Upload
melinda-burns
View
214
Download
2
Tags:
Embed Size (px)
Citation preview
© 2002 Prentice-Hall, Inc. Chap 15-1
Statistics for Managers Using Microsoft Excel
3rd Edition
Chapter 15Statistical Applications in Quality and Productivity
Management
© 2002 Prentice-Hall, Inc. Chap 15-2
Chapter Topics
Total quality management (TQM) Theory of process management
(Deming’s fourteen points) The theory of control charts
Common cause variation vs. Special cause variation
Control charts for the proportion of nonconforming items
© 2002 Prentice-Hall, Inc. Chap 15-3
Chapter Topics
Process variability The c chart Control charts for the mean and the
range Process capability
(continued)
© 2002 Prentice-Hall, Inc. Chap 15-4
Themes of Quality Management
1. Primary focus is on process improvement2. Most variations in process are due to
systems3. Teamwork is integral to quality
management4. Customer satisfaction is a primary goal5. Organization transformation is necessary6. It is important to remove fear7. Higher quality costs less
© 2002 Prentice-Hall, Inc. Chap 15-5
Deming’s 14 Points: Point 1
Plan
DoStudy
Act
Point 1. Create Constancy of Purpose
The Shewhart-Deming CycleFocuses on Constant Improvement
© 2002 Prentice-Hall, Inc. Chap 15-6
Deming’s 14 Points: Points 2 and 3
Point 2. Adopt a New Philosophy
Better to be proactive and change before crisis occurs.
Point 3. Cease Dependence on mass inspection achieve quality.
Any inspection the purpose of which is to improve quality is too late.
© 2002 Prentice-Hall, Inc. Chap 15-7
Point 4. End the practice of awarding business on the basis of price tag alone
Develop a 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
© 2002 Prentice-Hall, Inc. Chap 15-8
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.
© 2002 Prentice-Hall, Inc. Chap 15-9
8. Drive out fear
9. Break down barriers between staff areas
10. Eliminate slogans
11. Eliminate numerical quotas for workforce and numerical goals for management
12. Remove barriers to pride of workmanship
Deming’s 14 Points: Points 8 to 12
© 2002 Prentice-Hall, Inc. Chap 15-10
Point 13. Encourage education and self improvement for everyone.
Improved knowledge of people will improve assets of organization.
Point 14. Take action to accomplish
transformation.
Continually strive toward improvement.
Deming’s 14 Points: Points 13 and 14
© 2002 Prentice-Hall, Inc. Chap 15-11
Control Charts
Monitors variation in data Exhibits trend -- make correction before
process is out of control A process -- A repeatable series of steps
leading to a specific goal
© 2002 Prentice-Hall, Inc. Chap 15-12
Control Charts
Show when changes in data are due to: Special or assignable causes
Fluctuations not inherent to a process Represents problems to be corrected Data outside control limits or trend
Chance or common causes Inherent random variations Consist of numerous small causes of random
variability
(continued)
© 2002 Prentice-Hall, Inc. Chap 15-13
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
© 2002 Prentice-Hall, Inc. Chap 15-14
Control Limits
UCL = Process Average + 3 Standard Deviations
LCL = Process Average - 3 Standard Deviations
Process Average
UCL
LCL
X
+ 3
- 3
TIME
© 2002 Prentice-Hall, Inc. Chap 15-15
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
© 2002 Prentice-Hall, Inc. Chap 15-16
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
© 2002 Prentice-Hall, Inc. Chap 15-17
When to Take Corrective Action
Take corrective action when you observe 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)
© 2002 Prentice-Hall, Inc. Chap 15-18
Out-of-control Processes
When 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 the quality, assignable
causes of variation must be removed If increases quality, assignable causes must
be incorporated into the process design
© 2002 Prentice-Hall, Inc. Chap 15-19
In-control Process
When the control chart does not indicate any out-of-control condition Contains only common causes of variation Sometimes said to be in a state of statistical
control If the common causes of variation is small,
then control chart can be used to monitor the process
If the common causes of variation is too large, you need to alter the process
© 2002 Prentice-Hall, Inc. Chap 15-20
p Chart Control chart for proportions
Is an attribute chart Shows proportion of nonconforming
(success) items e.g.: Count the number defective chairs and
divide by total chairs inspected Chair is either defective or not defective
Used with equal or unequal sample sizes over time Unequal sizes should not differ by more
than ±25% from average sample size
© 2002 Prentice-Hall, Inc. Chap 15-21
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
iik
ii
Xp
n
Average Proportion of Nonconforming Items
# Defective Items in Sample i
Size of Sample i
# of Samples
© 2002 Prentice-Hall, Inc. Chap 15-22
p Chart Example
You’re manager of a 500-room hotel. You want to achieve the highest level of service. For seven days, you collect data on the readiness of 200 rooms. Is the process in control?
You’re manager of a 500-room hotel. You want to achieve the highest level of service. For seven days, you collect data on the readiness of 200 rooms. Is the process in control?
© 2002 Prentice-Hall, Inc. Chap 15-23
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
© 2002 Prentice-Hall, Inc. Chap 15-24
1
1
121.0864
1400
k
iik
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
© 2002 Prentice-Hall, Inc. Chap 15-25
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
© 2002 Prentice-Hall, Inc. Chap 15-26
p Chart in PHStat
PHStat | control charts | p chart …
Excel spreadsheet for the hotel room example
Microsoft Excel Worksheet
© 2002 Prentice-Hall, Inc. Chap 15-27
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) spent three days to collect beads, at 50 beads per day. The expected number of red bead to be collected per day per worker is 10 or 20%.
© 2002 Prentice-Hall, Inc. Chap 15-28
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
© 2002 Prentice-Hall, Inc. Chap 15-29
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
_
© 2002 Prentice-Hall, Inc. Chap 15-30
Morals of the Example
1. Variation is an inherent part of any process.
2. The system is primarily responsible for worker performance.
3. Only management can change the system.
4. Some workers will always be above average, and some will be below.
© 2002 Prentice-Hall, Inc. Chap 15-31
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 number of defective chairs
manufactured per day Assume that the size of each subgroup
unit remains constant
© 2002 Prentice-Hall, Inc. Chap 15-32
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
© 2002 Prentice-Hall, Inc. Chap 15-33
c Chart: Example
You’re manager of a 500-room hotel. You want to achieve the highest level of service. For seven days, you collect data on the readiness of 200 rooms. Is the process in control?
You’re manager of a 500-room hotel. You want to achieve the highest level of service. For seven days, you collect data on the readiness of 200 rooms. Is the process in control?
© 2002 Prentice-Hall, Inc. Chap 15-34
c Chart: Hotel Data
# NotDay # Rooms Ready
1 200 162 200 73 200 214 200 175 200 256 200 197 200 16
© 2002 Prentice-Hall, Inc. Chap 15-35
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
© 2002 Prentice-Hall, Inc. Chap 15-36
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
© 2002 Prentice-Hall, Inc. Chap 15-37
Variable Control Charts: R Chart
Monitors variability in process Characteristic of interest is measured on
numerical scale Is a variables control chart
Shows sample range over time Difference between smallest and largest
values in inspection sample e.g.: Amount of time required for luggage
to be delivered to hotel room
© 2002 Prentice-Hall, Inc. Chap 15-38
R Chart Control Limits
Sample Range at Time i or subgroup i
# Samples
From Table4RUCL D R
3RLCL D R
1
k
ii
RR
k
© 2002 Prentice-Hall, Inc. Chap 15-39
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?
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?
© 2002 Prentice-Hall, Inc. Chap 15-40
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
© 2002 Prentice-Hall, Inc. Chap 15-41
R Chart Control Limits Solution
From Table E.11 (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
© 2002 Prentice-Hall, Inc. Chap 15-42
R Chart Control Chart Solution
UCL
02468
1 2 3 4 5 6 7
Minutes
Day
LCL
R_
© 2002 Prentice-Hall, Inc. Chap 15-43
Variables Control Charts: Mean Chart (The Chart)
Shows sample mean 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
© 2002 Prentice-Hall, Inc. Chap 15-44
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
© 2002 Prentice-Hall, Inc. Chap 15-45
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 seven days, you collect data on five deliveries per day. Is the process in control?
You’re manager of a 500-room hotel. You want to analyze the time it takes to deliver luggage to the room. For seven days, you collect data on five deliveries per day. Is the process in control?
© 2002 Prentice-Hall, Inc. Chap 15-46
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
© 2002 Prentice-Hall, Inc. Chap 15-47
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 E.9 (n = 5)
© 2002 Prentice-Hall, Inc. Chap 15-48
Mean Chart Control Chart Solution
UCL
LCL
02468
1 2 3 4 5 6 7
Minutes
Day
X__
© 2002 Prentice-Hall, Inc. Chap 15-49
R Chart and Mean Chart in PHStat
PHStat | control charts | R & Xbar charts …
Excel spreadsheet for the hotel room example
Microsoft Excel Worksheet
© 2002 Prentice-Hall, Inc. Chap 15-50
Process Capability Process capability is the ability of a
process to consistently meet specified customer-driven requirement
Specification limits are set by management in response to customers’ expectations
The upper specification limit (USL) is the largest value that can be obtained and still conform to customers’ expectations
The lower specification limit (LSL) is the smallest value that is still conforming
© 2002 Prentice-Hall, Inc. Chap 15-51
Estimating Process Capability
Must first have an in-control process 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
X
2/R d
© 2002 Prentice-Hall, Inc. Chap 15-52
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 XZ
R d R d
© 2002 Prentice-Hall, Inc. Chap 15-53
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 XZ
R d
© 2002 Prentice-Hall, Inc. Chap 15-54
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 XZ
R d
© 2002 Prentice-Hall, Inc. Chap 15-55
You’re manager of a 500-room hotel. You have instituted a policy that 99% of all luggage deliveries must be completed within ten minutes or less. For seven days, you collect data on five deliveries per day. Is the process capable?
You’re manager of a 500-room hotel. You have instituted a policy that 99% of all luggage deliveries must be completed within ten minutes or less. For seven days, you collect data on five deliveries per day. Is the process capable?
Process CapabilityExample
© 2002 Prentice-Hall, Inc. Chap 15-56
Process Capability: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
© 2002 Prentice-Hall, Inc. Chap 15-57
Process Capability:Hotel Example Solution
5.813X 3.894R 2and 2.326d
P(A delivery is made within specification)
= P( 10)
10 5.813= P
3.894 / 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 ten minutes or less specification. The process is capable of meeting the 99% goal.
© 2002 Prentice-Hall, Inc. Chap 15-58
Capability Indices
Aggregate measures of a process’s 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 a process has the potential of having more than 99.73% of outcomes within specifications
2
specification spread
process spread6 /p
USL LSLC
R d
© 2002 Prentice-Hall, Inc. Chap 15-59
Capability Indices
Measures of actual process performance For one-sided specification limits
CPL (CPU) >1 implies that the process mean is more than 3 standard deviation away from the lower (upper) specification limit
(continued)
23 /
X LSLCPL
R d
23 /
USL XCPU
R d
© 2002 Prentice-Hall, Inc. Chap 15-60
Capability Indices
For two-sided specification limits Cpk = 1 indicates that the process average is 3
standard deviation away from the closest specification limit.
Larger Cpk indicates larger capability of meeting the requirements
(continued)
min ,pkC CPL CPU
© 2002 Prentice-Hall, Inc. Chap 15-61
You’re manager of a 500-room hotel. You have instituted a policy that all luggage deliveries must be completed within ten minutes or less. For seven days, you collect data on five deliveries per day. Compute an appropriate capability index for the delivery process.
You’re manager of a 500-room hotel. You have instituted a policy that all luggage deliveries must be completed within ten minutes or less. For seven days, you collect data on five deliveries per day. Compute an appropriate capability index for the delivery process.
Process CapabilityExample
© 2002 Prentice-Hall, Inc. Chap 15-62
Process Capability: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
© 2002 Prentice-Hall, Inc. Chap 15-63
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 deviation above the mean.
2
10 5.8130.833672
3 3.894 / 2.3263 /
USL XCPU
R d
© 2002 Prentice-Hall, Inc. Chap 15-64
Chapter Summary
Described total quality management (TQM)
Addressed the theory of process management Deming’s fourteen points
Discussed the theory of control charts Common cause variation vs. special cause
variation
© 2002 Prentice-Hall, Inc. Chap 15-65
Chapter Summary
Computed control charts for the proportion of nonconforming items
Described process variability Described c chart Computed control charts for the
mean and the range Discussed process capability
(continued)