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Transcript of © 2003 Prentice-Hall, Inc. Quantitative Analysis Chapter 17 Statistical Quality Control Chap 17-1.
© 2003 Prentice-Hall, Inc.
Quantitative Analysis
Chapter 17Statistical Quality Control
Chap 17-1
© 2003 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 Charts
Common-cause variation versus special-cause variation
Control Charts for the Proportion of Nonconforming Items
© 2003 Prentice-Hall, Inc. Chap 18-3
Chapter Topics
Process Variability The c Chart Control Charts for the Mean and the
Range Process Capability
(continued)
© 2003 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
© 2003 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
© 2003 Prentice-Hall, Inc. Chap 18-6
Point 2. Adopt New Philosophy
Better to be proactive and change before crisis occurs.
Point 3. Cease Dependence on Mass Inspection to Achieve Quality
Any inspection whose purpose is to improve quality is too late.
Deming’s 14 Points: Points 2 and 3
© 2003 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 the Shewhart-Deming cycle.
Deming’s 14 Points: Points 4 and 5
© 2003 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.
© 2003 Prentice-Hall, Inc. Chap 18-9
Points 8-12.
Drive Out Fear
Break Down Barriers between Staff Areas
Eliminate Slogans
Eliminate Numerical Quotas for Workforce and Numerical Goals for Management
Remove Barriers to Pride of Workmanship
Deming’s 14 Points: Points 8 to 12
300
© 2003 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 Transformation
Continually strive toward improvement.
Deming’s 14 Points: Points 13 and 14
Quality is important
© 2003 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 Million
A Method for Breaking Processes into a Series of Steps in Order to Eliminate Defects and Produce Near Perfect Results (1) Define:Define: Define the problem along with
costs, benefits and the impact on customers (2) MeasureMeasure: Develop operational definitions
for each Critical-to-Quality characteristic and verify measurement procedure to achieve consistency over repeated measurements
© 2003 Prentice-Hall, Inc. Chap 18-12
Six Sigma® Management
(3) AnalyzeAnalyze: Use control charts to monitor defects and determine the root causes of defects
(4) ImproveImprove: 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) ControlControl: Avoid potential problems that occur when a process is changed and maintain the gains that have been made in the long term
(continued)
© 2003 Prentice-Hall, Inc. Chap 18-13
Control Charts
Monitor Variation in Data Exhibit trend - make correction before
process is out of control A Process - A Repeatable Series of Steps
Leading to a Specific Goal
© 2003 Prentice-Hall, Inc. Chap 18-14
Characteristics for which you focus on defects
Classify products as either ‘good’ or ‘bad’, or count # defects e.g., radio works or
not
Categorical or discrete random variables
AttributesVariables
Quality Characteristics
Characteristics that you measure, e.g., weight, length
May be in whole or in fractional numbers
Continuous random variables
© 2003 Prentice-Hall, Inc. Chap 18-15
Statistical technique used to ensure process is making product to standard
All process are subject to variability Common (or Natural) causes: Random
variations Special (or Assignable) causes: Correctable
problems
Machine wear, unskilled workers, poor material
Objective: Identify assignable causes Uses process control charts
Statistical Process Control (SPC)
© 2003 Prentice-Hall, Inc. Chap 18-16
Graph of sample data plotted over time
Process Control Chart
020406080
1 3 5 7 9 11
X
Time
Special Cause Variation
Common Cause Variation
Process Average
Mean
UCL
LCL
© 2003 Prentice-Hall, Inc. Chap 18-17
Control Charts
Show When Changes in Data are Due to: Special (or Assignable) causes
Fluctuations not inherent to a process Represent problems to be corrected Data outside control limits or trend
Common causes (or Natural Causes) Inherent random variations Consist of numerous small causes of random
variability
(continued)
© 2003 Prentice-Hall, Inc. Chap 18-18
Control Limits
UCL = Process Average + 3 Standard Deviations
LCL = Process Average - 3 Standard Deviations
Process Average
UCL
LCL
X
+ 3
- 3
TIME
© 2003 Prentice-Hall, Inc. Chap 18-19
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 variation The assignable causes of variation must be
identified If detrimental to quality, assignable causes of
variation must be removed If increases quality, assignable causes must
be incorporated into the process design
© 2003 Prentice-Hall, Inc. Chap 18-20
In-Control Process
If the Control Chart is Not Indicating Any Out-of-Control Condition, then Only common causes of variation exist It 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 process
If the common-cause variation is too large, the process needs to be altered
© 2003 Prentice-Hall, Inc. Chap 18-21
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
© 2003 Prentice-Hall, Inc. Chap 18-22
Control Chart Patterns: How to tell the Process is Out of ControlUpper controlchart limit
Target
Lower controlchart limit
Normal behavior. One point out above.Investigate for cause.
One point out below.Investigate for cause.
© 2003 Prentice-Hall, Inc. Chap 18-23
Control Chart Patterns: How to tell the Process is Out of Control (Cont.)
Upper control limit
Target
Lower control limit
Run of 5 points belowcentral line. Investigate for cause.
Trends in eitherDirection.Investigate for cause of progressive change.
Erratic behavior. Investigate.
© 2003 Prentice-Hall, Inc. Chap 18-24
Control Chart Patterns: How to tell the Process is Out of Control cont.
Upper control chart limit
Target
Lower control chart limit
Two points near upper control. Investigatefor cause.
Two points near lowercontrol. Investigatefor cause.
Run of 5 points above central line. Investigate for cause.
© 2003 Prentice-Hall, Inc. Chap 18-25
Produce GoodProvide Service
Stop Process
Yes
No
Assign.Causes?Take Sample
Inspect Sample
Find Out WhyCreate
Control Chart
Start
Statistical Process Control Steps
© 2003 Prentice-Hall, Inc. Chap 18-26
4 Basic Types of Control Charts
Control Charts
For Variables For Attributes
Chart for meansof sample n
R Chart RangeOf sample n
p - Chart
Sample Size, n known
c - Chart
Sample Size, n unknown
X
What is the difference between Variables and Attributes?
© 2003 Prentice-Hall, Inc. Chap 18-27
Variables Control Charts: R Chart
Monitors Variability in Process Characteristic of interest is measured on
numerical scale Is a variables control chartvariables control chart
Shows Sample Range Over Time Difference between smallest & largest
values in inspection sample E.g., Amount of time required for luggage to
be delivered to hotel room
© 2003 Prentice-Hall, Inc. Chap 18-28
R Chart Control Limits
Sample Range at Time i or Subgroup i
# Samples
From Table 17.2 Page 683
4RUCL D R
3RLCL D R
1
k
ii
RR
k
© 2003 Prentice-Hall, Inc. Chap 18-29
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?
© 2003 Prentice-Hall, Inc. Chap 18-30
R Chart and Mean Chart Hotel Data
Sample SampleDay Average Range
1 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
© 2003 Prentice-Hall, Inc. Chap 18-31
R Chart Control Limits Solution
From Table 17.2 page 683 (n = 5)
1 3.85 4.27 4.223.894
7
k
ii
RR
k
4
3
2.114 3.894 8.232
0 3.894 0
R
R
UCL D R
LCL D R
© 2003 Prentice-Hall, Inc. Chap 18-32
R Chart Control Chart Solution
UCL
02468
1 2 3 4 5 6 7
Minutes
Day
LCL
R_
© 2003 Prentice-Hall, Inc. Chap 18-33
Variables Control Charts: Mean Chart (The Chart)
Shows Sample Means Over Time Compute mean of inspection sample over
time E.g., Average luggage delivery time in hotel
Monitors Process Average Must be preceded by examination of the R
chart to make sure that the process is in control
X
© 2003 Prentice-Hall, Inc. Chap 18-34
Mean Chart
Sample Range at Time i
# Samples
Sample Mean at Time i
Computed From Table 17.2 Page 683
2XUCL X A R
2XLCL X A R
1 1 and
k k
i ii i
X RX R
k k
© 2003 Prentice-Hall, Inc. Chap 18-35
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?
© 2003 Prentice-Hall, Inc. Chap 18-36
R Chart and Mean Chart Hotel Data
Sample SampleDay Average Range
1 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
© 2003 Prentice-Hall, Inc. Chap 18-37
Mean Chart Control Limits Solution
1
1
2
2
5.32 6.59 6.795.813
7
3.85 4.27 4.223.894
7
5.813 0.577 3.894 8.060
5.813 0.577 3.894 3.566
k
i
i
k
ii
X
X
XX
k
RR
k
UCL X A R
LCL X A R
From Table 17.2 Page 683(n = 5)
© 2003 Prentice-Hall, Inc. Chap 18-38
Mean Chart Control Chart Solution
UCL
LCL
02468
1 2 3 4 5 6 7
Minutes
Day
X__
© 2003 Prentice-Hall, Inc. Chap 18-39
R Chart and Mean Chartin PHStat
PHStat | Control Charts | R & Xbar Charts …
Excel Spreadsheet for the Hotel Room Example
Microsoft Excel Worksheet
© 2003 Prentice-Hall, Inc. Chap 18-40
Examples
17.8 Monitor the performance of Refrigerators. Calculate Upper and Lower Control Limits for Average and Range.
Overall average Temperature =46 o Fahrenheit Average Range is 2 o Fahrenheit Samples of 6 have been taken to get this data. (Samples
Size, n= 6)
17.10 Monitor the Weight of Cereal in Boxes. Calculate Upper and Lower Control Limits for Average and Range.
Overall average Weight = 17 grams Average Range is 0.5 grams Samples of 8 Boxes have been taken to get this data.
(Samples Size, n= 8)
© 2003 Prentice-Hall, Inc. Chap 18-41
Do Example 17.5
Time Sample Taken Box1 Box2 Box3 Box49 9.89 10.4 9.9 10.3
10 10.1 10.2 9.9 9.811 9.9 10.5 10.3 10.112 9.7 9.8 10.3 10.21 9.7 10.1 9.9 9.9
Total
Raw Data
Find UCL and LCL for Mean Chart and Range Chart.
You need to Know: -
1. the Mean of the Sample Averages (Symbol__)
2. the Mean of the Range (Symbol ___)
3. the Sample Size (Symbol n)
© 2003 Prentice-Hall, Inc. Chap 18-42
Other Examples
Do 17-12 for Homework
© 2003 Prentice-Hall, Inc. Chap 18-43
p Chart Control Chart for Proportions
Is an attribute chartattribute chart Shows Proportion of Nonconforming
(Success Success ) Items E.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
© 2003 Prentice-Hall, Inc. Chap 18-44
p Chart Control Limits
(1 )max 0, 3p
p pLCL p
n
(1 )3p
p pUCL p
n
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
© 2003 Prentice-Hall, Inc. Chap 18-45
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?
© 2003 Prentice-Hall, Inc. Chap 18-46
p Chart Hotel Data
# NotDay # Rooms Ready Proportion
1 200 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
© 2003 Prentice-Hall, Inc. Chap 18-47
1
1
121.0864
1400
k
ii
k
ii
Xp
n
p Chart Control Limits Solution
16 + 7 +...+ 16
1 1400200
7
k
ii
nn
k
1 .0864 1 .08643 .0864 3
200
.0864 .0596 or .0268,.1460
p pp
n
© 2003 Prentice-Hall, Inc. Chap 18-48
Mean
p Chart Control Chart Solution
UCL
LCL
0.00
0.05
0.10
0.15
1 2 3 4 5 6 7
P
Day
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.
p
p
© 2003 Prentice-Hall, Inc. Chap 18-49
p Chart in PHStat
PHStat | Control Charts | p Chart …
Excel Spreadsheet for the Hotel Room Example
Microsoft Excel Worksheet
© 2003 Prentice-Hall, Inc. Chap 18-50
Example
Day Number of Packages Late Packages1 136 42 153 63 127 24 157 75 144 56 122 57 154 68 132 39 160 8
10 142 711 157 612 150 913 142 814 137 1015 147 816 132 717 136 618 137 719 153 1120 141 7
The Delivery company wants to monitor its delivery service.
Draw a p-chart.
Does the process give an out of Control Signal? Control Chart Patterns:
How to tell if
the Process is
Out of Control
© 2003 Prentice-Hall, Inc. Chap 18-51
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%.
© 2003 Prentice-Hall, Inc. Chap 18-52
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
113.1883
50(12)p
(1 ) .1883(1 .1883)3 .1883 3
50 .1883 .1659
p pp
n
_
.1883 .1659 .0224
.1883 +.1659 .3542
LCL
UCL
© 2003 Prentice-Hall, Inc. Chap 18-53
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
_
© 2003 Prentice-Hall, Inc. Chap 18-54
Morals of the Example
Variation is an inherent part of any process. The system is primarily responsible for worker performance. Only management can change the system. Some workers will always be above average, and some will be below.
© 2003 Prentice-Hall, Inc. Chap 18-55
The c Chart
Control Chart for Number of Nonconformities (Occurrences) in a Unit (an Area of Opportunity) Is an attribute chartattribute 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
© 2003 Prentice-Hall, Inc. Chap 18-56
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
© 2003 Prentice-Hall, Inc. Chap 18-57
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?
© 2003 Prentice-Hall, Inc. Chap 18-58
c Chart: Hotel Data
# NotDay # Rooms Ready
1 200 162 200 73 200 214 200 175 200 256 200 197 200 16
© 2003 Prentice-Hall, Inc. Chap 18-59
c Chart: Control Limits Solution
1 16 7 19 1617.286
7
3 17.286 3 17.285 4.813
3 29.759
k
ii
c
c
cc
k
LCL c c
UCL c c
© 2003 Prentice-Hall, Inc. Chap 18-60
c Chart: Control Chart Solution
UCL
LCL0
10
20
30
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
© 2003 Prentice-Hall, Inc. Chap 18-61
Example 17.8
Number of small paint errors on each Ornaments.
1. Draw a c-chart.2. Does the process give an out of Control
Signal?
Ornament Number 1 2 3 4 5 6 7 8 9 10Number of Defects 0 2 1 0 0 3 2 0 4 1Ornament Number 11 12 13 14 15 16 17 18 19 20Number of Defects 2 0 0 1 2 1 0 0 0 1
© 2003 Prentice-Hall, Inc. Chap 18-62
Example 17.8 (cont)
The same exercise is repeated one week later. Number of small paint errors on each Ornaments are recorded as follows.
1. Draw a c-chart.2. Does the process give an out of Control
Signal? Control Chart Patterns:
How to tell if
the Process is
Out of Control
Ornament Number 1 2 3 4 5 6 7 8 9 10Number of Defects 0 2 1 0 1 2 3 4 0 3Ornament Number 11 12 13 14 15 16 17 18 19 20Number of Defects 2 0 0 1 2 1 0 0 0 1
© 2003 Prentice-Hall, Inc. Chap 18-63
Chapter Summary
Described Total Quality Management (TQM)
Addressed the Theory of Management Deming’s 14 Points
Described the Six Sigma® Management Approach
Discussed the Theory of Control Charts Common-cause variation versus special-
cause variation
© 2003 Prentice-Hall, Inc. Chap 18-64
Chapter Summary
Computed Control Charts for the Mean and the Range
Computed Control Charts for the Proportion of Nonconforming Items
Described Process Variability Described c Chart
(continued)