Sigma
What is
Total Quality Management?
Total Quality Management (TQM)
Is a quality strategy that focuses on achieving high levels of process performance and quality by stressing three principles:
Customer Satisfaction
Employee Involvement
Continuous Improvement
Customer Satisfaction
Conformance to Specifications
Value
Fitness for Use
Support
Psychological Impressions
Total Quality Management
Principles
Customer satisfaction (internal or external): when customers’ expectations have been met or exceeded.
Conformance to specifications
It is the processes that produced the service or product that are really being judged.
Specifications may relate to consistent quality, on-time delivery, or delivery speed.
Value
How well the service or product serves its intended purpose at a price customers are willing to pay.
Fitness for use: customer may consider the convenience of a service or the mechanical features of a product.
Support: the service or product support may be as important to the customer as the service or product itself.
Psychological impressions: atmosphere, image, or aesthetics
9
Employee Involvement
Cultural Change
Quality at the Source
Teams
Employee Empowerment
Problem-solving teams
Special-purpose teams
Self-managed teams
Total Quality Management
Principles
Employee involvement
Cultural change
Challenge is to define customer for each employee
External customers buy the service or product.
Internal customers are employees in the firm who rely on output of other employees. An assembly line is a chain of internal customer-supplier relationships, with an external customer purchasing the finished goods.
Top management must motivate cultural change.
Everyone is expected to contribute and share the view that quality control is an end to itself
Quality at the source
Teams
Employee involvement is a key tactic for improving processes and quality
Small groups of people
Common purpose.
Set their own performance goals and approaches
Hold themselves accountable for success
Three employee-empowerment approaches to teamwork
Problem-solving teams (also called quality circles)
Special-purpose teams
Self-managing teams, the highest level of worker participation
10
Continuous Improvement
Kaizen
Problem-solving tools
Plan-Do-Study-Act Cycle
Total Quality Management
Principles
Based on the Japanese concept, kaizen
The philosophy of continually seeking ways to improve processes.
Not unique to quality. Applies to process improvement as well.
Getting started
SPC training
Make SPC a normal aspect of daily operations.
Build work teams and employee involvement.
Utilize problem-solving tools within the work teams.
Develop operator ownership in the process.
11
Plan-Do-Study-Act Cycle
Total Quality Management
Principles
Problem-solving process: The Deming Wheel
Plan—select a process needing improvement, document process, analyze data, set improvement goals, discuss alternatives, assess benefits and costs, develop a plan and improvement measures.
Do—implement plan, monitor improvements.
Study—analyze data to evaluate effectiveness of the plan.
Act—document and disseminate improved process as a standard procedure.
12
What is Six Sigma?
Six Sigma
A comprehensive and flexible system for achieving, sustaining, and maximizing business success by minimizing defects and reducing variation in processes.
Six Sigma
Project Frameworks
DMAIC
DFSS (Define for Six Sigma)
DMADV
IDOV
DMAIC
5 – 15
Control
An improvement system for existing processes falling below specification and looking for incremental improvement
Define
Measure
Analyze
Improve
DMADV
Verify
An improvement system used to develop new processes or products at Six Sigma quality levels
Define
Measure
Analyze
Design
IDOV
Used for designing a completely new product or business process to meet customer needs and specifications or to achieve Six Sigma quality levels
Identify
Design
Optimize
Verify
The Tools
Six Sigma Tools
[Introduce the Tools]
Standard Work
The best combination of machines and people working together to produce a product or service at a particular point in time.
5S
5S is a workplace organization method used to assure work can be done effectively and efficiently.
SIPOC
SIPOC is a tool that summarizes the inputs, outputs and steps of one or more processes in table form.
RACI
RACI is a method to identify the roles and responsibilities of participants in a cross organizational team.
5Ys
Statistics
Waste
Worker Realignment
Workplace Reorganization
DIG
CAPA
Affinity
Fishbone
Setup Reduction
Visual Controls
Small Lots
Kanban
A3
1-Piece Flow
SPC
Kaizen
Cycle Time Reduction
TPM
FMEA
DOE
Project Management
Reengineering
Six Sigma Project
Balanced Scorecard
QFD
Hoshin Planning
VOC
18
Six Sigma Certifications
Master Black Belt
Black Belt
Green Belt
Yellow Belt
Certifying Organizations?
Acceptance Sampling
Acceptance Sampling
The application of statistical techniques to determine if a quantity of material from a supplier should be accepted or rejected based on the inspection or test of one or more samples.
Acceptable Quality Level
The quality level desired by the consumer.
Acceptance Sampling
Acceptance Sampling
Firm A uses TQM or Six
Sigma to achieve internal
process performance
Supplier uses TQM or Six
Sigma to achieve internal
process performance
Yes
No
Yes
No
Fan motors
Fan blades
Accept
blades?
Supplier
Manufactures
fan blades
TARGET: Firm A’s specs
Accept
motors?
Motor sampling
Blade sampling
Firm A
Manufacturers
furnace fan motors
TARGET: Buyer’s specs
Buyer
Manufactures furnaces
Six Sigma Approach
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Process average OK;
too much variation
Process variability OK;
process off target
Process
on target with
low variability
Reduce
spread
Center
process
X
X
X
X
X
X
X
X
X
Statistical Process Control
Statistical Process Control (SPC)
SPC
The application of statistical techniques to determine whether a process is delivering what the customer wants.
Performance Measurements
Variables (Continuous) – Characteristics that can be measured.
Attributes (Discrete) – Characteristics that can be counted.
Statistical Process Control (SPC)
A process that is in statistical control:
Is stable and predictable
Variation will be limited to an expected range
But still may not be capable
A process that is out of statistical control:
Is unstable and unpredictable
Variation will not be limited to the expected range
Variation may be extreme
Types of Variation
Common cause
Variation that is random, unidentifiable and unavoidable
Special cause
Variation that can be identified and eliminated
Effects of Special Cause Variation on the Process Distribution
Control Charts
Time-ordered diagram used to determine whether observed variations are abnormal
Control Charting
A control chart always has a central line for the average, an upper line for the upper control limit and a lower line for the lower control limit.
By comparing current data to these lines, one can make conclusions about whether the process variation is in control or out of control (special cause variation)
Variable data control charts use two charts with attribute data using one chart
[Explain]
Describe the anatomy of a control chart – use the bullets as a guideline for your explanation.
[Draw this on the Board]
[Insert graphic from supplemental PPT, slide 7]
Remember the Galton box?
If you turn the SPC on its end and shook all of the points to the bottom, you would be a Probability Density Function (PDF) that would appear to be a normal distribution.
[Next Slide]
Control charting process
29
Types of
Control Charts
Variable Data Control Charts
X-bar Chart – Measures whether the process is generating output consistent with a target value.
R Chart – Measures the variability of the process.
S Chart – Measures the Standard Deviation of the process.
Attribute Data Control Charts
p-chart – Measures the proportion of defective services of products in a process.
c-chart – Measures the proportion of defects in one service or product.
Continuous Control Charts
Charts
R Charts
S Charts
[Explain]
Describe the anatomy of a control chart – use the bullets as a guideline for your explanation.
[Draw this on the Board]
[Insert graphic from supplemental PPT, slide 7]
Remember the Galton box?
If you turn the SPC on its end and shook all of the points to the bottom, you would be a Probability Density Function (PDF) that would appear to be a normal distribution.
[Next Slide]
Control charting process
31
– Chart
Data are collected in a face-and-plunge operation done on a lathe. The dimension being measured is the groove inside diameter (ID), which has a tolerance of 7.125 ± 0.010. Four parts are measured every hour. These values have been entered in the table below.
Chart
Control Limits
=
=
Where:
= the central line of the chart
= a constant to provide three-sigma limits for the sample mean
Calculating Control Chart Factors
Chart
Control Limits
=
=
Plot data over time
Centerline =
Upper and Lower Control Limits
LCL
UCL
=
=
Where:
= average of several R values and the central line of the R control chart
, = constants that provide three standard deviation limits for the given sample size
R-Chart
Control Limits
Calculating Control Chart Factors
R-Chart
Control Limits
=
= 2.282(0.0037) = 0.008443
=
= 0(0.0037) = 0
Plot the Range of each subgroup overtime, the calculated value is the centerline.
R-Chart
Variation and out of control data points
Common
Cause
Variation
Out-of-control point (Special Cause)
Time plot of sequential process measurements
Sample Number 1 2 3 4 5
1 0.5014 0.5022 0.5009 0.5027 0.5045
2 0.5021 0.5041 0.5024 0.5020 0.5062
3 0.5018 0.5026 0.5035 0.5023 0.5054
4 0.5008 0.5034 0.5024 0.5015 0.5047
5 0.5041 0.5056 0.5034 0.5047 0.5043
0.50204 0.50358 0.50252 0.50264 0.50502 0.50316
R 0.0033 0.0034 0.0026 0.0032 0.0019 0.00288
Example
The management of West Allis Industries is concerned about the production of a special metal screw used by several of the company’s largest customers. The diameter of the screw is critical to the customers. Data from five samples appear in the accompanying table. The sample size is 5. Is the process in statistical control?
=
0.5032 + 0.577(0.0029) = 0.5048
=
0.5032 – 0.577(0.0029) = 0.5015
Example
Compute the mean for each sample and the control limits.
Process average is NOT in statistical control.
Example
05- 46
Compute the range for each sample and the control limits
= = 2.114(0.0029) = 0.0061
= = 0(0.0029) = 0
Example
Process variability is in statistical control.
Example
=
=
Where:
= average of several Stdev values and the central line of the S control chart
, = constants that provide three standard deviation limits for the given sample size
S-Chart
Control Limits
S – Chart
Subgroup Obs 1 Obs 2 Obs 3 Obs 4 Obs 5 Obs 6 Obs 7 Obs 8 Obs 9 Obs 10
1 46.8204 58.8572 67.7175 51.3078 53.3025 51.3258 59.0268 49.9933 47.086 60.4783
2 53.9847 47.4005 59.1598 57.2251 57.3207 50.4045 54.8046 55.7574 58.8662 59.2083
3 52.4315 63.2146 61.4096 59.342 57.4605 53.7083 57.0489 58.4325 48.5544 61.4105
4 50.9712 53.4314 52.9449 66.827 43.9849 67.8154 57.4312 44.3194 60.5493 59.6383
5 62.0421 57.1784 60.1955 56.4687 64.9641 52.9195 48.6739 56.3773 60.3216 58.9171
6 53.1269 58.374 63.7938 50.8965 52.4253 52.696 64.2078 65.9364 55.8426 54.478
7 55.0507 53.8931 51.8424 68.7073 50.173 58.0991 59.3456 57.9232 69.2396 60.2033
8 54.3315 52.3679 65.2346 62.6795 61.5929 54.0084 61.4465 58.4423 55.7608 54.1888
9 59.9584 59.1762 51.5629 63.0753 59.4856 63.2215 50.8982 62.4343 49.4303 48.9902
10 54.0402 56.3253 53.3773 54.7368 59.8292 54.6631 62.2161 61.5533 66.2283 63.0929
11 57.2273 65.8816 67.9839 51.7812 63.3054 56.5156 54.5318 54.4049 54.6459 52.6297
12 51.5133 61.0216 61.2776 62.1072 56.1983 54.805 59.083 58.8301 51.2939 54.9033
13 41.6784 46.7246 90.9593 57.7698 57.6619 53.9903 47.1248 50.2183 52.0052 57.2942
14 52.8303 42.4179 58.0054 60.1385 59.9954 60.5936 49.6827 68.2645 53.5693 60.6435
15 58.1128 53.4343 49.8567 53.3065 48.6588 53.4726 61.1457 61.6733 54.4246 51.8054
16 59.4674 66.2816 71.1186 63.6602 65.4012 53.2372 55.0633 46.6954 57.0477 61.8819
17 63.6288 47.3453 45.6509 40.2198 51.7382 51.0804 56.4197 57.7979 65.3047 66.539
18 59.5853 50.9825 56.2445 103.441 52.6224 63.7297 43.3771 58.7982 59.8339 57.9202
19 57.8042 49.2275 56.9069 55.4057 60.342 62.0972 57.2 38.6509 61.459 59.144
20 53.2788 62.1238 48.7058 58.0984 52.3153 56.8277 53.3615 64.6894 56.0133 56.9455
21 61.0891 52.2114 55.0061 50.2427 55.6495 53.7419 63.6856 56.5452 55.6084 67.2915
22 47.6385 62.0744 71.2102 64.6661 58.1218 56.8151 62.913 53.8949 64.6937 53.5819
23 46.1471 57.2321 60.0446 59.5476 54.4676 48.8446 57.6602 58.5467 65.4449 50.6271
24 53.1199 52.4063 53.1227 52.1897 56.6952 53.0823 61.1469 50.5565 56.9315 60.0423
25 55.3156 60.7648 55.0855 56.2381 60.3981 61.7266 69.0841 51.4446 58.1248 50.136
54.44778 55.61393 59.53668 59.20314 56.56439 55.97686 57.06316 56.08721 57.5312 57.67965 56.9704
Stdev 5.286458 6.28949 9.49476 11.10656 5.147585 4.750668 5.9335 6.835565 5.76572 4.830527 6.544084
Calculating Control Chart Factors
Chart
Control Limits when using large sample sizes (S Chart)
=
=
S-Chart
Control Limits
=
= 1.436(6.5441) = 9.3973
=
= 0.564(6.5441) = 3.6909
54.447775999999983 55.613932000000005 59.53667999999999 59.203140000000012 56.564391999999991 55.976856000000005 57.063160000000011 56.087208000000011 57.531196000000001 57.679648
56.970398800000012 56.970398800000012 56.970398800000012 56.970398800000012 56.97039880000001 2 56.970398800000012 56.970398800000012 56.970398800000012 56.970398800000012 56.970398800000012
53.002844821727074 53.002844821727074 53.002844821727074 53.002844821727074 53.002844821727074 53.002844821727074 53.002844821727074 53.002844821727074 53.002844821727074 53.002844821727074
60.937952778272951 60.937952778272951 60.937952778272951 60.937952778272951 60.937952778272951 60.937952778272951 60.937952778272951 60.937952778272951 60.937952778272951 60.937952778272951
X-Bar: Stacked Data (Y)
5.2864584810532644 6.2894901987177159 9.4947599494406294 11.106561756232184 5.1475848615248676 4.7506682219522194 5.9335003652986451 6.8355648020676014 5.7657197453628175 4.8305269359839684
6.5440835317633903 6.5440835317633903 6.5440835317633903 6.5440835317633903 6.5440835317633903 6.5440835317633903 6.5440835317633903 6.5440835317633903 6.5440835317633903 6.5440835317633903
3.6959524205845296 3.6959524205845296 3.6959524205845296 3.6959524205845296 3.6959524205845296 3.6959524205845296 3.6959524205845296 3.6959524205845296 3.6959524205845296 3.6959524205845296
9.3922146429422515 9.3922146429422515 9.3922146429422515 9.3922146429422515 9.3922146429422515 9.3922146429422515 9.3922146429422515 9.3922146429422515 9.392214642942251 5 9.3922146429422515
S: Stacked Data (Y)
Control Chart Evaluation
Control Chart Rules
Rule Name Out of Control Condition Chart Type
Variables Attributes
Beyond Limits One or more points beyond the control limits X X
Zone C 9 or more consecutive points on one side of the average (in Zone C or beyond) X X
Trend 7 consecutive points trending up or trending down X X
Over-control 14 consecutive points alternating up and down X X
Zone A 2 out of 3 consecutive points in Zone A or beyond X
Zone B 4 out of 5 consecutive points in Zone B or beyond X
Stratification 15 consecutive points in Zone C X
Mixture 8 consecutive points with no points in Zone C X
Discrete Control Charts
c-charts
np-charts
56
Control Charts for Attributes
Data
c-chart
c-charts count the number of defects per unit of service encounter
The underlying distribution is the Poisson distribution
The mean of the distribution is and the standard deviation is .
c-chart example
The Woodland Paper Company produces paper for the newspaper industry. As a final step in the process, the paper passes through a machine that measures various product quality characteristics. When the paper production process is in control, it averages 20 defects per roll.
a. Set up a control chart for the number of defects per roll. For this example, use two-sigma control limits.
b. Five rolls had the following number of defects: 16, 21, 17, 22, and 24, respectively. The sixth roll, using pulp from a different supplier, had 5 defects. Is the paper production process in control?
a. The average number of defects per roll is 20. Therefore:
c-chart example
Example 5.4
The process is out of control due to Sample 6.
c-chart example
However, sample 6 is from a new supplier and results in a better product.
16 21 17 22 24 5
20 20 20 20 20 20
11.06 11.06 11.06 11.06 11.06 11.06
28.94 28.94 28.94 28.94 28.94 28.94
C – Defects
np-chart
np-charts are used to control the proportion defective
Sampling involves yes/no decisions so the underlying distribution is the binomial distribution
np-chart
np-chart
example
A Test was conducted to determine the presence of the Rh factor in 13 samples of donated blood. The results of the test are given in the table on the next slide.
Using three-sigma control limits, is the accuracy of the blood testing process in statistical control?
np-chart
example
Example 5.3
189
1614
= = 0.1171
p =
Total defectives
Total number of observations
Calculate the sample proportion defective and plot each sample proportion defective on the chart.
np-chart example
np-chart example
np-chart example
The process is in statistical control.
Control Chart Evaluation
Control Chart Rules
Rule Name Out of Control Condition Chart Type
Variables Attributes
Beyond Limits One or more points beyond the control limits X X
Zone C 9 or more consecutive points on one side of the average (in Zone C or beyond) X X
Trend 7 consecutive points trending up or trending down X X
Over-control 14 consecutive points alternating up and down X X
Zone A 2 out of 3 consecutive points in Zone A or beyond X
Zone B 4 out of 5 consecutive points in Zone B or beyond X
Stratification 15 consecutive points in Zone C X
Mixture 8 consecutive points with no points in Zone C X
Continuous
Discrete
n = 1 n = 2 to 9 n = 10+
I-MR
chart
Xbar-R chart
Xbar-S chart
Defects
Defectives
Yes No
c chart
u chart
Yes No
np chart
p chart
Type of Data
Subgroup Size
Defectives or Defects
Constant Sample Size
Constant Sample Size
Basic Control Charting Decision Tree
Process Capability – The ability of the process to meet the design specification for a service or product
Process Capability
Process Capability
20
25
30
Minutes
Upper
specification
Lower
specification
Nominal
value
(a) Process is capable
Process distribution
20
25
30
Minutes
Upper
specification
Lower
specification
Nominal
value
(b) Process is not capable
Process distribution
Process Capability
Process Capability
Lower
specification
Mean
Upper
specification
Nominal value
Six sigma
Four sigma
Two sigma
Process Capability
Process Capability Ratio
A test to see if the process variability is capable of producing output within a product’s specifications.
Cp =
Upper specification – Lower specification
6σ
Process Capability Ratio
Example 5.5
The intensive care unit lab process has an average turnaround time of 26.2 minutes and a standard deviation of 1.53 minutes.
The nominal value for this service is 25 minutes ± 5 minutes.
Is the lab process capable of four sigma-level performance?
Upper specification = 30 minutes
Lower specification = 20 minutes
Average service = 26.2 minutes
= 1.53 minutes
Process Capability Ratio
Example 5.5
Process did not meet 4-sigma level of 1.33
Process Capability Ratio
Process Capability Index
Measures how well a process is centered and whether the variability is acceptable
Cpk = Minimum of ,
x – Lower specification
3σ
Upper specification – x
3σ
where
σ = standard deviation of the process distribution
Process Capability Index
Example 5.5
The intensive care unit lab process has an average turnaround time of 26.2 minutes and a standard deviation of 1.53 minutes.
The nominal value for this service is 25 minutes ± 5 minutes.
Is the lab process capable of four sigma-level performance?
Upper specification = 30 minutes
Lower specification = 20 minutes
Average service = 26.2 minutes
= 1.53 minutes
Process Capability Index
Example 5.5
Cpk = Minimum of 26.2 – 20 , 30 – 26.2
3 ( 1.53) 3( 1.53)
Cpk = Minimum of ,
Process does not meets 4-sigma level of 1.33
Cpk = Minimum of 1.35, 0.83
Cpk = 0.83
Process Capability Index
Example 5.5
New Data is collected:
Upper specification = 30 minutes
Lower specification = 20 minutes
Average service = 26.1 minutes
= 1.20 minutes
Process meets 4-sigma level of 1.33 for variability
Process Capability Ratio
Example 5.5
Cpk = Minimum of 26.1 – 20 , 30 – 26.1
3 ( 1.20) 3 ( 1.20)
Cpk = 0.59
Process does not meets 4-sigma level of 1.33
Process Capability Index
Cpk = Minimum of ,
x – Lower specification
3σ
Upper specification – x
3σ
Cpk = Minimum of 0.59 1.08
Example 5.5
Process Capability Failure Rates
10.04
17.58
25.11
5.40
10.40
15.40
20.40
25.40
30.40
05101520
Chart3
1 1 1 1
2 2 2 2
3 3 3 3
4 4 4 4
5 5 5 5
6 6 6 6
7 7 7 7
8 8 8 8
9 9 9 9
10 10 10 10
11 11 11 11
12 12 12 12
13 13 13 13
14 14 14 14
15 15 15 15
16 16 16 16
17 17 17 17
18 18 18 18
19 19 19 19
Y
LCL
Avg
UCL
10.04
17.58
25.11
17
10.0434860744
17.5789470673
25.1144080602
20
10.0434860744
17.5789470673
25.1144080602
18
10.0434860744
17.5789470673
25.1144080602
19
10.0434860744
17.5789470673
25.1144080602
16
10.0434860744
17.5789470673
25.1144080602
15
10.0434860744
17.5789470673
25.1144080602
18
10.0434860744
17.5789470673
25.1144080602
19
10.0434860744
17.5789470673
25.1144080602
20
10.0434860744
17.5789470673
25.1144080602
21
10.0434860744
17.5789470673
25.1144080602
19
10.0434860744
17.5789470673
25.1144080602
6
10.0434860744
17.5789470673
25.1144080602
15
10.0434860744
17.5789470673
25.1144080602
17
10.0434860744
17.5789470673
25.1144080602
19
10.0434860744
17.5789470673
25.1144080602
20
10.0434860744
17.5789470673
25.1144080602
18
10.0434860744
17.5789470673
25.1144080602
17
10.0434860744
17.5789470673
25.1144080602
20
10.0434860744
17.5789470673
25.1144080602
Sheet1
8 15
7 17
8 20
9 18
7 19
10 16
8 15
7 18
6 19
8 20
9 21
5 19
6 6
7 15
5 17
8 19
6 20
4 18
6 17
8 20
Sheet1
1 1 1 1
2 2 2 2
3 3 3 3
4 4 4 4
5 5 5 5
6 6 6 6
7 7 7 7
8 8 8 8
9 9 9 9
10 10 10 10
11 11 11 11
12 12 12 12
13 13 13 13
14 14 14 14
15 15 15 15
16 16 16 16
17 17 17 17
18 18 18 18
19 19 19 19
Y
LCL
Avg
UCL
2.18
7.05
11.93
7
2.1767448534
7.0526313782
11.928517903
8
2.1767448534
7.0526313782
11.928517903
9
2.1767448534
7.0526313782
11.928517903
7
2.1767448534
7.0526313782
11.928517903
10
2.1767448534
7.0526313782
11.928517903
8
2.1767448534
7.0526313782
11.928517903
7
2.1767448534
7.0526313782
11.928517903
6
2.1767448534
7.0526313782
11.928517903
8
2.1767448534
7.0526313782
11.928517903
9
2.1767448534
7.0526313782
11.928517903
5
2.1767448534
7.0526313782
11.928517903
6
2.1767448534
7.0526313782
11.928517903
7
2.1767448534
7.0526313782
11.928517903
5
2.1767448534
7.0526313782
11.928517903
8
2.1767448534
7.0526313782
11.928517903
6
2.1767448534
7.0526313782
11.928517903
4
2.1767448534
7.0526313782
11.928517903
6
2.1767448534
7.0526313782
11.928517903
8
2.1767448534
7.0526313782
11.928517903
Sheet2
1 1 1 1
2 2 2 2
3 3 3 3
4 4 4 4
5 5 5 5
6 6 6 6
7 7 7 7
8 8 8 8
9 9 9 9
10 10 10 10
11 11 11 11
12 12 12 12
13 13 13 13
14 14 14 14
15 15 15 15
16 16 16 16
17 17 17 17
18 18 18 18
19 19 19 19
Y
LCL
Avg
UCL
10.04
17.58
25.11
17
10.0434860744
17.5789470673
25.1144080602
20
10.0434860744
17.5789470673
25.1144080602
18
10.0434860744
17.5789470673
25.1144080602
19
10.0434860744
17.5789470673
25.1144080602
16
10.0434860744
17.5789470673
25.1144080602
15
10.0434860744
17.5789470673
25.1144080602
18
10.0434860744
17.5789470673
25.1144080602
19
10.0434860744
17.5789470673
25.1144080602
20
10.0434860744
17.5789470673
25.1144080602
21
10.0434860744
17.5789470673
25.1144080602
19
10.0434860744
17.5789470673
25.1144080602
6
10.0434860744
17.5789470673
25.1144080602
15
10.0434860744
17.5789470673
25.1144080602
17
10.0434860744
17.5789470673
25.1144080602
19
10.0434860744
17.5789470673
25.1144080602
20
10.0434860744
17.5789470673
25.1144080602
18
10.0434860744
17.5789470673
25.1144080602
17
10.0434860744
17.5789470673
25.1144080602
20
10.0434860744
17.5789470673
25.1144080602
Sheet3
QCCharts XYZZ
Sheet1 Chart 1 Sheet1 Chart 2
Obs Y LCL Avg UCL Obs Y LCL Avg UCL
1 7.00 2.18 7.05 11.93 1 17.00 10.04 17.58 25.11
2 8.00 2.18 7.05 11.93 2 20.00 10.04 17.58 25.11
3 9.00 2.18 7.05 11.93 3 18.00 10.04 17.58 25.11
4 7.00 2.18 7.05 11.93 4 19.00 10.04 17.58 25.11
5 10.00 2.18 7.05 11.93 5 16.00 10.04 17.58 25.11
6 8.00 2.18 7.05 11.93 6 15.00 10.04 17.58 25.11
7 7.00 2.18 7.05 11.93 7 18.00 10.04 17.58 25.11
8 6.00 2.18 7.05 11.93 8 19.00 10.04 17.58 25.11
9 8.00 2.18 7.05 11.93 9 20.00 10.04 17.58 25.11
10 9.00 2.18 7.05 11.93 10 21.00 10.04 17.58 25.11
11 5.00 2.18 7.05 11.93 11 19.00 10.04 17.58 25.11
12 6.00 2.18 7.05 11.93 12 6.00 10.04 17.58 25.11
13 7.00 2.18 7.05 11.93 13 15.00 10.04 17.58 25.11
14 5.00 2.18 7.05 11.93 14 17.00 10.04 17.58 25.11
15 8.00 2.18 7.05 11.93 15 19.00 10.04 17.58 25.11
16 6.00 2.18 7.05 11.93 16 20.00 10.04 17.58 25.11
17 4.00 2.18 7.05 11.93 17 18.00 10.04 17.58 25.11
18 6.00 2.18 7.05 11.93 18 17.00 10.04 17.58 25.11
19 8.00 2.18 7.05 11.93 19 20.00 10.04 17.58 25.11
DateNumber of DefectivesSample Sizep
08-Sep121150.104348
09-Sep141250.11200
10-Sep181110.162162
11-Sep131330.097744
12-Sep171200.141667
13-Sep151180.127119
14-Sep151370.109489
15-Sep161080.148148
16-Sep111100.10000
17-Sep141240.11290
18-Sep131280.101563
19-Sep141440.097222
20-Sep171410.120567
0.118072
ҧൌ
Control Chart Diagram
xbar-R
Sample 7am 8am 9am 10am 11am 12pm 1pm 2pm 3pm 4pm
1 7.127 7.125 7.123 7.127 7.128 7.125 7.126 7.126 7.127 7.128
2 7.123 7.126 7.129 7.127 7.125 7.125 7.123 7.126 7.129 7.123
3 7.123 7.121 7.129 7.124 7.126 7.127 7.123 7.127 7.128 7.122
4 7.126 7.122 7.124 7.125 7.127 7.128 7.125 7.128 7.129 7.124
Average 7.12475 7.1235 7.12625 7.12575 7.1265 7.12625 7.12425 7.12675 7.12825 7.12425 7.12565
Range (R) 0.004 0.005 0.006 0.003 0.003 0.003 0.003 0.002 0.002 0.006 0.0037
7.1283473
7.1229527
0.0084434
0
Data are collected in a face-and-plunge operation done on a lathe. The dimensions being measured is the grouve inside diameter (ID), which has a tolerance of 7.125 ± 0.010. Four parts are measured every hour. These values have been entered in the table below.
xbar-S
Subgroup Obs 1 Obs 2 Obs 3 Obs 4 Obs 5 Obs 6 Obs 7 Obs 8 Obs 9 Obs 10
1 46.8204 58.8572 67.7175 51.3078 53.3025 51.3258 59.0268 49.9933 47.086 60.4783
2 53.9847 47.4005 59.1598 57.2251 57.3207 50.4045 54.8046 55.7574 58.8662 59.2083
3 52.4315 63.2146 61.4096 59.342 57.4605 53.7083 57.0489 58.4325 48.5544 61.4105
4 50.9712 53.4314 52.9449 66.827 43.9849 67.8154 57.4312 44.3194 60.5493 59.6383
5 62.0421 57.1784 60.1955 56.4687 64.9641 52.9195 48.6739 56.3773 60.3216 58.9171
6 53.1269 58.374 63.7938 50.8965 52.4253 52.696 64.2078 65.9364 55.8426 54.478
7 55.0507 53.8931 51.8424 68.7073 50.173 58.0991 59.3456 57.9232 69.2396 60.2033
8 54.3315 52.3679 65.2346 62.6795 61.5929 54.0084 61.4465 58.4423 55.7608 54.1888
9 59.9584 59.1762 51.5629 63.0753 59.4856 63.2215 50.8982 62.4343 49.4303 48.9902
10 54.0402 56.3253 53.3773 54.7368 59.8292 54.6631 62.2161 61.5533 66.2283 63.0929
11 57.2273 65.8816 67.9839 51.7812 63.3054 56.5156 54.5318 54.4049 54.6459 52.6297
12 51.5133 61.0216 61.2776 62.1072 56.1983 54.805 59.083 58.8301 51.2939 54.9033
13 41.6784 46.7246 90.9593 57.7698 57.6619 53.9903 47.1248 50.2183 52.0052 57.2942
14 52.8303 42.4179 58.0054 60.1385 59.9954 60.5936 49.6827 68.2645 53.5693 60.6435
15 58.1128 53.4343 49.8567 53.3065 48.6588 53.4726 61.1457 61.6733 54.4246 51.8054
16 59.4674 66.2816 71.1186 63.6602 65.4012 53.2372 55.0633 46.6954 57.0477 61.8819
17 63.6288 47.3453 45.6509 40.2198 51.7382 51.0804 56.4197 57.7979 65.3047 66.539
18 59.5853 50.9825 56.2445 103.441 52.6224 63.7297 43.3771 58.7982 59.8339 57.9202
19 57.8042 49.2275 56.9069 55.4057 60.342 62.0972 57.2 38.6509 61.459 59.144
20 53.2788 62.1238 48.7058 58.0984 52.3153 56.8277 53.3615 64.6894 56.0133 56.9455
21 61.0891 52.2114 55.0061 50.2427 55.6495 53.7419 63.6856 56.5452 55.6084 67.2915
22 47.6385 62.0744 71.2102 64.6661 58.1218 56.8151 62.913 53.8949 64.6937 53.5819
23 46.1471 57.2321 60.0446 59.5476 54.4676 48.8446 57.6602 58.5467 65.4449 50.6271
24 53.1199 52.4063 53.1227 52.1897 56.6952 53.0823 61.1469 50.5565 56.9315 60.0423
25 55.3156 60.7648 55.0855 56.2381 60.3981 61.7266 69.0841 51.4446 58.1248 50.136
54.447776 55.613932 59.53668 59.20314 56.564392 55.976856 57.06316 56.087208 57.531196 57.679648 56.9703988
5.2864584811 6.2894901987 9.4947599494 11.1065617562 5.1475848615 4.750668222 5.9335003653 6.8355648021 5.7657197454 4.830526936 6.5440835318
60.9361134202
53.0046841798
9.3907598681
3.6974071954
I-mR
Reading Individual Data Element
1 290
2 288 2
3 285 3
4 290 5
5 291 1
6 287 4
7 284 3
8 290 6
9 290 0
10 288 2
288.3 2.8888888889
295.9844444444
280.6155555556
9.438
0
c-chart
Date Number of Defects Sample Size
15-May 19 150
16-May 12 150
17-May 13 150
18-May 12 150
19-May 18 150
20-May 19 150
21-May 17 150
22-May 20 150
23-May 22 150
24-May 18 150
25-May 19 150
26-May 17 150
27-May 11 150
217
16.6923076923
28.9491738999
4.4354414847
Panes of glass are inspected for defects such as bubbles, scratches, chips, inclusions, waves and dips. The results of the inspection are given in the table below.
u-chart
Date Number of Defects Sample Size
4-Jul 4 125 0.1048159691 -0.0112558233
5-Jul 8 111 0.1083672378 -0.014807092
6-Jul 3 133 0.103043461 -0.0094833152
7-Jul 7 120 0.1060127114 -0.0124525656
8-Jul 5 118 0.1065125738 -0.0130
9-Jul 5 137 0.1022160132 -0.0086558674
10-Jul 6 108 0.1092167561 -0.0156566103
11-Jul 10 110 0.1086465461 -0.0150864003
12-Jul 4 124 0.1050495149 -0.0114893691
13-Jul 3 128 0.1041318286 -0.0105716827
14-Jul 4 144 0.1008518267 -0.0072916809
15-Jul 7 138 0.1020147931 -0.0084546473
16-Jul 11 150 0.0997593554 -0.0061992096
sum 77 1646
0.0467800729
Panes of glass are inspected for defects such as bubbles, scratches, chips, inclusions, waves, and dips. The results of the inspection are given in the table below.
np-chart
Date number of defectives sample size
8-Sep 9 1000 0.009
9-Sep 12 1000 0.012
10-Sep 13 1000 0.013
11-Sep 12 1000 0.012
12-Sep 11 1000 0.011
13-Sep 9 1000 0.009
14-Sep 7 1000 0.007
15-Sep 0 1000 0
16-Sep 12 1000 0.012
17-Sep 8 1000 0.008
18-Sep 9 1000 0.009
19-Sep 7 1000 0.007
20-Sep 11 1000 0.011
0.0092307692
9.2307692308
18.3032583695
0.1582800921
Packages containing 1000 lightbulbs are randomly selected, and all 1000 bulbs are light-tested. The results of the tests are given in the below table.
p-chart
Date Number of Defectives Sample Size p LCL UCL
8-Sep 12 115 0.1043478261 0.02780 0.2083455413
9-Sep 14 125 0.11200 0.0314840857 0.2046593271
10-Sep 18 111 0.1621621622 0.0261857113 0.2099577015
11-Sep 13 133 0.0977443609 0.0341286086 0.2020148041
12-Sep 17 120 0.1416666667 0.02970 0.2064448267
13-Sep 15 118 0.1271186441 0.0289528081 0.2071906046
14-Sep 15 137 0.1094890511 0.0353631332 0.2007802796
15-Sep 16 108 0.1481481481 0.0249182584 0.2112251544
16-Sep 11 110 0.10000 0.0257689926 0.2103744202
17-Sep 14 124 0.11290 0.0311356432 0.2050077696
18-Sep 13 128 0.1015625 0.03250 0.2036386122
19-Sep 14 144 0.0972222222 0.03740 0.1987449588
20-Sep 17 141 0.1205673759 0.036544745 0.19960
0.1180717064
A test was conducted to determine the presence of the Rh factor in 13 samples of donated blood. The results of the test are given in the below table.
Constants
Sample Size = n
2 1.880 2.659 1.128 0 3.267 0 3.267 2.660
3 1.023 1.954 1.693 0 2.574 0 2.568 1.772
4 0.729 1.628 2.059 0 2.282 0 2.266 1.457
5 0.577 1.427 2.326 0 2.114 0 2.089 1.290
6 0.483 1.287 2.534 0 2.004 0.030 1.970 1.184
7 0.419 1.182 2.704 0.076 1.924 0.118 1.882 1.109
8 0.373 1.099 2.847 0.136 1.864 0.185 1.815 1.054
9 0.337 1.032 2.970 0.184 1.816 0.239 1.761 1.010
10 0.308 0.975 3.078 0.223 1.777 0.284 1.716 0.975
11 0.285 0.927 3.173 0.256 1.744 0.321 1.679 0.945
12 0.266 0.886 3.258 0.283 1.717 0.354 1.646 0.921
13 0.249 0.850 3.336 0.307 1.693 0.382 1.618 0.899
14 0.235 0.817 3.407 0.328 1.672 0.406 1.594 0.881
15 0.223 0.789 3.472 0.347 1.653 0.428 1.572 0.864
16 0.212 0.763 3.532 0.363 1.637 0.448 1.552 0.849
17 0.203 0.739 3.588 0.378 1.622 0.466 1.534 0.836
18 0.194 0.718 3.640 0.391 1.608 0.482 1.518 0.824
19 0.187 0.698 3.689 0.403 1.597 0.497 1.503 0.813
20 0.180 0.680 3.735 0.415 1.585 0.510 1.490 0.803
21 0.173 0.663 3.778 0.425 1.575 0.523 1.477 0.794
22 0.167 0.647 3.819 0.434 1.566 0.534 1.466 0.786
23 0.162 0.633 3.858 0.443 1.557 0.545 1.455 0.778
24 0.157 0.619 3.895 0.451 1.548 0.555 1.445 0.770
25 0.153 0.606 3.931 0.459 1.541 0.565 1.435 0.763
DateNumber of DefectivesSample SizeLCLUCL
08-Sep121150.027150.207052
09-Sep141250.030820.203379
10-Sep181110.025540.208658
11-Sep131330.033460.200743
12-Sep171200.029040.205158
13-Sep151180.028300.205901
14-Sep151370.034690.199513
15-Sep161080.024280.209921
16-Sep111100.025130.209073
17-Sep141240.030470.203726
18-Sep131280.031840.202361
19-Sep141440.036720.197485
20-Sep171410.035860.198336
0.11710037
ҧൌ
Control Chart Diagram
xbar-R
Sample 7am 8am 9am 10am 11am 12pm 1pm 2pm 3pm 4pm
1 7.127 7.125 7.123 7.127 7.128 7.125 7.126 7.126 7.127 7.128
2 7.123 7.126 7.129 7.127 7.125 7.125 7.123 7.126 7.129 7.123
3 7.123 7.121 7.129 7.124 7.126 7.127 7.123 7.127 7.128 7.122
4 7.126 7.122 7.124 7.125 7.127 7.128 7.125 7.128 7.129 7.124
Average 7.12475 7.1235 7.12625 7.12575 7.1265 7.12625 7.12425 7.12675 7.12825 7.12425 7.12565
Range (R) 0.004 0.005 0.006 0.003 0.003 0.003 0.003 0.002 0.002 0.006 0.0037
7.1283473
7.1229527
0.0084434
0
Data are collected in a face-and-plunge operation done on a lathe. The dimensions being measured is the grouve inside diameter (ID), which has a tolerance of 7.125 ± 0.010. Four parts are measured every hour. These values have been entered in the table below.
xbar-S
Subgroup Obs 1 Obs 2 Obs 3 Obs 4 Obs 5 Obs 6 Obs 7 Obs 8 Obs 9 Obs 10
1 46.8204 58.8572 67.7175 51.3078 53.3025 51.3258 59.0268 49.9933 47.086 60.4783
2 53.9847 47.4005 59.1598 57.2251 57.3207 50.4045 54.8046 55.7574 58.8662 59.2083
3 52.4315 63.2146 61.4096 59.342 57.4605 53.7083 57.0489 58.4325 48.5544 61.4105
4 50.9712 53.4314 52.9449 66.827 43.9849 67.8154 57.4312 44.3194 60.5493 59.6383
5 62.0421 57.1784 60.1955 56.4687 64.9641 52.9195 48.6739 56.3773 60.3216 58.9171
6 53.1269 58.374 63.7938 50.8965 52.4253 52.696 64.2078 65.9364 55.8426 54.478
7 55.0507 53.8931 51.8424 68.7073 50.173 58.0991 59.3456 57.9232 69.2396 60.2033
8 54.3315 52.3679 65.2346 62.6795 61.5929 54.0084 61.4465 58.4423 55.7608 54.1888
9 59.9584 59.1762 51.5629 63.0753 59.4856 63.2215 50.8982 62.4343 49.4303 48.9902
10 54.0402 56.3253 53.3773 54.7368 59.8292 54.6631 62.2161 61.5533 66.2283 63.0929
11 57.2273 65.8816 67.9839 51.7812 63.3054 56.5156 54.5318 54.4049 54.6459 52.6297
12 51.5133 61.0216 61.2776 62.1072 56.1983 54.805 59.083 58.8301 51.2939 54.9033
13 41.6784 46.7246 90.9593 57.7698 57.6619 53.9903 47.1248 50.2183 52.0052 57.2942
14 52.8303 42.4179 58.0054 60.1385 59.9954 60.5936 49.6827 68.2645 53.5693 60.6435
15 58.1128 53.4343 49.8567 53.3065 48.6588 53.4726 61.1457 61.6733 54.4246 51.8054
16 59.4674 66.2816 71.1186 63.6602 65.4012 53.2372 55.0633 46.6954 57.0477 61.8819
17 63.6288 47.3453 45.6509 40.2198 51.7382 51.0804 56.4197 57.7979 65.3047 66.539
18 59.5853 50.9825 56.2445 103.441 52.6224 63.7297 43.3771 58.7982 59.8339 57.9202
19 57.8042 49.2275 56.9069 55.4057 60.342 62.0972 57.2 38.6509 61.459 59.144
20 53.2788 62.1238 48.7058 58.0984 52.3153 56.8277 53.3615 64.6894 56.0133 56.9455
21 61.0891 52.2114 55.0061 50.2427 55.6495 53.7419 63.6856 56.5452 55.6084 67.2915
22 47.6385 62.0744 71.2102 64.6661 58.1218 56.8151 62.913 53.8949 64.6937 53.5819
23 46.1471 57.2321 60.0446 59.5476 54.4676 48.8446 57.6602 58.5467 65.4449 50.6271
24 53.1199 52.4063 53.1227 52.1897 56.6952 53.0823 61.1469 50.5565 56.9315 60.0423
25 55.3156 60.7648 55.0855 56.2381 60.3981 61.7266 69.0841 51.4446 58.1248 50.136
54.447776 55.613932 59.53668 59.20314 56.564392 55.976856 57.06316 56.087208 57.531196 57.679648 56.9703988
5.2864584811 6.2894901987 9.4947599494 11.1065617562 5.1475848615 4.750668222 5.9335003653 6.8355648021 5.7657197454 4.830526936 6.5440835318
60.9361134202
53.0046841798
9.3907598681
3.6974071954
I-mR
Reading Individual Data Element
1 290
2 288 2
3 285 3
4 290 5
5 291 1
6 287 4
7 284 3
8 290 6
9 290 0
10 288 2
288.3 2.8888888889
295.9844444444
280.6155555556
9.438
0
c-chart
Date Number of Defects Sample Size
15-May 19 150
16-May 12 150
17-May 13 150
18-May 12 150
19-May 18 150
20-May 19 150
21-May 17 150
22-May 20 150
23-May 22 150
24-May 18 150
25-May 19 150
26-May 17 150
27-May 11 150
217
16.6923076923
28.9491738999
4.4354414847
Panes of glass are inspected for defects such as bubbles, scratches, chips, inclusions, waves and dips. The results of the inspection are given in the table below.
u-chart
Date Number of Defects Sample Size
4-Jul 4 125 0.1048159691 -0.0112558233
5-Jul 8 111 0.1083672378 -0.014807092
6-Jul 3 133 0.103043461 -0.0094833152
7-Jul 7 120 0.1060127114 -0.0124525656
8-Jul 5 118 0.1065125738 -0.0130
9-Jul 5 137 0.1022160132 -0.0086558674
10-Jul 6 108 0.1092167561 -0.0156566103
11-Jul 10 110 0.1086465461 -0.0150864003
12-Jul 4 124 0.1050495149 -0.0114893691
13-Jul 3 128 0.1041318286 -0.0105716827
14-Jul 4 144 0.1008518267 -0.0072916809
15-Jul 7 138 0.1020147931 -0.0084546473
16-Jul 11 150 0.0997593554 -0.0061992096
sum 77 1646
0.0467800729
Panes of glass are inspected for defects such as bubbles, scratches, chips, inclusions, waves, and dips. The results of the inspection are given in the table below.
np-chart
Date number of defectives sample size
8-Sep 9 1000 0.009
9-Sep 12 1000 0.012
10-Sep 13 1000 0.013
11-Sep 12 1000 0.012
12-Sep 11 1000 0.011
13-Sep 9 1000 0.009
14-Sep 7 1000 0.007
15-Sep 0 1000 0
16-Sep 12 1000 0.012
17-Sep 8 1000 0.008
18-Sep 9 1000 0.009
19-Sep 7 1000 0.007
20-Sep 11 1000 0.011
0.0092307692
9.2307692308
18.3032583695
0.1582800921
Packages containing 1000 lightbulbs are randomly selected, and all 1000 bulbs are light-tested. The results of the tests are given in the below table.
p-chart
Date Number of Defectives Sample Size LCL UCL
8-Sep 12 115 0.02715 0.2070516084
9-Sep 14 125 0.03082 0.203378567
10-Sep 18 111 0.02554 0.2086580074
11-Sep 13 133 0.03346 0.2007434944
12-Sep 17 120 0.02904 0.205157686
13-Sep 15 118 0.02830 0.2059007989
14-Sep 15 137 0.03469 0.1995133815
15-Sep 16 108 0.02428 0.209920931
16-Sep 11 110 0.02513 0.2090732369
17-Sep 14 124 0.03047 0.2037257644
18-Sep 13 128 0.03184 0.2023614997
19-Sep 14 144 0.03672 0.1974853341
20-Sep 17 141 0.03586 0.1983359923
0.1171003717
A test was conducted to determine the presence of the Rh factor in 13 samples of donated blood. The results of the test are given in the below table.
Constants
Sample Size = n
2 1.880 2.659 1.128 0 3.267 0 3.267 2.660
3 1.023 1.954 1.693 0 2.574 0 2.568 1.772
4 0.729 1.628 2.059 0 2.282 0 2.266 1.457
5 0.577 1.427 2.326 0 2.114 0 2.089 1.290
6 0.483 1.287 2.534 0 2.004 0.030 1.970 1.184
7 0.419 1.182 2.704 0.076 1.924 0.118 1.882 1.109
8 0.373 1.099 2.847 0.136 1.864 0.185 1.815 1.054
9 0.337 1.032 2.970 0.184 1.816 0.239 1.761 1.010
10 0.308 0.975 3.078 0.223 1.777 0.284 1.716 0.975
11 0.285 0.927 3.173 0.256 1.744 0.321 1.679 0.945
12 0.266 0.886 3.258 0.283 1.717 0.354 1.646 0.921
13 0.249 0.850 3.336 0.307 1.693 0.382 1.618 0.899
14 0.235 0.817 3.407 0.328 1.672 0.406 1.594 0.881
15 0.223 0.789 3.472 0.347 1.653 0.428 1.572 0.864
16 0.212 0.763 3.532 0.363 1.637 0.448 1.552 0.849
17 0.203 0.739 3.588 0.378 1.622 0.466 1.534 0.836
18 0.194 0.718 3.640 0.391 1.608 0.482 1.518 0.824
19 0.187 0.698 3.689 0.403 1.597 0.497 1.503 0.813
20 0.180 0.680 3.735 0.415 1.585 0.510 1.490 0.803
21 0.173 0.663 3.778 0.425 1.575 0.523 1.477 0.794
22 0.167 0.647 3.819 0.434 1.566 0.534 1.466 0.786
23 0.162 0.633 3.858 0.443 1.557 0.545 1.455 0.778
24 0.157 0.619 3.895 0.451 1.548 0.555 1.445 0.770
25 0.153 0.606 3.931 0.459 1.541 0.565 1.435 0.763
𝐶
𝑝
𝑣𝑎𝑙𝑢𝑒 𝑍 𝑣𝑎𝑙𝑢𝑒 𝑝𝑝𝑚
0.33 1.00 317,311
0.67 2.00 45,500
1.00 3.00 2,700
1.10 3.30 967
1.20 3.60 318
1.30 3.90 96
1.33 4.00 63
1.40 4.20 27
1.50 4.50 6.8
1.60 4.80 1.6
1.67 5.00 0.57
1.80 5.40 0.067
2.00 6.00 0.002
Operations and Project Management
BBUS 340
4 April 2018
1
Today’s Agenda
Class Administration – Littlefield, OM Explorer download
Lecture – Capacity Planning
Lecture – Waiting Lines
Case Study
Definitions & Concepts
Long-term Capacity Decisions
Waiting Line Structure & Arrangements
Service Systems & Priority Rules
Probability Distributions
Single-Server Model
Multiple-Server Model
2
50,000 Feet Overview of OPM
Managing Processes
Process Strategy
Process Performance
& Quality
Constraint Management
Process Layout
Lean Systems
Process Analysis
Using Operations
to Compete
Operations As a
Competitive Weapon
Operations Strategy
Project Management
Managing Value Chains
Supply Chain Strategy
Inventory Management
Location
Forecasting
Sales & Operations
Planning
Scheduling
Resource Planning
Process Performance
& Quality
3
Service vs. Manufacturing
Small vs. Medium vs. Large Firms
Industry type: hightech, healthcare, aerospace, IT, etc ….
Capacity Planning
What is Capacity?
The maximum rate of output of a process or a system.
What is Capacity Management?
Measures of Capacity and Utilization
Utilization
Output measures
Input measures
Utilization = 100%
Average output rate
Maximum capacity
Measures of Capacity and Utilization
Use Output Measures when:
Process has high volume and the firm makes a small number of standardized products
Using Input Measures when:
Product variety and process divergence is high
The product or service mix is changing
Productivity rates are expected to change
Significant learning effects are expected
Economies and Diseconomies of Scale
Economies of scale
Spreading fixed costs
Reducing construction costs
Cutting costs of purchased materials
Finding process advantages
Diseconomies of scale
Complexity
Loss of focus
Inefficiencies
Economies and Diseconomies of Scale
Sizing Capacity Cushions
Capacity cushions – the amount of reserve capacity a process uses to handle sudden changes
Capacity cushion = 100% – Average Utilization rate (%)
Capacity cushions vary with industry
Capital intensive industries prefer cushions as small as 5 percent, while hotel industry can live with 30 to 40 percent cushion
Planned unused capacity
Time
Capacity
Forecast of capacity required
Time between increments
Capacity increment
(a) Expansionist strategy
Capacity Timing and Sizing
Capacity Timing and Sizing
Time
Capacity
(b) Wait-and-see strategy
Planned use of short-term options
Time between increments
Capacity increment
Forecast of capacity required
Capacity Timing and Sizing
Linking Capacity
Capacity decisions should be linked to processes and supply chains throughout the organization
Important issues are competitive priorities, quality, and process design
A Systematic Approach to Long-Term Capacity Decisions
Estimate
Estimate future capacity requirements
Identify
Identify gaps by comparing requirements with available capacity
Develop
Develop alternative plans for reducing the gaps
Evaluate
Evaluate each alternative, both qualitatively and quantitatively, and make a final choice
Step 1 Estimate Capacity Requirements
For one service or product processed at one operation with a one year time period, the capacity requirement, M, is
Capacity requirement
=
Processing hours required for year’s demand
Hours available from a single capacity unit
(such as an employee or machine) per year,
after deducting desired cushion
M =
Dp
N[1 – (C/100)]
Where:
D = demand forecast for the year (number of customers served or units produced)
p = processing time (in hours per customer served or unit produced)
N = total number of hours per year during which the process operates
C = desired capacity cushion (expressed as a percent)
For one service or product processed at one operation with a one year time period, the capacity requirement, M, is
Capacity requirement
=
Processing hours required for year’s demand,
Summed over all services or products
Hours available from a single capacity unit
per year, after deducting desired cushion
Step 1 (cont.) Estimate Capacity Requirements
T
M =
[Dp + (D/Q)s]product 1 + [Dp + (D/Q)s]product 2 + … + [Dp + (D/Q)s]product n
N[1 – (C/100)]
Where:
Q = number of units in each lot
s = setup time (in hours) per lot
Example
A copy center in an office building prepares bound reports for two clients. The center makes multiple copies (the lot size) of each report. The processing time to run, collate, and bind each copy depends on, among other factors, the number of pages. The center operates 250 days per year, with one 8-hour shift. Management believes that a capacity cushion of 15 percent (beyond the allowance built into time standards) is best. It currently has three copy machines. Based on the following information, determine how many machines are needed at the copy center.
Item Client X Client Y
Annual demand forecast (copies) 2,000 6,000
Standard processing time (hours per job) 0.5 0.7
Average lot size (copies per report) 20 30
Standard setup time (hours) 0.25 0.40
Example
Example
M =
[Dp + (D/Q)s]product 1 + [Dp + (D/Q)s]product 1 + … + [Dp + (D/Q)s]product n
N[1 – (C/100)]
=
[2,000(0.5) + (2,000/20)(0.25)]client X
+ [6,000(0.7) + (6,000/30)(0.40)]client Y
[(250 days per year)(1 shift per day)(8 hours per shift)][1.0 – (15/100)]
= = 3.12
5,305
1,700
Rounding up to the next integer gives a requirement of four machines.
Example
Where:
D = demand forecast for the year (number of customers served or units produced)
p = processing time (in hours per customer served or unit produced)
N = total number of hours per year during which the process operates
C = desired capacity cushion (expressed as a percent)
Q = number of units in each lot
s = setup time (in hours) per lot
You have been asked to put together a capacity plan for a critical operation at the Sugarfoot Sandal Company. Your capacity measure is number of machines. Three products (men’s, women’s, and children’s sandals) are manufactured. The time standards (processing and setup), lot sizes, and demand forecasts are given in the following table. The firm operates two 8-hour shifts, 5 days per week, 50 weeks per year. Experience shows that a capacity cushion of 5 percent is sufficient.
a. How many machines are needed?
b. If the operation currently has two machines, what is the capacity gap?
Time Standards
Product Processing
(hr/pair) Setup
(hr/pair) Lot size
(pairs/lot) Demand Forecast
(pairs/yr)
Men’s sandals 0.05 0.5 240 80,000
Women’s sandals 0.10 2.2 180 60,000
Children’s sandals 0.02 3.8 360 120,000
Application Problem
Application Problem
a. The number of hours of operation per year, N, is N = (2 shifts/day)(8 hours/shifts) (250 days/machine-year) = 4,000 hours/machine-year
The number of machines required, M, is the sum of machine-hour requirements for all three products divided by the number of productive hours available for one machine:
M =
[Dp + (D/Q)s]men + [Dp + (D/Q)s]women + [Dp + (D/Q)s]children
N[1 – (C/100)]
=
[80,000(0.05) + (80,000/240)0.5] + [60,000(0.10) + (60,000/180)2.2] + [120,000(0.02) + (120,000/360)3.8]
4,000[1 – (5/100)]
=
= 3.83 or 4 machines
14,567 hours/year
3,800 hours/machine-year
b. The capacity gap is 1.83 machines (3.83 –2). Two more machines should be purchased, unless management decides to use short-term options to fill the gap.
The Capacity Requirements Solver in OM Explorer confirms these calculations, as the figure shows, using only the “Expected” scenario for the demand forecasts.
Application Problem
Application Problem
Identify gaps between projected capacity requirements (M) and current capacity
Complicated by multiple operations and resource inputs
Step 2
Identify Gaps
Step 3
Develop Alternatives
Base case is to do nothing and suffer the consequences
Many different alternatives are possible
Step 4
Evaluate Alternatives
Qualitative concerns include strategic fit and uncertainties.
Quantitative concerns may include cash flows and other quantitative measures.
Waiting Lines
What are waiting lines and why do they form?
Waiting line
One or more customers waiting for service.
Waiting Lines form due to a temporary imbalance between the demand for service and the capacity of the system to provide the service.
Structure of Waiting-Line Problems
An input, or customer population, that generates potential customers
A waiting line of customers
The service facility, consisting of a person (or crew), a machine (or group of machines), or both necessary to perform the service for the customer
A priority rule, which selects the next customer to be served by the service facility
Service system: The number of lines and the arrangement of the facilities.
Customer population
Service system
Waiting line
Priority rule
Service facilities
Served customers
Structure of Waiting Line Problems
Waiting Line Arrangements
Service facilities
Service facilities
Single Line
Multiple Lines
The Service System
Number of lines
A single-line keeps servers uniformly busy and levels waiting times among customers
A multiple-line arrangement is favored when servers provide a limited set of services
Arrangement of service facilities
Single-channel, single-phase
Single-channel, multiple-phase
Multiple-channel, single-phase
Multiple-channel, multiple-phase
Mixed arrangement
32
Service Facility Arrangements
Service facility
Single channel, single phase
Single channel, multiple phase
Service facility 1
Service facility 2
Multiple channel,
multiple phase
Multiple channel,
single phase
Service facility 1
Service facility 2
Service Facility Arrangements
Service facility 3
Service facility 4
Service facility 1
Service facility 2
Service Facility Arrangements
Routing for : 1–2–4
Routing for : 2–4–3
Routing for : 3–2–1–4
Mixed arrangement
Service facility 1
Service facility 4
Service facility 3
Service facility 2
Priority Rules
First-come, first-served (FCFS) – most common
Earliest due date (EDD)
Shortest processing time (SPT)
Preemptive discipline – allows a higher priority customer to interrupt the service of another customer or be served ahead of another who would have been served first
Probability Distributions
The sources of variation in waiting line problems come from the random arrivals of customers and the variations in service times. Each of these sources can be described with a probability distribution.
Probability Distributions
Poisson
If a mean or average probability of an event happening per unit of time/per page/per mile cycled etc., is given, and you are asked to calculate a probability of n events happening in a given time/number of pages/number of miles cycled, then the Poisson Distribution is used.
Why use the Poisson distribution?
Probability Distributions
Arrival Times – Poisson Distribution
Pn = e-T for n = 0, 1, 2,…
(T)n
n!
Where:
Pn = Probability of n arrivals in T time periods
= Average numbers of customer arrivals per period
e = 2.7183
Poisson
Example
Management is redesigning the customer service process in a large department store. Accommodating four customers is important. Customers arrive at the desk at the rate of two customers per hour. What is the probability that four customers will arrive during any hour?
In this case customers per hour, T = 1 hour, and n = 4 customers. The probability that four customers will arrive in any hour is:
P4 =
= e–2 = 0.090
16
24
[2(1)]4
4!
e–2(1)
Pn = e-T
(T)n
n!
Probability Distributions
The Exponential distribution is the probability distribution that describes the time between events in a process in which events occur continuously and independently at a constant average rate.
Exponential
Why use the Exponential distribution?
41
P(t ≤ T) = 1 – e-T
Where:
μ = average number of customers completing service per period
t = service time of the customer
T = target service time
Probability Distributions
Service Time – Exponential Distribution
Exponential
42
Example
The management of the large department store must determine whether more training is needed for the customer service clerk. The clerk at the customer service desk can serve an average of three customers per hour. What is the probability that a customer will require less than 10 minutes of service?
Because = 3 customers per hour, we convert minutes of time to hours, or T = 10 minutes = 10/60 hour = 0.167 hour.
P(t ≤ T) = 1 – e–T
P(t ≤ 0.167 hour) = 1 – e–3(0.167) = 1 – 0.61 = 0.39
Using Waiting-Line Models
Balance costs against benefits
Operating characteristics
Line length
Number of customers in system
Waiting time in line
Total time in system
Service facility utilization
44
Single-Server Model
Single-server, single line of customers, and only one phase
Assumptions are:
Customer population is infinite and patient
Customers arrive according to a Poisson distribution, with a mean arrival rate of
Service distribution is exponential with a mean service rate of
Mean service rate exceeds mean arrival rate
Customers are served FCFS
The length of the waiting line is unlimited
45
= Average utilization of the system =
l
m
L = Average number of customers in the service system =
l
m – l
Lq = Average number of customers in the waiting line = L
W = Average time spent in the system, including service =
1
m – l
Wq = Average waiting time in line = W
Rn = Probability that n customers are in the system = (1 – r )r n
Single-Server Model
46
Single Server Model
Example
The manager of a grocery store in the retirement community of Sunnyville is interested in providing good service to the senior citizens who shop in her store. Currently, the store has a separate checkout counter for senior citizens. On average, 30 senior citizens per hour arrive at the counter, according to a Poisson distribution, and are served at an average rate of 35 customers per hour, with exponential service times characteristics:
a. Probability of zero customers in the system
b. Average utilization of the checkout clerk
c. Average number of customers in the system
d. Average number of customers in line
e. Average time spent in the system
f. Average waiting time in line
47
Application
Customers arrive at a checkout counter at an average 30 per hour, according to a Poisson distribution. They are served at an average rate of 35 per hour, with exponential service times. Use the single-server model to estimate the operating characteristics of this system.
= 30 customer arrival rate per hour
= 35 customer service rate per hour
2. Average number of customers in the service system
= = 6
30
35 – 30
L =
l
m – l
Lq = L
W =
1
m – l
Wq = W
3. Average number of customers in the waiting line
= 0.86(6) = 5.16
4. Average time spent in the system, including service
= = 0.20
1
35 – 30
5. Average waiting time in line
= 0.86(0.2) = 0.17
1. Average utilization of system
=
l
m
= = 0.86
30
35
Application
Single Server Model Example
The checkout counter can be modeled as a single-channel, single-phase system. The results from the Waiting-Lines Solver from OM Explorer are below:
50
Sunnyville
Example
The manager of the Sunnyville grocery wants answers to the following questions:
What service rate would be required so that customers average only 8 minutes in the system?
For that service rate, what is the probability of having more than four customers in the system?
51
a. We use the equation for the average time in the system and solve for
W =
1
–
8 minutes = 0.133 hour =
1
– 30
0.133 – 0.133(30) = 1
= 37.52 customers/hour
Sunnyville
Example
52
b. The probability of more than four customers in the system equals 1 minus the probability of four or fewer customers in the system.
P = 1 – Pn
4
n = 0
= 1 – (1 – ) n
4
n = 0
=
= 0.80
30
37.52
P = 1 – 0.2(1 + 0.8 + 0.82 + 0.83 + 0.84)
= 1 – 0.672 = 0.328
Therefore, there is a nearly 33 percent chance that more than four customers will be in the system.
Sunnyville
Example
53
Multiple
Server Model Assumptions
Service system has only one phase, multiple-channels
Assumptions (in addition to single-server model)
There are s identical servers
The service distribution for each server is exponential
The mean service time is 1/
s should always exceed
P0 = Probability that zero customers are in the system
=
= Average utilization of the system =
Multiple
Server Model Equations
Pn = Probability that n customers are in the system
=
Lq = Average number of customers in the waiting line
=
Wq = Average waiting time of customers in line =
W = Average time spent in the system, including service
=
= W
L = Average number of customers in the service system
Multiple
Server Model Equations
Example B.5
The management of the American Parcel Service terminal in Verona, Wisconsin, is concerned about the amount of time the company’s trucks are idle (not delivering on the road), which the company defines as waiting to be unloaded and being unloaded at the terminal.
The terminal operates with four unloading bays. Each bay requires a crew of two employees, and each crew costs $30 per hour.
The estimated cost of an idle truck is $50 per hour. Trucks arrive at an average rate of three per hour, according to a Poisson distribution.
On average, a crew can unload a semitrailer rig in one hour, with exponential service times.
What is the total hourly cost of operating the system?
Multiple
Server Model Example
Example B.5
To calculate the hourly cost of operating the system we need to know the following:
The average number of trucks in the system
The average time spent in the system
The average time spent in line
The average number of trucks in line
The probability of having zero trucks in line
The utilization
The below data is provided in the description:
Multiple
Server Model Example
4 Unloading bays Crew costs $30 per hour
2 Employees/crew Idle truck costs $50 per hour
Arrival rate = 3 per hour Service time = 1 hour
Multiple-Server Model
4 Unloading bays Crew costs $30/hour
2 Employees/crew Idle truck costs $50/hour
Arrival rate = 3/hour Service time = 1 hour
Utilization = r =
Average trucks in line = Lq =
0(l/m)sr
s!(1 – r)2
=
Average time in line = Wq =
Lq
l
=
Average time in system = W = Wq +
1
m
Average trucks in system = L = lW
3
1(4)
= 0.75
0 =
0.0377(3/1)4(0.75)
4!(1 – 0.75)2
= 1.53 trucks
1.53
3
= 0.51 hours
= 0.51 +
1
1
= 1.51 hours
= 3(1.51)
= 4.53 trucks
What is the total hourly cost of operating the system?
Labor cost: $30(s) = $30(4) = $120.00
Idle truck cost: $50(L) = $50(4.53) = 226.50
Total hourly cost = $346.50
Multiple
Server Model Example
4 Unloading bays Crew costs $30/hour
2 Employees/crew Idle truck costs $50/hour
Arrival rate = 3/hour Service time = 1 hour
Case Study: Custom Mold’s, Inc.
Fitness Plus is a full-service health, fitness, and sports club located in a growing market. The increase in demand on its facilities brought on by a sizable growth in membership over the past few years has led to membership’s complaints of overcrowding of club facilities and the unavailability of equipment. As with most service organizations, Fitness Plus experiences large shifts in demand both during the week and within each particular day. The owners are wondering what the existing capacity of the club is and whether it is time to think about a capacity expansion move.
Question 1: What method should be used to measure the capacity at Fitness Plus? Has Fitness Plus reached its capacity?
Question 2: Which capacity strategy would be appropriate for Fitness Plus? Justify your answer.
Question 3: How would you link the capacity decision being made by Fitness Plus to other types of operating decisions?
Case Study: Fitness Plus, Part A
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Operations and Project Management
BBUS 340
25 April 2018
1
Today’s Agenda
Class Administration – Littlefield, Midterm Grades, Lean Reflection
Lean Systems
Waste
Value Added
5S
TPS – Toyota Way – 14 Principles
Organizational Considerations
Kanban
Value Stream Mapping
2
50,000 Feet Overview of OPM
Managing Processes
Process Strategy
Process Performance
& Quality
Constraint Management
Process Layout
Lean Systems
Process Analysis
Using Operations
to Compete
Operations As a
Competitive Weapon
Operations Strategy
Project Management
Managing Value Chains
Supply Chain Strategy
Inventory Management
Location
Forecasting
Sales & Operations
Planning
Scheduling
Resource Planning
Constraint Management
3
LEAN Systems
Learning Objectives
Describe
Understand
Understand value stream mapping and its role in waste reduction
Explain
Explain the implementation issues associated with the application of lean systems
Identify the characteristics and strategic advantages of lean systems
Describe how lean systems can facilitate the continuous improvement of processes
Identify
What is a Lean System?
Lean Systems
Operations systems that maximize the value added of each activity by removing waste.
6
Just-in-Time Philosophy
Eliminate waste or muda by cutting excess capacity or inventory and removing non-value-added activities.
A JIT system organizes the resources, information flows, and decision rules that enable a firm to realize the benefits of JIT principles.
Eight Types of Waste or Muda
TIMWOOUD
Transportation
Inventory
Motion
Waiting
Over Processing
Over Production
Underutilization of Employees
Defects
Waste Wheel TIMWOOUD
Value Added
All tasks in the process must add value to the end product or service.
How do you decide what value added means?
Customers define output requirements – this is what you use to understand what adds value.
Customer willing pay for it
Transformative
Done right the first time
[Explain]
A process must add value.
A process transforms inputs into outputs – if the process added no value, then the process is useless.
Grab a marker or piece of paper declare:
My process has one input, this marker.
Hand the marker to any class member and then ask them to hand it back.
My process has two steps, hand the marker to
And
My process outputs this marker.
[Ask]
What value did my process add? Answer: none – because the marker wasn’t transformed.
Have you ever experienced a process like this? Answer: most people will say yes – consider transactional “paper” processes.
What could we have done to transform the marker? Answer: if the customer paid to have their markers refilled, then we could have had
[Explain]
Customer’s define value – it is essentially what they are willing to pay for.
[Next Slide]
Let’s consider another simple example.
Reference: Image: http://leadingagent.net/blog/?p=628
10
Continuous Improvement
Kaizen
Excess capacity or inventory hide underlying problems with the processes that produce the service or product
Supply Chain Considerations
Characteristics of lean systems that are related to creating and managing material flows in a supply chain are:
Close Supplier Ties
Small Lot Sizes
Single-digit setup
Process Considerations
Pull Method of Workflow
Customer demand activates the production of the service or item.
Quality at the Source
Jidoka – stopping the process when something is wrong and fixing the problems before sending the product forward.
Process Considerations
Poka-Yoke – mistake proofing aimed at designing fail-safe systems
Uniform Workstation Loads
Takt time
Cycle time needed to match production rate to demand
Heijunka
The leveling of production load by both volume and product mix.
Mixed-model assembly
Type of assembly that produces a mix of models in smaller lots
Standardized Components and Work Methods
Process Considerations
Flexible Workforce
Automation
Total Preventative Maintenance
5S
Process Considerations
5S
Seiri
Seiton
Seiso
Seiketsu
Shitsuke
House of Toyota
Toyota Way – 14 Principles
I. Long Term Philosophy
Base your management decisions on a long-term philosophy, even at the expense of short-term financial goals.
II. Right Processes Produce Right Results
Create a continuous process flow to bring problems to the surface.
Use “pull” systems to avoid overproduction.
Level out the workload (heijunka). (Work like the tortoise, not the hare).
Build a culture of stopping to fix problems, to get quality right the first time.
Standardized tasks and processes are the foundation for continuous improvement and employee empowerment.
Use visual control so no problems are hidden.
Use only reliable, thoroughly tested technology that serves your people and processes.
III. Add Value to the Organization by Developing Your People
Grow leaders who thoroughly understand the work, live the philosophy, and teach it to others.
Develop exceptional people and teams who follow your company’s philosophy.
Respect your extended network of partners and suppliers by challenging them and helping them improve.
IV. Continuously Solving Root Problems Drives Organizational Learning
Go and see for yourself to thoroughly understand the situation (genchi genbutsu).
Make decisions slowly by consensus, thoroughly considering all options; implement decisions rapidly (nemawashi).
Be a learning organization through relentless reflection (hansei) and continuous improvement (kaizen).
[Explain]
Section I: Long-Term Philosophy
Principle 1. Base your management decisions on a long-term philosophy, even at the expense of short-term financial goals.
Have a philosophical sense of purpose that supersedes any short-term decision making. Work, grow, and align the whole organization toward a common purpose that is bigger than making money. Understand your place in the history of the company and work to bring the company to the next level. Your philosophical mission is the foundation for all the other principles.
Generate value for the customer, society, and the economy—it is your starting point. Evaluate every function in the company in terms of its ability to achieve this.
Be responsible. Strive to decide your own fate. Act with self-reliance and trust in your own abilities. Accept responsibility for your conduct and maintain and improve the skills that enable you to produce added value.
Section II: The Right Process Will Produce the Right Results
Principle 2. Create a continuous process flow to bring problems to the surface.
Redesign work processes to achieve high value-added, continuous flow. Strive to cut back to zero the amount of time that any work project is sitting idle or waiting for someone to work on it.
Create flow to move material and information fast as well as to link processes and people together so that problems surface right away.
Make flow evident throughout your organizational culture. It is the key to a true continuous improvement process and to developing people.
Principle 3. Use “pull” systems to avoid overproduction.
Provide your downstream customers in the production process with what they want, when they want it, and in the amount they want. Material replenishment initiated by consumption is the basic principle of just-in-time.
Minimize your work in process and warehousing of inventory by stocking small amounts of each product and frequently restocking based on what the customer actually takes away.
Be responsive to the day-by-day shifts in customer demand rather than relying on computer schedules and systems to track wasteful inventory.
Principle 4. Level out the workload (heijunka). (Work like the tortoise, not the hare.)
Eliminating waste is just one-third of the equation for making lean successful. Eliminating overburden to people and equipment and eliminating unevenness in the production schedule are just as important—yet generally not understood at companies attempting to implement lean principles.
Work to level out the workload of all manufacturing and service processes as an alternative to the stop/start approach of working on projects in batches that is typical at most companies.
Principle 5. Build a culture of stopping to fix problems, to get quality right the first time.
Quality for the customer drives your value proposition.
Use all the modern quality assurance methods available.
Build into your equipment the capability of detecting problems and stopping itself. Develop a visual system to alert team or project leaders that a machine or process needs assistance. Jidoka (machines with human intelligence) is the foundation for “building in” quality.
Build into your organization support systems to quickly solve problems and put in place countermeasures.
Build into your culture the philosophy of stopping or slowing down to get quality right the first time to enhance productivity in the long run.
Principle 6. Standardized tasks and processes are the foundation for continuous improvement and employee empowerment.
Use stable, repeatable methods everywhere to maintain the predictability, regular timing, and regular output of your processes. It is the foundation for flow and pull.
Capture the accumulated learning about a process up to a point in time by standardizing today’s best practices. Allow creative and individual expression to improve upon the standard; then incorporate it into the new standard so that when a person moves on you can hand off the learning to the next person.
Principle 7. Use visual control so no problems are hidden.
Use simple visual indicators to help people determine immediately whether they are in a standard condition or deviating from it.
Avoid using a computer screen when it moves the worker’s focus away from the workplace.
Design simple visual systems at the place where the work is done, to support flow and pull.
Reduce your reports to one piece of paper whenever possible, even for your most important financial decisions.
Principle 8. Use only reliable, thoroughly tested technology that serves your people and processes.
Use technology to support people, not to replace people. Often it is best to work out a process manually before adding technology to support the process.
New technology is often unreliable and difficult to standardize and therefore endangers “flow.” A proven process that works generally takes precedence over new and untested technology.
Conduct actual tests before adopting new technology in business processes, manufacturing systems, or products.
Reject or modify technologies that conflict with your culture or that might disrupt stability, reliability, and predictability.
Nevertheless, encourage your people to consider new technologies when looking into new approaches to work. Quickly implement a thoroughly considered technology if it has been proven in trials and it can improve flow in your processes.
Section III: Add Value to the Organization by Developing Your People
Principle 9. Grow leaders who thoroughly understand the work, live the philosophy, and teach it to others.
Grow leaders from within, rather than buying them from outside the organization.
Do not view the leader’s job as simply accomplishing tasks and having good people skills. Leaders must be role models of the company’s philosophy and way of doing business.
A good leader must understand the daily work in great detail so he or she can be the best teacher of your company’s philosophy.
Principle 10. Develop exceptional people and teams who follow your company’s philosophy.
Create a strong, stable culture in which company values and beliefs are widely shared and lived out over a period of many years.
Train exceptional individuals and teams to work within the corporate philosophy to achieve exceptional results. Work very hard to reinforce the culture continually.
Use cross-functional teams to improve quality and productivity and enhance flow by solving difficult technical problems. Empowerment occurs when people use the company’s tools to improve the company.
Make an ongoing effort to teach individuals how to work together as teams toward common goals. Teamwork is something that has to be learned.
Principle 11. Respect your extended network of partners and suppliers by challenging them and helping them improve.
Have respect for your partners and suppliers and treat them as an extension of your business.
Challenge your outside business partners to grow and develop. It shows that you value them. Set challenging targets and assist your partners in achieving them.
Section IV: Continuously Solving Root Problems Drives Organizational Learning
Principle 12. Go and see for yourself to thoroughly understand the situation (genchi genbutsu).
Solve problems and improve processes by going to the source and personally observing and verifying data rather than theorizing on the basis of what other people or the computer screen tell you.
Think and speak based on personally verified data.
Even high-level managers and executives should go and see things for themselves, so they will have more than a superficial understanding of the situation.
Principle 13. Make decisions slowly by consensus, thoroughly considering all options; implement decisions rapidly (nemawashi).
Do not pick a single direction and go down that one path until you have thoroughly considered alternatives. When you have picked, move quickly and continuously down the path.
Nemawashi is the process of discussing problems and potential solutions with all of those affected, to collect their ideas and get agreement on a path forward. This consensus process, though time-consuming, helps broaden the search for solutions, and once a decision is made, the stage is set for rapid implementation.
Principle 14. Become a learning organization through relentless reflection (hansei) and continuous improvement (kaizen).
Once you have established a stable process, use continuous improvement tools to determine the root cause of inefficiencies and apply effective countermeasures.
Design processes that require almost no inventory. This will make wasted time and resources visible for all to see. Once waste is exposed, have employees use a continuous improvement process (kaizen) to eliminate it.
Protect the organizational knowledge base by developing stable personnel, slow promotion, and very careful succession systems.
[Next Slide]
Harvard Business Review Study by Spear and Bowen
[Reference]
The Toyota Way Fieldbook – A practical guide for implementing Toyota’s 4Ps
Summary: http://icos.groups.si.umich.edu/Liker04
eBook: http://waterveritas.files.wordpress.com/2012/07/book-lss-toyota-way
19
The four rules of TPS:
All work is highly specified in its content, sequence, timing and outcome.
Each worker knows who provides what to him/her and when.
Every product and service flows along a simple, specified path.
Any improvement to processes, worker/machine connections or flow path must be made in concert with the scientific method, under the guidance of a teacher, at the lowest level possible.
Harvard Business Review, Sept/Oct 1999
Toyota Production System
[Explain]
Steven Spear and H. Kent Bowen studied the TPS system for four years at over 40 plants in the US, Europe and Japan. Some operating to the TPS, some not.
The authors ‘claim’ that the TPS operates according to ‘unwritten’ rules, and attempt to make clear what those rules are in this article.
They suggest the ‘rules’ include three rules of design, i.e. how to set up the TPS operations
And one rule focused on improvement, i.e. how to evolve the TPS over time.
The rules are the opinion of the authors – and provide an easy to understand conceptual perspective on what drives the execution of the TPS.
All work is highly specified in its content, sequence, timing, and outcome.
Employees follow a well-defined sequence of steps for a particular job. This specificity enables people to see and address deviations immediately—encouraging continual learning and improvement.
Example:
Installing the right-front seat in a Camry requires seven tasks performed in a specific sequence over 55 seconds. If a worker finds himself doing task 6 before task 4 or falling behind schedule, he and his supervisor correct the problem promptly. Then they determine whether to change the task specifications or retrain the worker to prevent a recurrence.
Each worker knows who provides what to him, and when.
Workers needing parts submit cards specifying part number, quantity, and required destination.
Suppliers must respond to materials requests within specified periods of time.
Workers encountering a problem ask for help immediately.
Designated assistants must respond at once and resolve the problem within the worker’s cycle time (e.g., the 55 seconds it takes to install a front seat).
Failure to fulfill these specifications signals a search for potential causes—such as ambiguous requests from colleagues or an overwhelmed assistant.
Once the cause is identified, it’s resolved rather than kept hidden.
Every product and service flows along a simple, specified path.
Goods and services don’t flow to the next available person or machine—but to a specific person or machine.
Example:
If workers at an auto parts supplier find themselves waiting to send a product to the next designated machine they conclude that their demand on the next machine doesn’t match their expectations.
They revisit the organization of their production line to determine why the machine was not available, and redesign the flow path.
Any improvement to processes, worker/machine connections, or flow path must be made through the scientific method, under a teacher’s guidance, and at the lowest possible organizational level.
Frontline workers make improvements to their own jobs.
Supervisors provide direction and assistance as teachers.
Example:
At one Toyota factory, workers seeking to reduce a machine’s changeover time from15 to 5 minutes were able to reduce the time only to 7.5 minutes.
A manager asked why they hadn’t achieved their original 5-minute goal.
His question helped them see that their original goal had been a random guess, not based on a formal hypothesis about how fast it could be done and why.
Thus they couldn’t test the hypothesis to determine what caused the less-than ideal results.
[Next Slide]
Compare different Improvement Approaches
[Reference]
HBR Article: Decoding the DNA of the Toyota Production System http://clinicalmicrosystem.org/toolkits/getting_started/decoding_dna
20
Scientific Thinking
Clear Problem Statements
No “Lack of a Solution” problems
Do the Research
Facts and data based decision making
Collect what you know
Measure if missing
Find the root causes
Solutions should fix the problem.
Solve the root cause not the symptom
No “jumping to conclusions”
Experiment to Achieve Right Result
Make sure the problem is fixed.
[Remind]
Remind the participants of Toyota 14 principles, specifically:
#8: Use only reliable, thoroughly tested technology that serves your people and processes.
How will you know technology is reliable and tested?
#12: Go and see for yourself to thoroughly understand the situation.
Observation is a key tenet of Lean Thinking.
#13: Make decisions slowly by consensus, thoroughly considering all options; implement decisions rapidly.
How will you know you’ve considered “all” options without using a thoughtful approach, i.e. the Scientific Method.
From Spear and Bowen:
Any improvement to processes, worker/machine connections, or flow path must be made through the scientific method, under a teacher’s guidance, and at the lowest possible organizational level.
[Explain]
Everyone is responsible for their own quality, efficiency and effectiveness – therefore these basic skills should be understood and embraced by all workers.
[Breakdown the steps]
Ask a question
The scientific method starts when you ask a question about something that you observe: How, What, When, Who, Which, Why, or Where?
And, in order for the scientific method to answer the question it must be about something that can measured, preferably with a number.
Research
Rather than starting from scratch in putting together a plan for answering the question – start with what you know, e.g.
What data do I already have access to?
What other people may know about this issue?
Is there external information (e.g. the library, internet resources) that would be helpful in helping understand this question?
This will help to shorten the experimentation time and
Avoid making mistakes from the past.
Create a Hypothesis
A hypothesis is an educated guess about how things work:
“If _____[I do this] _____, then _____[this]_____ will happen.”
You must state the hypothesis in a way that can be easily measured, and of course, the hypothesis should be constructed in a way to help answer the original question.
Conduct Experiment
The experiment tests whether the hypothesis is supported or not.
It is important for the experiment to be a “fair” test. That is, if its possible to control for contributing factors (i.e. those things that affect the outcome – the “Xs”), then try to keep those factors from changing while the experiment is in process.
Collect the desired data – i.e. those pieces of information that will help to decide if the experiment is a “success”.
You should also repeat your experiments several times to make sure that the first results weren’t just an accident.
Analyze and Conclude
Once the experiment is complete, collect the measurements and analyze them to see if they support hypothesis or not.
Practitioners often find that their hypothesis was not supported, and in such cases they will construct a new hypothesis based on the information they learned during their experiment.
This starts the entire process of the scientific method over again. Even if they find that their hypothesis was supported, they may want to test it again in a new way.
Report
If the experiment is successful – then the “new” practices must be integrated into the Lean system.
This usually is the form of a work instruction change, or an update to a process.
[Next Slide]
Be Inclusive
References:
Overview of the Scientific Method (Science Buddies) – http://www.sciencebuddies.org/science-fair-projects/project_scientific_method.shtml?gclid=CO3ujvGCiLsCFYU5QgodeF8A0Q#overviewofthescientificmethod
Francis Bacon: http://www.biography.com/people/francis-bacon-9194632
21
Designing Lean System Layouts
Line flows are recommended in lean systems layouts because they reduce the frequency of setups. When volumes are not high enough to justify the dedication of a single line of multiple workers, you can setup line-flow layouts in portions of the facility.
Two techniques to accomplish this are:
One-Worker, Multiple Machines (OWMM)
Group Technology Cells (GT)
One-Worker, Multiple Machines
Group Technology Cells
Jumbled Flows without GT
Lines Flows with 3 GT cells
Kanban Systems
Kanban
A Japanese word meaning “card” or “visible record.”
through a factory.
In Lean, it is a tool that refers to cards used to control the flow of production.
It facilitates flow by preventing over-production by prior steps in the process and build-up of inventory/WIP
The cell only produces the quantity needed when the Kanban signals it is time.
Examples of Kanban in everyday life:
Grocery store shelves (stock acts as Kanban)
Empty glass at a bar
What is a Kanban?
Kanban Essentials
Simple and visual
Nothing is created or moved without a Kanban
Process should be improved and standardized before Kanban
Kanban is not the starting point for Lean
Kanban Essentials
Kanbans do need to be overly complex as the milk bottle, bar glass, or Chula Vista’s colored piece of paper demonstrate!
Kanbans are intended to prevent push production and resulting over-production.
Take steps to minimize and eliminate defects and other forms of waste before doing Kanbans. For example, Chula Vista got rid of old, obsolete forms before instituting a re-order Kanban!
Kanban is considered a more advanced technique, so it is not something you will necessarily do right away.
GFOA Lean Training: Module 4
Containerless System
Using visual means in lieu of containers as a signal device.
The Kanban System
Kanban Essentials
Simple and visual
Kanban Board
GFOA Lean Training: Module 4
Kanban Essentials
Kanban Board
GFOA Lean Training: Module 4
Kanban Essentials
Kanban Board
GFOA Lean Training: Module 4
Other Kanban Signals
Container System
Using the container itself as a signal device.
Works well with containers specifically designed for parts.
The Kanban System
Container System
Each container must have a card.
Assembly always withdraws from fabrication (pull system).
Containers cannot be moved without a kanban.
Containers should contain the same number of parts.
Only good parts are passed along.
Production should not exceed authorization.
The Kanban System
The Kanban System
Receiving post
Kanban card for product 1
Kanban card for product 2
Fabrication cell
O1
O2
O3
O2
Storage area
Empty containers
Full containers
Assembly line 1
Assembly line 2
34
The Kanban System
Storage area
Empty containers
Full containers
Receiving post
Kanban card for product 1
Kanban card for product 2
Fabrication cell
O1
O2
O3
O2
Assembly line 1
Assembly line 2
The Kanban System
35
The Kanban System
Storage area
Empty containers
Full containers
Receiving post
Kanban card for product 1
Kanban card for product 2
Fabrication cell
O1
O2
O3
O2
Assembly line 1
Assembly line 2
The Kanban System
36
The Kanban System
Storage area
Empty containers
Full containers
Receiving post
Kanban card for product 1
Kanban card for product 2
Fabrication cell
O1
O2
O3
O2
Assembly line 1
Assembly line 2
The Kanban System
37
The Kanban System
Storage area
Empty containers
Full containers
Receiving post
Kanban card for product 1
Kanban card for product 2
Fabrication cell
O1
O2
O3
O2
Assembly line 1
Assembly line 2
The Kanban System
38
The Kanban System
Storage area
Empty containers
Full containers
Receiving post
Kanban card for product 1
Kanban card for product 2
Fabrication cell
O1
O2
O3
O2
Assembly line 1
Assembly line 2
The Kanban System
39
The Kanban System
Storage area
Empty containers
Full containers
Receiving post
Kanban card for product 1
Kanban card for product 2
Fabrication cell
O1
O2
O3
O2
Assembly line 1
Assembly line 2
The Kanban System
40
Value Stream Mapping
What is a Value Stream Map?
Value Stream Mapping
A qualitative lean tool for eliminating waste or muda that involves a current state drawing, a future state drawing and an implementation plan.
Product Family
Current state drawing
Future state drawing
Implementation plan
The value stream map is a unique flowchart because it combines the flow of material or service and the flow of information.
VSM Icons
08- 43
VSM Metrics
Takt Time
Cycle time needed to match the rate of production to the rate of sales or consumption.
Daily availability/Daily Demand
Cycle Time
The average time between completed units taking into account all resources available at a process step.
Processing Time
The time to complete one unit.
Jensen Bearings, Inc makes two types of retainers that are packaged and shipped in returnable trays with 60 retainers in each tray. The operations data is on the following slides.
Create a VSM for Jensen Bearings
What is the takt time?
What is the lead time at each cell?
What is the total processing time?
What is the capacity?
Jensen Bearings Example
Data
Jensen Bearings Example – data
Jensen Bearings Example – data cont.
Data
Create a VSM for Jensen Bearings
48
Daily Demand
[(1000+2200) pieces /week]/5 days =
640 pieces per day
Daily Availability
(7 hours/day) x (3600 seconds per hour) =
25,200 seconds per day
Takt Time = Daily availability/Daily Demand =
25,200/640 =
39.375 seconds per piece
What is the takt time?
Production Lead time = Inventory/Daily Demand
Raw Material Lead Time – 5 days
WIP between Press and Pierce/Form = (2250/640) = 3.5 days
WIP between Pierce/Form and Finish/Grind = (3350/640) = 5.2 days
WIP between Finish/Grind and Shipping= (1475/640) = 2.3 days
Total Production Lead Time = (5 + 3.5 + 5.2 + 2.3) = 16 days
Total Processing Time = Sum of the Cycle Times
(3 + 22 + 35) = 60 seconds
What is the lead time at each cell?
What is the total processing time?
Grinding is the bottleneck
Capacity = 25200/37.7 = 668 units/day
What is the capacity?
Capacity at Press Capacity at Pierce & Form Capacity at finish Grind
Cycle time = 3 seconds Cycle time = 22 seconds Cycle time = 35 seconds
Setup time = (2hrs x 3,600 seconds per hour)/1000
units per batch = 7.2 seconds Setup time = (30 minutes x 60 seconds per minute)/1000 units per batch = 1.8 seconds Setup time = (45 minutes x 60 seconds per minute)/1000 units per batch = 2.7 seconds
Per Unit Processing Time =
(3 + 7.2) = 10.2 seconds Per Unit Processing Time = (22 + 1.8) = 23.8 seconds Per Unit Processing Time = (35 + 2.7) = 37.7 seconds
Organizational Considerations to Lean Implementation
Worker stress
Lean systems coupled with SPC create a need for a high level of regimentation which can stress a workforce causing productivity losses or reductions in quality.
Trust between workers and mgt
In a Lean system roles of responsibility are pushed down to the lowest level. Work relationships must be reoriented to accommodate the Lean system.
Organizational Considerations to Lean Implementation
Reward systems
Should be revamped to encourage organization over functional group and prevent the silo effect
Labor classifications
If unions are involved, labor classifications may need to be renegotiated to accommodate the news roles associated with the Lean system
Operations and Project Management
ELCBUS 340
11 April 2018
1
Today’s Agenda
Class Administration – Littlefield Teams Verification
Forecasting
Solved Problems
Demand Patterns & Management
Forecast Error Measures
Forecasting Technique Parts I, II, and III
Criteria for Selecting a Time-Series Method
Discussion on Reading
2
50,000 Feet Overview of OPM
Managing Processes
Process Strategy
Process Performance
& Quality
Constraint Management
Process Layout
Lean Systems
Process Analysis
Using Operations
to Compete
Operations As a
Competitive Weapon
Operations Strategy
Project Management
Managing Value Chains
Supply Chain Strategy
Inventory Management
Location
Forecasting
Sales & Operations
Planning
Scheduling
Resource Planning
Forecasting
3
Service vs. Manufacturing
Small vs. Medium vs. Large Firms
Industry type: hightech, healthcare, aerospace, IT, etc ….
A prediction of future events used for planning purposes.
What is a Forecast?
4
Finalize
and communicate
6
Review by Operating Committee
5
Revise forecasts
4
Consensus meetings and collaboration
3
Prepare initial forecasts
2
Adjust history file
1
Forecasting as a Process
5
SOME PRINCIPLES FOR THE FORECASTING PROCESS
Better processes yield better forecasts
Demand forecasting is being done in virtually every company, either formally or informally. The challenge is to do it well—better than the competition
Better forecasts result in better customer service and lower costs, as well as better relationships with suppliers and customers
The forecast can and must make sense based on the big picture, economic outlook, market share, and so on
The best way to improve forecast accuracy is to focus on reducing forecast error
Bias is the worst kind of forecast error; strive for zero bias
Whenever possible, forecast at more aggregate levels. Forecast in detail only where necessary
Far more can be gained by people collaborating and communicating well than by using the most advanced forecasting technique or model
Forecasting Principles
6
Collaborative planning, forecasting, and replenishment (CPFR)
A process for supply chain integration that allows a supplier and its customers to collaborate on making the forecast.
Adding Collaboration to the Process
Demand Patterns & Management
8
There are five basic time series patterns:
Horizontal
Trend
Seasonal
Cyclical
Random
A time series is the repeated observations of demand for a service or product in their order of occurrence. Time series plots are used to visualize Demand Patterns.
Demand Patterns
9
(a) Horizontal (b) Trend
(a) Seasonal (b) Cyclical
Demand Patterns
10
The process of changing demand patterns using one or more demand options.
Demand Management
Demand Management Options:
Complementary Products
Promotional Pricing
Prescheduled Appointments
Reservations
Revenue Management
Backlogs
Backorders and Stockouts
What?
How? (Forecasting Technique)
Key Decisions for Making Forecasts
Judgment methods
Causal methods
Time-series analysis
Trend projection using regression
Level of aggregation
Units of measurement
12
Forecast Error Measures
13
For any forecasting method, it is important to measure the accuracy of its forecasts.
Forecast error is simply the difference found by subtracting the forecast from actual demand for a given period, or
Where:
Et = forecast error for period t
Dt = actual demand in period t
Ft = forecast for period t
Et = Dt – Ft
Measures of Forecast Error
(|Et |/ Dt)(100)
n
MAPE =
CFE = Et
Et2
n
MSE =
|Et |
n
MAD =
Cumulative sum of forecast errors (Bias)
Average forecast error
Mean Squared Error
Mean Absolute Percent Error
Mean Absolute Deviation
Standard deviation
CFE
n
Ē=
=
(Et – Ē)2
n – 1
Measures of Forecast Error
15
74
Month
t Demand
Dt Forecast
Ft Error
Et Error2
Et2 Absolute Error |Et| Absolute % Error (|Et|/Dt)(100)
1 200 225 –25
2 240 220 20
3 300 285 15
4 270 290 –20
5 230 250 –20 400 20 8.7
6 260 240 20 400 20 7.7
7 210 250 –40 1,600 40 19.0
8 275 240 35 1,225 35 12.7
Total –15 5,275 195 81.3%
Example
The following table shows the actual sales of upholstered chairs for a furniture manufacturer and the forecasts made for each of the last eight months.
Calculate CFE, MSE, σ, MAD, and MAPE for this product.
16
The following table shows the actual sales of upholstered chairs for a furniture manufacturer and the forecasts made for each of the last eight months.
Calculate CFE, MSE, σ, MAD, and MAPE for this product.
625 25 12.5%
400 20 8.3
225 15 5.0
400 20 7.4
Month
t Demand
Dt Forecast
Ft Error
Et Error2
Et2 Absolute Error |Et| Absolute % Error (|Et|/Dt)(100)
1 200 225 –25
2 240 220 20
3 300 285 15
4 270 290 –20
5 230 250 –20 400 20 8.7
6 260 240 20 400 20 7.7
7 210 250 –40 1,600 40 19.0
8 275 240 35 1,225 35 12.7
Total –15 5,275 195 81.3%
Example
17
Using the formulas for the measures, we get:
CFE =
–15
Average forecast error (mean bias):
Mean squared error:
Cumulative forecast error (mean bias):
MSE =
Et2
n
5,275
8
=
659.4
=
CFE
n
–1.875
= =
15
8
Ē =
Example
18
Standard deviation:
Mean absolute deviation:
Mean absolute percent error:
S[Et – (–1.875)]2
n – 1
s =
S|Et |
n
MAD =
(S|Et |/ Dt)(100)
n
MAPE =
= 27.4
= = 24.4
195
8
= = 10.2%
81.3%
8
Example
19
A Cumulative Forecast Error (CFE) of –15 indicates that the forecast has a slight bias to overestimate demand.
The Mean Square Error (MSE), σ, and Mean Absolute Deviation (MAD) statistics provide measures of forecast error variability.
A MAD of 24.4 means that the average forecast error was 24.4 units in absolute value.
The value of σ, 27.4, indicates that the sample distribution of forecast errors has a standard deviation of 27.4 units.
A Mean Absolute Percent Error (MAPE) of 10.2 percent implies that, on average, the forecast error was about 10 percent of actual demand.
These measures become more reliable as the number of periods of data increases.
Example
20
Forecasting Techniques – Part I (Overview)
Judgment Methods
Casual Methods
Time-Series Analysis
21
Judgmental forecasts use contextual knowledge gained through experience and translate them into quantitative estimates.
Salesforce estimates
Executive opinion
Market research
Delphi method
Judgment Methods
Causal Methods are a quantitative forecasting method that uses historical data on independent variables, such as promotional campaigns, economic conditions, and competitors’ actions to predict demand.
Casual Methods
Time-Series Analysis is a statistical approach that relies heavily on historical demand data to project the future size of demand and recognizes trends and seasonal patterns.
Time-Series Analysis
Forecasting Techniques – Part II
Simple Moving Average
Weighted Moving Average
Exponential Smoothing
25
Naïve forecast
The forecast for the next period equals the demand for the current period (Forecast = Dt)
Horizontal Patterns: Estimating the average
Simple moving average
Weighted moving average
Exponential smoothing
Time Series Methods
Specifically, the forecast for period t + 1 can be calculated at the end of period t (after the actual demand for period t is known) as
Ft+1 = =
Sum of last n demands
n
Dt + Dt-1 + Dt-2 + … + Dt-n+1
n
where
Dt = actual demand in period t
n = total number of periods in the average
Ft+1 = forecast for period t + 1
Simple Moving Averages
a. Compute a three-week moving average forecast for the arrival of medical clinic patients in week 4. The numbers of arrivals for the past three weeks were as follows:
b. If the actual number of patient arrivals in week 4 is 415, what is the forecast error for week 4?
c. What is the forecast for week 5?
Week Patient Arrivals
1 400
2 380
3 411
Simple Moving Averages – Example
28
a. The moving average forecast at the end of week 3 is:
Week Patient Arrivals
1 400
2 380
3 411
b. The forecast error for week 4 is
F4 =
= 397.0
411 + 380 + 400
3
E4 = D4 – F4
= 415 – 397 = 18
c. The forecast for week 5 requires the actual arrivals from weeks 2 through 4, the three most recent weeks of data
F5 =
= 402.0
415 + 411 + 380
3
Simple Moving Averages – Example
29
Estimating with Simple Moving Average using the following customer-arrival data:
Month Customer arrival
1 800
2 740
3 810
4 790
Use a three-month moving average to forecast customer arrivals for month 5
F5 =
= 780
D4 + D3 + D2
3
790 + 810 + 740
3
=
Forecast for month 5 is 780 customer arrivals
Simple Moving Averages – Example 2
If the actual number of arrivals in month 5 is 805, what is the forecast for month 6?
F6 =
= 801.667
D5 + D4 + D3
3
805 + 790 + 810
3
=
Forecast for month 6 is 802 customer arrivals
Month Customer arrival
1 800
2 740
3 810
4 790
Simple Moving Averages – Example 2
Forecast error is simply the difference found by subtracting the forecast from actual demand for a given period, or
Given the three-month moving average forecast for month 5, and the number of patients that actually arrived (805), what is the forecast error?
Forecast error for month 5 is 25
Et = Dt – Ft
E5 =
805 – 780
= 25
Simple Moving Averages – Example 2
In the weighted moving average method, each historical demand in the average can have its own weight, provided that the sum of the weights equals 1.0.
The average is obtained by multiplying the weight of each period by the actual demand for that period, and then adding the products together
Ft+1 = W1D1 + W2D2 + … + WnDt-n+1
Weighted Moving Averages
33
Using the customer arrival data in Example 2, let
W1 = 0.50, W2 = 0.30, and W3 = 0.20. Use the weighted moving average method to forecast arrivals for month 5.
= 0.50(790) + 0.30(810) + 0.20(740)
F5 = W1D4 + W2D3 + W3D2
= 786
Forecast for month 5 is 786 customer arrivals.
Given the number of customers that actually arrived (805),
what is the forecast error?
Forecast error for month 5 is 19.
E5 =
805 – 786
= 19
Weighted Moving Averages – Example
34
If the actual number of arrivals in month 5 is 805, compute the forecast for month 6:
= 0.50(805) + 0.30(790) + 0.20(810)
F6 = W1D5 + W2D4 + W3D3
= 801.5
Forecast for month 6 is 802 customer arrivals.
Weighted Moving Averages – Example
35
A sophisticated weighted moving average that calculates the average of a time series by implicitly giving recent demands more weight than earlier demands
Requires only three items of data
The last period’s forecast
The demand for this period
A smoothing parameter, alpha (α), where 0 ≤ α ≤ 1.0
The equation for the forecast is
Ft+1 = α(Demand this period) + (1 – α)(Forecast calculated last period)
= αDt + (1 – α)Ft
Exponential Smoothing
36
The emphasis given to the most recent demand levels can be adjusted by changing the smoothing parameter.
Larger α values emphasize recent levels of demand and result in forecasts more responsive to changes in the underlying average.
Smaller α values treat past demand more uniformly and result in more stable forecasts.
Exponential Smoothing
37
Reconsider the patient arrival data. It is now the end of week 3 so the actual arrivals is known to be 411 patients. Using α = 0.10, calculate the exponential smoothing forecast for week 4.
What was the forecast error for week 4 if the actual demand turned out to be 415?
What is the forecast for week 5?
Exponential Smoothing – Example
Week Patient Arrivals
1 400
2 380
3 411
38
a. To obtain the forecast for week 4, using exponential smoothing with and the initial forecast of 390*, we calculate the average at the end of week 3 as:
F4 =
Thus, the forecast for week 4 would be 392 patients.
0.10(411) + 0.90(390) = 392.1
* Here the initial forecast of 390 is the average of the first two weeks of demand. POM for Windows and OM Explorer, on the other hand, simply use the actual demand for the first week as the default setting for the initial forecast for period 1, and do not begin tracking forecast errors until the second period.
Exponential Smoothing – Example
39
b. The forecast error for week 4 is
c. The new forecast for week 5 would be
E4 =
F5 =
or 394 patients.
415 – 392 = 23
0.10(415) + 0.90(392.1) = 394.4
Exponential Smoothing – Example
Week Patient Arrivals
2 380
3 411
4 415
40
Forecasting Techniques – Part III
Trend Patterns Using Linear Regression
Multiplicative Seasonal Method
41
A dependent variable is related to one or more independent variables by a linear equation
The independent variables are assumed to “cause” the results observed in the past
Simple linear regression model is a straight line
Y = a + bX
where
Y = dependent variable
X = independent variable
a = Y-intercept of the line
b = slope of the line
Linear Regression
Dependent variable
Independent variable
X
Y
Estimate of
Y from
regression
equation
Regression
equation:
Y = a + bX
Actual
value
of Y
Value of X used
to estimate Y
Deviation,
or error
Linear Regression
The sample correlation coefficient, r
Measures the direction and strength of the relationship between the independent variable and the dependent variable.
The value of r can range from –1.00 ≤ r ≤ 1.00
The sample coefficient of determination, r2
Measures the amount of variation in the dependent variable about its mean that is explained by the regression line
The values of r2 range from 0.00 ≤ r2 ≤ 1.00
The standard error of the estimate, syx
Measures how closely the data on the dependent variable cluster around the regression line
Linear Regression
A trend in a time series is a systematic increase or decrease in the average of the series over time.
The forecast can be improved by calculating an estimate of the trend.
Trend Projection with Regression accounts for the trend with simple regression analysis.
Trend Patterns Using Regression
45
Medanalysis, Inc., provides medical laboratory services
Managers are interested in forecasting the number of blood analysis requests per week
There has been a national increase in requests for standard blood tests.
The arrivals over the next 16 weeks are given in the Table on the next slide.
What is the forecasted demand for the next three periods?
Trend Patterns – Regression Example
46
Week Arrivals Week Arrivals
1 28 9 61
2 27 10 39
3 44 11 55
4 37 12 54
5 35 13 52
6 53 14 60
7 38 15 60
8 57 16 75
Arrivals at Medanalysis, Inc.
Trend Patterns – Regression Example
Trend Patterns – Regression Example
Trend Patterns – Regression Example
Use OM Explorer to project the following weekly demand data using trend projection with regression.
What is the forecasted demand for periods 11-14?
Week Demand Week Demand
1
2
3
4
5 24
34
29
27
39 6
7
8
9
10 42
39
56
45
43
Trend Patterns – Regression Example 2
Trend Patterns – Regression Example 2
Trend Patterns – Regression Example 2
Multiplicative seasonal method
A method whereby seasonal factors are multiplied by an estimate of average demand to arrive at a seasonal forecast.
Additive seasonal method
A method in which seasonal forecasts are generated by adding a constant to the estimate of average demand per season.
Seasonal Factors
53
For each year, calculate the average demand for each season by dividing annual demand by the number of seasons per year.
For each year, divide the actual demand for each season by the average demand per season, resulting in a seasonal factor for each season.
Calculate the average seasonal factor for each season using the results from Step 2.
Calculate each season’s forecast for next year.
Multiplicative seasonal method
Multiplicative Seasonal Method
54
The manager wants to forecast customer demand for each quarter of year 5, based on an estimate of total year 5 demand of 2,600 customers.
The manager of the Stanley Steemer carpet cleaning company needs a quarterly forecast of the number of customers expected next year. The carpet cleaning business is seasonal, with a peak in the third quarter and a trough in the first quarter. The quarterly demand data from the past 4 years are on the next two slides.
Multiplicative Seasonal Method – Example
55
60
YEAR 1 YEAR 2
Q Demand Seasonal
Factor (1) Demand Seasonal
Factor (2)
1 45 45/250 = 0.18 70 70/300 = 0.23
2 335 335/250 = 1.34 370 370/300 = 1.23
3 520 520/250 = 2.08 590 590/300 = 1.97
4 100 100/250 = 0.40 170 170/300 = 0.57
Total 1,000 1,200
Average 1,000/4 = 250 1,200/4 = 300
Multiplicative Seasonal Method – Example
YEAR 3 YEAR 4
Q Demand Seasonal
Factor (3) Demand Seasonal
Factor (4)
1 100 100/450 = 0.22 100 100/550 = 0.18
2 585 585/450 = 1.30 725 725/550 = 1.32
3 830 830/450 = 1.84 1160 1160/550 = 2.11
4 285 285/450 = 0.63 215 215/550 = 0.39
Total 1,800 2,200
Average 1,800/4 = 450 2,200/4 = 550
Multiplicative Seasonal Method – Example
Quarterly Forecasts
Quarter Forecast
1 650 x 0.2043 = 132.795
2 650 x 1.2979 = 843.635
3 650 x 2.001 = 1,300.06
4 650 x 0.4977 = 323.505
Quarter Average Seasonal Factor
1 0.2043
2 1.2979
3 2.0001
4 0.4977
Average Seasonal Factor
Multiplicative Seasonal Method – Example
58
60
Figure 8.7
Multiplicative Seasonal Method – Example
59
Suppose the multiplicative seasonal method is being used to forecast customer demand. The actual demand and seasonal indices are shown below.
Year 1 Year 2 Average Index
Quarter Demand Index Demand Index
1 100 0.40 192 0.64 0.52
2 400 1.60 408 1.36 1.48
3 300 1.20 384 1.28 1.24
4 200 0.80 216 0.72 0.76
Average 250 300
Multiplicative Seasonal Method – Example 2
1400 units ÷ 4 quarters = 350 units
Quarter Average Index
1 0.52
2 1.48
3 1.24
4 0.76
Forecast for Quarter 1 =
Forecast for Quarter 2 =
Forecast for Quarter 3 =
Forecast for Quarter 4 =
0.52(350) ≈ 182 units
1.48(350) ≈ 518 units
1.24(350) ≈ 434 units
0.76(350) ≈ 266 units
Multiplicative Seasonal Method – Example 2
1320 units ÷ 4 quarters = 330 units
Quarter Average Index
1 0.52
2 1.48
3 1.24
4 0.76
If the projected demand for Year 3 is 1320 units, what is the forecast for each quarter of that year?
Forecast for Quarter 1 =
Forecast for Quarter 2 =
Forecast for Quarter 3 =
Forecast for Quarter 4 =
0.52(330) ≈ 172 units
1.48(330) ≈ 488 units
1.24(330) ≈ 409 units
0.76(330) ≈ 251 units
Multiplicative Seasonal Method – Example 2
Time Series-Method Selection
63
Criteria:
Minimizing bias (CFE)
Minimizing MAPE, MAD, or MSE
Maximizing r2 for trend projections using regression
Using a holdout sample analysis
Using a tracking signal
Meeting managerial expectations of changes in the components of demand.
Minimizing the forecast errors in recent periods.
Time-Series Method Selection Criteria
64
Using Statistical Criteria:
For more stable demand patterns, use lower a values or larger n values to emphasize historical experience.
For more dynamic demand patters, use higher a values or smaller n values.
Choosing a Time-Series Method
Holdout sample
Actual demands from the more recent time periods in the time series that are set aside to test different models developed from the earlier time periods.
Choosing a Time-Series Method
A measure that indicates whether a method of forecasting is accurately predicting actual changes in demand.
Tracking signal =
CFE
MAD
Each period, the CFE and MAD are updated to reflect current error, and the tracking signal is compared to some predetermined limits.
CFE
MADt
or
Tracking Signals
The MAD can be calculated as the simple average of all absolute errors or as a weighted average determined by the exponential smoothing method
MADt = α|Et| + (1 – α)MADt-1
If forecast errors are normally distributed with a mean of 0, the relationship between σ and MAD is simple
σ = ( /2)(MAD) 1.25(MAD)
MAD = 0.7978σ 0.8σ where p = 3.1416
Tracking Signals
+2.0 –
+1.5 –
+1.0 –
+0.5 –
0 –
–0.5 –
–1.0 –
–1.5 –
| | | | |
0 5 10 15 20 25
Observation number
Tracking signal
Out of control
Control limit
Control limit
Figure 8.8
Tracking Signals
69
86
This slide completes Figure 13.9 and shows the use of a tracking signal.
Solved Problems
70
Chicken Palace periodically offers carryout five-piece chicken dinners at special prices. Let Y be the number of dinners sold and X be the price. Based on the historical observations and calculations in the following table, determine the regression equation, correlation coefficient, and coefficient of determination. How many dinners can Chicken Palace expect to sell at $3.00 each?
Observation Price (X) Dinners Sold (Y)
1 $2.70 760
2 $3.50 510
3 $2.00 980
4 $4.20 250
5 $3.10 320
6 $4.05 480
Total $19.55 3,300
Average $ 3.26 550
Solved Problem 1
We use the computer to calculate the best values of a, b, the correlation coefficient, and the coefficient of determination
r 2 = 0.71
r = –0.84
b = –277.63
a = 1,454.60
The regression line is
Y = a + bX =
1,454.60 – 277.63X
For an estimated sales price of $3.00 per dinner
Y = a + bX =
1,454.60 – 277.63(3.00)
= 621.71 or 622 dinners
Solved Problem 1
The Polish General’s Pizza Parlor is a small restaurant catering to patrons with a taste for European pizza. One of its specialties is Polish Prize pizza. The manager must forecast weekly demand for these special pizzas so that he can order pizza shells weekly. Recently, demand has been as follows:
Week Pizzas Week Pizzas
June 2 50 June 23 56
June 9 65 June 30 55
June 16 52 July 7 60
a. Forecast the demand for pizza for June 23 to July 14 by using the simple moving average method with n = 3 then using the weighted moving average method with and weights of 0.50, 0.30, and 0.20, with 0.50.
b. Calculate the MAD for each method.
Solved Problem 2
a. The simple moving average method and the weighted moving average method give the following results:
Current Week Simple Moving Average Forecast for Next Week Weighted Moving Average Forecast
for Next Week
June 16
June 23
June 30
July 7
= 55.7 or 56
52 + 65 + 50
3
[(0.5 52) + (0.3 65) + (0.2 50)] = 55.5 or 56
= 57.7 or 58
56 + 52 + 65
3
= 54.3 or 54
55 + 56 + 52
3
[(0.5 56) + (0.3 52) + (0.2 65)] = 56.6 or 57
[(0.5 55) + (0.3 56) + (0.2 52)] = 54.7 or 55
= 57.0 or 57
60 + 55 + 56
3
[(0.5 60) + (0.3 55) + (0.2 56)] = 57.7 or 58
Solved Problem 2
b. The mean absolute deviation is calculated as follows:
Simple Moving Average Weighted Moving Average
Week Actual Demand Forecast for This Week Absolute Errors |Et| Forecast for This Week Absolute Errors |Et|
June 23 56 56 56
June 30 55 58 57
July 7 60 54 55
|56 – 56| = 0
|55 – 58| = 3
|60 – 54| = 6
MAD = = 3
0 + 3 + 6
3
MAD = = 2.3
0 + 2 + 2
3
|56 – 56| = 0
|55 – 57| = 2
|60 – 55| = 5
For this limited set of data, the weighted moving average method resulted in a slightly lower mean absolute deviation. However, final conclusions can be made only after analyzing much more data.
Solved Problem 2
The monthly demand for units manufactured by the Acme Rocket Company has been as follows:
Month Units Month Units
May 100 September 105
June 80 October 110
July 110 November 125
August 115 December 120
a. Use the exponential smoothing method to forecast June to January. The initial forecast for May was 105 units; α = 0.2.
b. Calculate the absolute percentage error for each month from June through December and the MAD and MAPE of forecast error as of the end of December.
c. Calculate the tracking signal as of the end of December. What can you say about the performance of your forecasting method?
Solved Problem 3
a.
Current Month, t Calculating Forecast for Next Month Ft+1 = αDt + (1 – α)Ft Forecast for Month t + 1
May June
June July
July August
August September
September October
October November
November December
December January
0.2(100) + 0.8(105)
= 104.0 or 104
0.2(80) + 0.8(104.0)
0.2(110) + 0.8(99.2)
= 99.2 or 99
= 101.4 or 101
0.2(115) + 0.8(101.4)
0.2(105) + 0.8(104.1)
0.2(110) + 0.8(104.3)
0.2(125) + 0.8(105.4)
0.2(120) + 0.8(109.3)
= 104.1 or 104
= 104.3 or 104
= 105.4 or 105
= 109.3 or 109
= 111.4 or 111
Solved Problem 3
b.
–24
24
30.0%
11
11
10.0
Month, t Actual Demand, Dt Forecast, Ft Error,
Et = Dt – Ft Absolute Error, |Et| Absolute Percent Error, (|Et|/Dt)(100)
June 80 104
July 110 99
August 115 101
September 105 104
October 110 104
November 125 105
December 120 109
Total 765
14 14 12.0
1 1 1.0
6 6 5.5
20 20 16.0
11 11 9.2
39 87 83.7%
|Et |
n
MAD =
(|Et |/Dt)(100)
n
MAPE =
= = 11.96%
83.7%
7
= = 12.4
87
7
Solved Problem 3
c. As of the end of December, the cumulative sum of forecast errors (CFE) is 39. Using the mean absolute deviation calculated in part (b), we calculate the tracking signal:
The probability that a tracking signal value of 3.14 could be generated completely by chance is small. Consequently, we should revise our approach. The long string of forecasts lower than actual demand suggests use of a trend method.
Tracking signal =
CFE
MAD
= = 3.14
39
12.4
Solved Problem 3
The Northville Post Office experiences a seasonal pattern of daily mail volume every week. The following data for two representative weeks are expressed in thousands of pieces of mail:
Day Week 1 Week 2
Sunday 5 8
Monday 20 15
Tuesday 30 32
Wednesday 35 30
Thursday 49 45
Friday 70 70
Saturday 15 10
Total 224 210
a. Calculate a seasonal factor for each day of the week.
b. If the postmaster estimates 230,000 pieces of mail to be sorted next week, forecast the volume for each day.
Solved Problem 4
Week 1 Week 2
Day Mail Volume Seasonal Factor (1) Mail Volume Seasonal Factor (2) Average Seasonal Factor
[(1) + (2)]/2
Sunday 5 8
Monday 20 15
Tuesday 30 32
Wednesday 35 30
Thursday 49 45
Friday 70 70
Saturday 15 10
Total 224 210
Average 224/7 = 32 210/7 = 30
5/32 = 0.15625
20/32 = 0.62500
30/32 = 0.93750
8/30 = 0.26667
15/30 = 0.50000
32/30 = 1.06667
0.21146
0.56250
1.00209
35/32 = 1.09375
49/32 = 1.53125
70/32 = 2.18750
15/32 = 0.46875
30/30 = 1.00000
45/30 = 1.50000
70/30 = 2.33333
10/30 = 0.33333
1.04688
1.51563
2.26042
0.40104
Solved Problem 4
b. The average daily mail volume is expected to be 230,000/7 = 32,857 pieces of mail. Using the average seasonal factors calculated in part (a), we obtain the following forecasts:
6,948
18,482
32,926
0.21146(32,857) =
0.56250(32,857) =
1.00209(32,857) =
34,397
49,799
74,271
13,177
230,000
1.04688(32,857) =
1.51563(32,857) =
2.26042(32,857) =
0.40104(32,857) =
Day Calculations Forecast
Sunday
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
Total
Solved Problem 4