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Statistics for Managers Using Microsoft Excel, 2/e © 1999 Prentice-Hall, Inc.
Chapter 18 Student Lecture Notes 18-1
© 2004 Prentice-Hall, Inc.
Basic Business Statistics(9th Edition)
Chapter 18Statistical Applications in Quality and Productivity Management
Chap 18-1
© 2004 Prentice-Hall, Inc. Chap 18-2
Chapter Topics
Total Quality Management (TQM)
Theory of Management (Deming’s Fourteen Points)
Six Sigma® Management Approach
The Theory of Control ChartsCommon-cause variation versus special-cause variation
Control Charts for the Proportion of Nonconforming Items
© 2004 Prentice-Hall, Inc. Chap 18-3
Chapter Topics
Process Variability
The c Chart
Control Charts for the Mean and the Range
Process Capability
(continued)
Statistics for Managers Using Microsoft Excel, 2/e © 1999 Prentice-Hall, Inc.
Chapter 18 Student Lecture Notes 18-2
© 2004 Prentice-Hall, Inc. Chap 18-4
Themes of Quality Management
1. Primary Focus on Process Improvement2. Most Variation in Process Due to System3. Teamwork is Integral to Quality Management4. Customer Satisfaction is a Primary Goal5. Organizational Transformation Necessary6. Remove Fear7. Higher Quality Costs Less
© 2004 Prentice-Hall, Inc. Chap 18-5
Deming’s 14 Points: Point 1:
Plan
DoStudy
Act
Point 1. Create Constancy of Purpose
The Shewhart-Deming CycleFocuses on Constant Improvement
© 2004 Prentice-Hall, Inc. Chap 18-6
Point 2. Adopt New PhilosophyBetter to be proactive and change before
crisis occurs.Point 3. Cease Dependence on Mass
Inspection to Achieve QualityAny inspection whose purpose is to improve
quality is too late.
Deming’s 14 Points: Points 2 and 3
Statistics for Managers Using Microsoft Excel, 2/e © 1999 Prentice-Hall, Inc.
Chapter 18 Student Lecture Notes 18-3
© 2004 Prentice-Hall, Inc. Chap 18-7
Point 4. End the Practice of Awarding Business on the Basis of Price Tag Alone
Develop long term relationship between purchaser and supplier.
Point 5. Improve Constantly and Forever
Reinforce the importance of theShewhart-Deming cycle.
Deming’s 14 Points: Points 4 and 5
© 2004 Prentice-Hall, Inc. Chap 18-8
Deming’s 14 Points: Points 6 and 7
Point 6. Institute Training
Especially important for managers to understand the difference between special causes and common causes.
Point 7. Adopt and Institute Leadership
Differentiate between leadership and supervision. Leadership is to improve the system and achieve greater consistency of performance.
© 2004 Prentice-Hall, Inc. Chap 18-9
8. Drive Out Fear9. Break Down Barriers between Staff Areas10. Eliminate Slogans11. Eliminate Numerical Quotas for Workforce and Numerical Goals for Management12. Remove Barriers to Pride of Workmanship
Deming’s 14 Points: Points 8 to 12
300
Statistics for Managers Using Microsoft Excel, 2/e © 1999 Prentice-Hall, Inc.
Chapter 18 Student Lecture Notes 18-4
© 2004 Prentice-Hall, Inc. Chap 18-10
Point 13. Encourage Education and Self-Improvement for Everyone
Improved knowledge of people will improve the assets of
the organization.
Point 14. Take Action to Accomplish TransformationContinually strive toward improvement.
Deming’s 14 Points: Points 13 and 14
Quality is important
© 2004 Prentice-Hall, Inc. Chap 18-11
Six Sigma® Management
A Managerial Approach Designed to Create Processes that Result in No More Than 3.4 Defects Per MillionA Method for Breaking Processes into a Series of Steps in Order to Eliminate Defects and Produce Near Perfect Results
(1) Define: Define the problem along with costs, benefits and the impact on customers(2) Measure: Develop operational definitions for each Critical-to-Quality characteristic and verify measurement procedure to achieve consistency over repeated measurements
© 2004 Prentice-Hall, Inc. Chap 18-12
Six Sigma® Management
(3) Analyze: Use control charts to monitor defects and determine the root causes of defects(4) Improve: Study the importance of each process variable on the Critical-to-Quality characteristic to determine and maintain the best level for each variable in the long term(5) Control: Avoid potential problems that occur when a process is changed and maintain the gains that have been made in the long term
(continued)
Statistics for Managers Using Microsoft Excel, 2/e © 1999 Prentice-Hall, Inc.
Chapter 18 Student Lecture Notes 18-5
© 2004 Prentice-Hall, Inc. Chap 18-13
Control Charts
Monitor Variation in DataExhibit trend - make correction before process is out of control
A Process - A Repeatable Series of Steps Leading to a Specific Goal
© 2004 Prentice-Hall, Inc. Chap 18-14
Control Charts
Show When Changes in Data are Due to:Special or assignable causes
Fluctuations not inherent to a processRepresent problems to be correctedData outside control limits or trend
Chance or common causesInherent random variationsConsist of numerous small causes of random variability
(continued)
© 2004 Prentice-Hall, Inc. Chap 18-15
Graph of sample data plotted over time
Process Control Chart
020406080
1 2 3 4 5 6 7 8 9 101112
X
Time
Special Cause Variation
Common Cause Variation
Process Average ±3σ
Mean
UCL
LCL
Statistics for Managers Using Microsoft Excel, 2/e © 1999 Prentice-Hall, Inc.
Chapter 18 Student Lecture Notes 18-6
© 2004 Prentice-Hall, Inc. Chap 18-16
Control Limits
UCL = Process Average + 3 Standard DeviationsLCL = Process Average - 3 Standard Deviations
Process Average
UCL
LCL
X
+ 3σ
- 3σ
TIME
© 2004 Prentice-Hall, Inc. Chap 18-17
Types of Error
First Type: Belief that observed value represents special cause when, in fact, it is due to common cause
Second Type: Treating special cause variation as if it is common cause variation
© 2004 Prentice-Hall, Inc. Chap 18-18
Comparing Control Chart Patterns
X XX
Common Cause Variation: No Points
Outside Control Limits
Special Cause Variation: 2 Points
Outside Control Limits
Downward Pattern: No Points Outside Control Limits but
Trend Exists
Statistics for Managers Using Microsoft Excel, 2/e © 1999 Prentice-Hall, Inc.
Chapter 18 Student Lecture Notes 18-7
© 2004 Prentice-Hall, Inc. Chap 18-19
When to Take Corrective Action
Corrective Action Should Be Taken When Observing Points Outside the Control Limits or when a Trend Has Been Detected
Eight consecutive points above the center line (or eight below)Eight consecutive points that are increasing (decreasing)
© 2004 Prentice-Hall, Inc. Chap 18-20
Out-of-Control Processes
If the Control Chart Indicates an Out-of-Control Condition (a Point Outside the Control Limits or Exhibiting Trend)
Contains both common causes of variation and assignable causes of variationThe assignable causes of variation must be identified
If detrimental to quality, assignable causes of variation must be removedIf increases quality, assignable causes must be incorporated into the process design
© 2004 Prentice-Hall, Inc. Chap 18-21
In-Control Process
If the Control Chart is Not Indicating Any Out-of-Control Condition, then
Only common causes of variation existIt is sometimes said to be in a state of statistical control
If the common-cause variation is small, then control chart can be used to monitor the processIf the common-cause variation is too large, the process needs to be altered
Statistics for Managers Using Microsoft Excel, 2/e © 1999 Prentice-Hall, Inc.
Chapter 18 Student Lecture Notes 18-8
© 2004 Prentice-Hall, Inc. Chap 18-22
p Chart
Control Chart for ProportionsIs an attribute chart
Shows Proportion of Nonconforming ItemsE.g., Count # of nonconforming chairs & divide by total chairs inspected
Chair is either conforming or nonconforming
Used with Equal or Unequal Sample Sizes Over Time
Unequal sizes should not differ by more than ±25% from average sample size
© 2004 Prentice-Hall, Inc. Chap 18-23
p Chart Control Limits
(1 )3pp pLCL p
n−
= −(1 )3p
p pUCL pn−
= +
1
k
ii
nn
k==∑
Average Group Size
1
1
k
ii
k
ii
Xp
n
=
=
=∑
∑
Average Proportion of Nonconforming Items
# Defective Items in Sample i
Size of Sample i
# of Samples
© 2004 Prentice-Hall, Inc. Chap 18-24
p Chart Example
You’re manager of a 500-room hotel. You want to achieve the highest level of service. For 7 days, you collect data on the readiness of 200 rooms. Is the process in control?
Statistics for Managers Using Microsoft Excel, 2/e © 1999 Prentice-Hall, Inc.
Chapter 18 Student Lecture Notes 18-9
© 2004 Prentice-Hall, Inc. Chap 18-25
p Chart Hotel Data
# NotDay # Rooms Ready Proportion1 200 16 0.0802 200 7 0.0353 200 21 0.1054 200 17 0.0855 200 25 0.1256 200 19 0.0957 200 16 0.080
© 2004 Prentice-Hall, Inc. Chap 18-26
1
1
121 .08641400
k
ii
k
ii
Xp
n
=
=
= = =∑
∑
p Chart Control Limits Solution
16 + 7 +...+ 16
1 1400 2007
k
ii
nn
k== = =∑
( ) ( )
( )
1 .0864 1 .08643 .0864 3
200.0864 .0596 or .0268,.1460
p pp
n
− −± = ±
= ±
© 2004 Prentice-Hall, Inc. Chap 18-27
Mean
p Chart Control Chart Solution
UCL
LCL0.000.050.100.15
1 2 3 4 5 6 7
P
DayIndividual points are distributed around without any pattern. Any improvement in the process must come from reduction of common-cause variation, which is the responsibility of the management.
p
p
Statistics for Managers Using Microsoft Excel, 2/e © 1999 Prentice-Hall, Inc.
Chapter 18 Student Lecture Notes 18-10
© 2004 Prentice-Hall, Inc. Chap 18-28
p Chart in PHStat
PHStat | Control Charts | p Chart …
Excel Spreadsheet for the Hotel Room Example
Microsoft Excel Worksheet
© 2004 Prentice-Hall, Inc. Chap 18-29
Worker Day 1 Day 2 Day 3 All Days
A 9 (18%) 11 (12%) 6 (12%) 26 (17.33%)
B 12 (24%) 12 (24%) 8 (16%) 32 (21.33%)
C 13 (26%) 6 (12%) 12 (24%) 31(20.67%)
D 7 (14%) 9 (18%) 8 (16%) 24 (16.0%)
Totals 41 38 34 113
Understanding Process Variability:Red Bead Example
Four workers (A, B, C, D) spend 3 days to collect beads, at 50 beads per day. The expected number of red beads to be collected per day per worker is 10 or 20%.
© 2004 Prentice-Hall, Inc. Chap 18-30
Average Day 1 Day 2 Day 3 All Days
X 10.25 9.5 8.5 9.42
p 20.5% 19% 17% 18.83%
Understanding Process Variability:Example Calculations
113 .188350(12)
p = =(1 ) .1883(1 .1883)3 .1883 3
50 .1883 .1659
p ppn− −
± = ±
= ±
_
.1883 .1659 .0224
.1883 +.1659 .3542LCLUCL
= − == =
Statistics for Managers Using Microsoft Excel, 2/e © 1999 Prentice-Hall, Inc.
Chapter 18 Student Lecture Notes 18-11
© 2004 Prentice-Hall, Inc. Chap 18-31
0 A1 B1 C1 D1 A2 B2 C2 D2 A3 B3 C3 D3
Understanding Process Variability:Example Control Chart
.30
.20
.10
p
UCL
LCL
_
© 2004 Prentice-Hall, Inc. Chap 18-32
Morals of the Example
Variation is an inherent part of any process.The system is primarilyresponsible for workerperformance.Only management can change the system.Some workers will always be above average,and some will be below.
© 2004 Prentice-Hall, Inc. Chap 18-33
The c Chart
Control Chart for Number of Nonconformities (Occurrences) in a Unit (an Area of Opportunity)
Is an attribute chart
Shows Total Number of Nonconforming Items in a Unit
E.g., Count # of defective chairs manufactured per day
Assume that the Size of Each Subgroup Unit Remains Constant
Statistics for Managers Using Microsoft Excel, 2/e © 1999 Prentice-Hall, Inc.
Chapter 18 Student Lecture Notes 18-12
© 2004 Prentice-Hall, Inc. Chap 18-34
c Chart Control Limits
3cLCL c c= − 3cUCL c c= +
1
k
ii
cc
k==∑
Average Number of Occurrences
# of Samples
# of Occurrences in Sample i
© 2004 Prentice-Hall, Inc. Chap 18-35
c Chart: Example
You’re manager of a 500-room hotel. You want to achieve the highest level of service. For 7 days, you collect data on the readiness of 200 rooms. Is the process in control?
© 2004 Prentice-Hall, Inc. Chap 18-36
c Chart: Hotel Data
# NotDay # Rooms Ready1 200 162 200 73 200 214 200 175 200 256 200 197 200 16
Statistics for Managers Using Microsoft Excel, 2/e © 1999 Prentice-Hall, Inc.
Chapter 18 Student Lecture Notes 18-13
© 2004 Prentice-Hall, Inc. Chap 18-37
c Chart: Control Limits Solution
1 16 7 19 16 17.2867
3 17.286 3 17.285 4.813
3 29.759
k
ii
c
c
cc
kLCL c c
UCL c c
= + + + += = =
= − = − =
= + =
∑ L
© 2004 Prentice-Hall, Inc. Chap 18-38
c Chart: Control Chart Solution
UCL
LCL0102030
1 2 3 4 5 6 7
c
Day
c
Individual points are distributed around without any pattern. Any improvement in the process must come from reduction of common-cause variation, which is the responsibility of the management.
c
© 2004 Prentice-Hall, Inc. Chap 18-39
Variables Control Charts: R Chart
Monitors Variability in ProcessCharacteristic of interest is measured on numerical scaleIs a variables control chart
Shows Sample Range Over TimeDifference between smallest & largest values in inspection sampleE.g., Amount of time required for luggage to be delivered to hotel room
Statistics for Managers Using Microsoft Excel, 2/e © 1999 Prentice-Hall, Inc.
Chapter 18 Student Lecture Notes 18-14
© 2004 Prentice-Hall, Inc. Chap 18-40
R Chart Control Limits
Sample Range at Time i or Sample i
# Samples
From Table4RUCL D R=
3RLCL D R=
1
k
ii
RR
k==∑
© 2004 Prentice-Hall, Inc. Chap 18-41
R Chart Example
You’re manager of a 500-room hotel. You want to analyze the time it takes to deliver luggage to the room. For 7 days, you collect data on 5 deliveries per day. Is the process in control?
© 2004 Prentice-Hall, Inc. Chap 18-42
R Chart and Mean Chart Hotel Data
Sample SampleDay Average Range1 5.32 3.852 6.59 4.273 4.88 3.284 5.70 2.995 4.07 3.616 7.34 5.047 6.79 4.22
Statistics for Managers Using Microsoft Excel, 2/e © 1999 Prentice-Hall, Inc.
Chapter 18 Student Lecture Notes 18-15
© 2004 Prentice-Hall, Inc. Chap 18-43
R Chart Control Limits Solution
From Table (n = 5)
1 3.85 4.27 4.22 3.8947
k
ii
RR
k= + + +
= = =∑ L
4
3
2.114 3.894 8.232
0 3.894 0R
R
UCL D R
LCL D R
= ⋅ = ⋅ =
= ⋅ = ⋅ =
© 2004 Prentice-Hall, Inc. Chap 18-44
R Chart Control Chart Solution
UCL
02468
1 2 3 4 5 6 7
Minutes
Day
LCL
R_
© 2004 Prentice-Hall, Inc. Chap 18-45
Variables Control Charts: Mean Chart (The Chart)
Shows Sample Means Over TimeCompute mean of inspection sample over timeE.g., Average luggage delivery time in hotel
Monitors Process AverageMust be preceded by examination of the R chart to make sure that the process is in control
X
Statistics for Managers Using Microsoft Excel, 2/e © 1999 Prentice-Hall, Inc.
Chapter 18 Student Lecture Notes 18-16
© 2004 Prentice-Hall, Inc. Chap 18-46
Mean Chart
Sample Range at Time i
# Samples
Sample Mean at Time i
Computed From Table
2XUCL X A R= +
2XLCL X A R= −
1 1 and
k k
i ii i
X RX R
k k= == =∑ ∑
© 2004 Prentice-Hall, Inc. Chap 18-47
Mean Chart Example
You’re manager of a 500-room hotel. You want to analyze the time it takes to deliver luggage to the room. For 7 days, you collect data on 5 deliveries per day. Is the process in control?
© 2004 Prentice-Hall, Inc. Chap 18-48
R Chart and Mean Chart Hotel Data
Sample SampleDay Average Range1 5.32 3.852 6.59 4.273 4.88 3.284 5.70 2.995 4.07 3.616 7.34 5.047 6.79 4.22
Statistics for Managers Using Microsoft Excel, 2/e © 1999 Prentice-Hall, Inc.
Chapter 18 Student Lecture Notes 18-17
© 2004 Prentice-Hall, Inc. Chap 18-49
Mean Chart Control Limits Solution
1
1
2
2
5.32 6.59 6.79 5.8137
3.85 4.27 4.22 3.8947
5.813 0.577 3.894 8.060
5.813 0.577 3.894 3.566
k
ii
k
ii
X
X
XX
k
RR
k
UCL X A R
LCL X A R
=
=
+ + += = =
+ + += = =
= + ⋅ = + ⋅ =
= − ⋅ = − ⋅ =
∑
∑
L
L
From Table E.9 (n = 5)
© 2004 Prentice-Hall, Inc. Chap 18-50
Mean Chart Control Chart Solution
UCL
LCL02468
1 2 3 4 5 6 7
Minutes
Day
X__
© 2004 Prentice-Hall, Inc. Chap 18-51
R Chart and Mean Chartin PHStat
PHStat | Control Charts | R & Xbar Charts …
Excel Spreadsheet for the Hotel Room Example
Microsoft Excel Worksheet
Statistics for Managers Using Microsoft Excel, 2/e © 1999 Prentice-Hall, Inc.
Chapter 18 Student Lecture Notes 18-18
© 2004 Prentice-Hall, Inc. Chap 18-52
Process CapabilityProcess Capability is the Ability of a Process to Consistently Meet Specified Customer-Driven RequirementsSpecification Limits are Set by Management in Response to Customer’s ExpectationsThe Upper Specification Limit (USL) is the Largest Value that Can Be Obtained and Still Conform to Customer’s ExpectationThe Lower Specification Limit (LSL) is the Smallest Value that is Still Conforming
© 2004 Prentice-Hall, Inc. Chap 18-53
Estimating Process Capability
Must Have an In-Control Process First
Estimate the Percentage of Product or Service Within Specification
Assume the Population of X Values is Approximately Normally Distributed with Mean Estimated by and Standard Deviation Estimated by
X2/R d
© 2004 Prentice-Hall, Inc. Chap 18-54
Estimating Process Capability
For a Characteristic with an LSL and a USL
where Z is a standardized normal random variable
(continued)
2 2
P(an outcome will be within specification) P( )
= P/ /
LSL X USL
LSL X USL XZR d R d
= < <
⎛ ⎞− −⎜ ⎟< <⎜ ⎟⎝ ⎠
Statistics for Managers Using Microsoft Excel, 2/e © 1999 Prentice-Hall, Inc.
Chapter 18 Student Lecture Notes 18-19
© 2004 Prentice-Hall, Inc. Chap 18-55
Estimating Process Capability
For a Characteristic with Only a LSL
where Z is a standardized normal random variable
(continued)
2
P(an outcome will be within specification) P( )
= P/
LSL X
LSL X ZR d
= <
⎛ ⎞−⎜ ⎟<⎜ ⎟⎝ ⎠
© 2004 Prentice-Hall, Inc. Chap 18-56
Estimating Process Capability
For a Characteristic with Only a USL
where Z is a standardized normal random variable
(continued)
2
P(an outcome will be within specification) P( )
= P/
X USL
USL XZR d
= <
⎛ ⎞−⎜ ⎟<⎜ ⎟⎝ ⎠
© 2004 Prentice-Hall, Inc. Chap 18-57
You’re manager of a 500-room hotel. You have instituted a policy that 99% of all luggage deliveries must be completed within 10 minutes or less. For 7 days, you collect dataon 5 deliveries per day. Is the process capable?
Process Capability Example
Statistics for Managers Using Microsoft Excel, 2/e © 1999 Prentice-Hall, Inc.
Chapter 18 Student Lecture Notes 18-20
© 2004 Prentice-Hall, Inc. Chap 18-58
Process Capability:Hotel Data
Sample SampleDay Average Range1 5.32 3.852 6.59 4.273 4.88 3.284 5.70 2.995 4.07 3.616 7.34 5.047 6.79 4.22
© 2004 Prentice-Hall, Inc. Chap 18-59
Process Capability:Hotel Example Solution
5.813X = 3.894R = 2and 2.326d =
P(A delivery is made within specification)= P( 10)
10 5.813= P3.894 / 2.326
= P( 2.50) .9938
X
Z
Z
<
−⎛ ⎞<⎜ ⎟⎝ ⎠
< =
5n =
Therefore, we estimate that 99.38% of the luggage deliveries will be made within the 10 minutes or less specification. The process is capable of meeting the 99% goal.
© 2004 Prentice-Hall, Inc. Chap 18-60
Capability Indices
Aggregate Measures of a Process’ Ability to Meet Specification Limits
The larger (>1) the values, the more capable a process is of meeting requirements
Measure of Process Potential Performance
Cp>1 implies that a process has the potential of having more than 99.73% of outcomes within specifications
( )2
specification spreadprocess spread6 /p
USL LSLCR d−
= =
Statistics for Managers Using Microsoft Excel, 2/e © 1999 Prentice-Hall, Inc.
Chapter 18 Student Lecture Notes 18-21
© 2004 Prentice-Hall, Inc. Chap 18-61
Capability Indices
Measures of Actual Process PerformanceFor one-sided specification limits
CPL (CPU) >1 implies that the process mean is more than 3 standard deviations away from the lower (upper) specification limit
(continued)
( )23 /X LSLCPL
R d−
=
( )23 /USL XCPU
R d−
=
© 2004 Prentice-Hall, Inc. Chap 18-62
Capability Indices
For two-sided specification limits
Cpk = 1 indicates that the process average is 3 standard deviations away from the closest specification limitLarger Cpk indicates larger capability of meeting the requirements
(continued)
( )min ,pkC CPL CPU=
© 2004 Prentice-Hall, Inc. Chap 18-63
You’re manager of a 500-room hotel. You have instituted a policy that all luggage deliveries must be completed within 10 minutes or less. For 7 days, you collect data on 5 deliveries per day. Compute an appropriate capability index for the delivery process.
Process Capability Example
Statistics for Managers Using Microsoft Excel, 2/e © 1999 Prentice-Hall, Inc.
Chapter 18 Student Lecture Notes 18-22
© 2004 Prentice-Hall, Inc. Chap 18-64
Process Capability:Hotel Data
Sample SampleDay Average Range1 5.32 3.852 6.59 4.273 4.88 3.284 5.70 2.995 4.07 3.616 7.34 5.047 6.79 4.22
© 2004 Prentice-Hall, Inc. Chap 18-65
Process Capability:Hotel Example Solution
5.813X = 3.894R = 2and 2.326d =5n =
Since there is only the upper specification limit, we need to only compute CPU. The capability index for the luggage delivery process is .8337, which is less than 1. The upper specification limit is less than 3 standard deviations above the mean.
( ) ( )2
10 5.813 0.8336723 3.894 / 2.3263 /
USL XCPUR d− −
= = =
© 2004 Prentice-Hall, Inc. Chap 18-66
Chapter Summary
Described Total Quality Management (TQM)Addressed the Theory of Management
Deming’s 14 Points
Described the Six Sigma® Management ApproachDiscussed the Theory of Control Charts
Common-cause variation versus special-cause variation
Statistics for Managers Using Microsoft Excel, 2/e © 1999 Prentice-Hall, Inc.
Chapter 18 Student Lecture Notes 18-23
© 2004 Prentice-Hall, Inc. Chap 18-67
Chapter Summary
Computed Control Charts for the Proportion of Nonconforming ItemsDescribed Process VariabilityDescribed c ChartComputed Control Charts for the Mean and the RangeDiscussed Process Capability
(continued)