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![Page 1: Chapter Topics Total Quality Management (TQM) Theory of Process Management (Deming’s Fourteen points) The Theory of Control Charts Common Cause Variation.](https://reader030.fdocuments.us/reader030/viewer/2022033100/56649c9e5503460f9495df15/html5/thumbnails/1.jpg)
Chapter Topics
• Total Quality Management (TQM)
• Theory of Process Management (Deming’s Fourteen points)
• The Theory of Control ChartsCommon Cause Variation Vs Special Cause Variation
• Control Charts for the Proportion of Nonconforming Items
• Process Variability
• Control charts for the Mean and the Range
![Page 2: Chapter Topics Total Quality Management (TQM) Theory of Process Management (Deming’s Fourteen points) The Theory of Control Charts Common Cause Variation.](https://reader030.fdocuments.us/reader030/viewer/2022033100/56649c9e5503460f9495df15/html5/thumbnails/2.jpg)
Control Charts• Monitors Variation in Data
– Exhibits Trend - Make Correction Before Process is Out of control
• 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
![Page 3: Chapter Topics Total Quality Management (TQM) Theory of Process Management (Deming’s Fourteen points) The Theory of Control Charts Common Cause Variation.](https://reader030.fdocuments.us/reader030/viewer/2022033100/56649c9e5503460f9495df15/html5/thumbnails/3.jpg)
0
20
40
60
1 3 5 7 9 11
X
Time
0
20
40
60
1 3 5 7 9 11
X
Time
• Graph of sample data plotted over time
Assignable Cause Variation
Random Variation
Process Average
Mean
Process Control Chart
UCL
LCL
![Page 4: Chapter Topics Total Quality Management (TQM) Theory of Process Management (Deming’s Fourteen points) The Theory of Control Charts Common Cause Variation.](https://reader030.fdocuments.us/reader030/viewer/2022033100/56649c9e5503460f9495df15/html5/thumbnails/4.jpg)
Control Limits
• UCL = Process Average + 3 Standard Deviations
• LCL = Process Average - 3 Standard Deviations
Process Average
UCL
LCL
X
+ 3
- 3
TIME
![Page 5: Chapter Topics Total Quality Management (TQM) Theory of Process Management (Deming’s Fourteen points) The Theory of Control Charts Common Cause Variation.](https://reader030.fdocuments.us/reader030/viewer/2022033100/56649c9e5503460f9495df15/html5/thumbnails/5.jpg)
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
![Page 6: Chapter Topics Total Quality Management (TQM) Theory of Process Management (Deming’s Fourteen points) The Theory of Control Charts Common Cause Variation.](https://reader030.fdocuments.us/reader030/viewer/2022033100/56649c9e5503460f9495df15/html5/thumbnails/6.jpg)
Comparing Control Chart Patterns
X XX
Common Cause Variation: No Points
Outside Control Limit
Special Cause Variation: 2 Points
Outside Control Limit
Downward Pattern: No Points Outside
Control Limit
![Page 7: Chapter Topics Total Quality Management (TQM) Theory of Process Management (Deming’s Fourteen points) The Theory of Control Charts Common Cause Variation.](https://reader030.fdocuments.us/reader030/viewer/2022033100/56649c9e5503460f9495df15/html5/thumbnails/7.jpg)
When to Take Corrective Action
• 1. Eight Consecutive Points Above the Center Line (or Eight Below)
• 2. Eight Consecutive Points that are Increasing (Decreasing)
Corrective Action should be Taken When Observing Points Outside the Control Limits or When a Trend Has Been Detected:
![Page 8: Chapter Topics Total Quality Management (TQM) Theory of Process Management (Deming’s Fourteen points) The Theory of Control Charts Common Cause Variation.](https://reader030.fdocuments.us/reader030/viewer/2022033100/56649c9e5503460f9495df15/html5/thumbnails/8.jpg)
p Chart• Control Chart for Proportions
• Shows Proportion of Nonconforming Items– e.g., Count # defective chairs & 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
![Page 9: Chapter Topics Total Quality Management (TQM) Theory of Process Management (Deming’s Fourteen points) The Theory of Control Charts Common Cause Variation.](https://reader030.fdocuments.us/reader030/viewer/2022033100/56649c9e5503460f9495df15/html5/thumbnails/9.jpg)
p Chart Control Limits
n
)p(pp
13
n
)p(pp
13
k
nn
k
ii
1
Average Group Size
k
ii
k
ii
n
X
1
1
Average Proportion of Nonconforming Items
# Defective Items in Sample i
Size of Sample i
# of Samples
LCLp = UCLp =
p_
![Page 10: Chapter Topics Total Quality Management (TQM) Theory of Process Management (Deming’s Fourteen points) The Theory of Control Charts Common Cause Variation.](https://reader030.fdocuments.us/reader030/viewer/2022033100/56649c9e5503460f9495df15/html5/thumbnails/10.jpg)
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?
![Page 11: Chapter Topics Total Quality Management (TQM) Theory of Process Management (Deming’s Fourteen points) The Theory of Control Charts Common Cause Variation.](https://reader030.fdocuments.us/reader030/viewer/2022033100/56649c9e5503460f9495df15/html5/thumbnails/11.jpg)
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
![Page 12: Chapter Topics Total Quality Management (TQM) Theory of Process Management (Deming’s Fourteen points) The Theory of Control Charts Common Cause Variation.](https://reader030.fdocuments.us/reader030/viewer/2022033100/56649c9e5503460f9495df15/html5/thumbnails/12.jpg)
n
n
kp
X
n
p
ii
k
ii
k
ii
k
1 1
1
1400
7200
121
14000864
3 0864 30864 1 0864
200
0864 0596 .1460
.
.. .
. . or , .0268
p Chart Control Limits Solution
16 + 7 +...+ 16
( )
( )
n
)p(p 1_
![Page 13: Chapter Topics Total Quality Management (TQM) Theory of Process Management (Deming’s Fourteen points) The Theory of Control Charts Common Cause Variation.](https://reader030.fdocuments.us/reader030/viewer/2022033100/56649c9e5503460f9495df15/html5/thumbnails/13.jpg)
p Chart Control Chart Solution
UCL
LCL
0.00
0.05
0.10
0.15
1 2 3 4 5 6 7
P
Day
Mean p_
![Page 14: Chapter Topics Total Quality Management (TQM) Theory of Process Management (Deming’s Fourteen points) The Theory of Control Charts Common Cause Variation.](https://reader030.fdocuments.us/reader030/viewer/2022033100/56649c9e5503460f9495df15/html5/thumbnails/14.jpg)
Variable Control Charts: R Chart
•Monitors Variability in Process
•Characteristic of interest is measured on interval or ratio scale.
•Shows Sample Range Over Time
•Difference between smallest & largest values ininspection sample
•e.g., Amount of time required for luggage to be delivered to hotel room
![Page 15: Chapter Topics Total Quality Management (TQM) Theory of Process Management (Deming’s Fourteen points) The Theory of Control Charts Common Cause Variation.](https://reader030.fdocuments.us/reader030/viewer/2022033100/56649c9e5503460f9495df15/html5/thumbnails/15.jpg)
UCL D R
LCL D R
R
R
k
R
R
ii
k
4
3
1
R Chart Control Limits
Sample Range at Time i
# Samples
From Table
![Page 16: Chapter Topics Total Quality Management (TQM) Theory of Process Management (Deming’s Fourteen points) The Theory of Control Charts Common Cause Variation.](https://reader030.fdocuments.us/reader030/viewer/2022033100/56649c9e5503460f9495df15/html5/thumbnails/16.jpg)
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?
![Page 17: Chapter Topics Total Quality Management (TQM) Theory of Process Management (Deming’s Fourteen points) The Theory of Control Charts Common Cause Variation.](https://reader030.fdocuments.us/reader030/viewer/2022033100/56649c9e5503460f9495df15/html5/thumbnails/17.jpg)
R Chart & 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
![Page 18: Chapter Topics Total Quality Management (TQM) Theory of Process Management (Deming’s Fourteen points) The Theory of Control Charts Common Cause Variation.](https://reader030.fdocuments.us/reader030/viewer/2022033100/56649c9e5503460f9495df15/html5/thumbnails/18.jpg)
R
R
k
UCL D R
LCL D R
ii
k
R
R
1
4
3
3 85 4 27 4 22
73 894
2114 3 894 8 232
0 3 894 0
. . ..
. . .
.
R Chart Control Limits Solution
From Table E.9 (n = 5)
_
![Page 19: Chapter Topics Total Quality Management (TQM) Theory of Process Management (Deming’s Fourteen points) The Theory of Control Charts Common Cause Variation.](https://reader030.fdocuments.us/reader030/viewer/2022033100/56649c9e5503460f9495df15/html5/thumbnails/19.jpg)
R Chart Control Chart Solution
UCL
02468
1 2 3 4 5 6 7
Minutes
Day
LCL
R_
![Page 20: Chapter Topics Total Quality Management (TQM) Theory of Process Management (Deming’s Fourteen points) The Theory of Control Charts Common Cause Variation.](https://reader030.fdocuments.us/reader030/viewer/2022033100/56649c9e5503460f9495df15/html5/thumbnails/20.jpg)
Mean Chart (The X Chart)
• Shows Sample Means Over Time– Compute mean of inspection sample over time– e.g., Average luggage delivery time in hotel
• Monitors Process Average
![Page 21: Chapter Topics Total Quality Management (TQM) Theory of Process Management (Deming’s Fourteen points) The Theory of Control Charts Common Cause Variation.](https://reader030.fdocuments.us/reader030/viewer/2022033100/56649c9e5503460f9495df15/html5/thumbnails/21.jpg)
UCL X A R
LCL X A R
XX
kR
R
k
X
X
ii
k
ii
k
2
2
1 1and
Mean Chart
Sample Range at Time i
# Samples
Sample Mean at Time i
Computed From Table
_
__ _
_
_
__
__ _
_
![Page 22: Chapter Topics Total Quality Management (TQM) Theory of Process Management (Deming’s Fourteen points) The Theory of Control Charts Common Cause Variation.](https://reader030.fdocuments.us/reader030/viewer/2022033100/56649c9e5503460f9495df15/html5/thumbnails/22.jpg)
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?
![Page 23: Chapter Topics Total Quality Management (TQM) Theory of Process Management (Deming’s Fourteen points) The Theory of Control Charts Common Cause Variation.](https://reader030.fdocuments.us/reader030/viewer/2022033100/56649c9e5503460f9495df15/html5/thumbnails/23.jpg)
R Chart & 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
![Page 24: Chapter Topics Total Quality Management (TQM) Theory of Process Management (Deming’s Fourteen points) The Theory of Control Charts Common Cause Variation.](https://reader030.fdocuments.us/reader030/viewer/2022033100/56649c9e5503460f9495df15/html5/thumbnails/24.jpg)
X
X
R
X
R
R
X
k
R
k
UCL A
LCL A
ii
k
ii
k
X
X
1
1
2
2
5 32 6 59 6 79
75 813
3 85 4 27 4 22
73 894
5 813 0 577 3 894 8 060
5 813 0 577 3 894 3 566
. . ..
. . ..
. . . .
. . . .
Mean Chart Control Limits Solution
From Table E.9 (n = 5)
__
_
__ _
__ __
_
_
![Page 25: Chapter Topics Total Quality Management (TQM) Theory of Process Management (Deming’s Fourteen points) The Theory of Control Charts Common Cause Variation.](https://reader030.fdocuments.us/reader030/viewer/2022033100/56649c9e5503460f9495df15/html5/thumbnails/25.jpg)
Mean Chart Control Chart Solution
UCL
LCL
02468
1 2 3 4 5 6 7
Minutes
Day
X__
![Page 26: Chapter Topics Total Quality Management (TQM) Theory of Process Management (Deming’s Fourteen points) The Theory of Control Charts Common Cause Variation.](https://reader030.fdocuments.us/reader030/viewer/2022033100/56649c9e5503460f9495df15/html5/thumbnails/26.jpg)
Six sigmaSIGMA PPM
(best case)
PPM (worst case)
Misspellings Examples
1 sigma 317,400 697,700 170 words per page Non-competitive
2 sigma 45,600 308,733 25 words per page IRS Tax Advice (phone-in)
3 sigma 2,700 66,803 1.5 words per page Doctors prescription writing (9,000 ppm)
4 sigma 64 6,200 1 word per 30 pages (1 per chapter)
Industry average
5 sigma 0.6 233 1 word in a set of encyclopedias
Airline baggage handling (3,000 ppm)
6 sigma 0.002 3.4 1 in all of the books in a small library
World class