Transcript The Great White Bead Company

The Great Blue Bead
Company
l
l
l ll ll
Quality Is Our Priority
Based on a term project by Elizabeth A. Hoffman
The Great Blue Bead Company
•
•
•
•
•
Forman: Mr. John Mainieri
6 willing workers
A recorder
2 inspectors
1 chief inspector
Quality Is Our Priority
The Great Blue Bead Company
Production Process
• Grasp the paddle and mix the raw materials.
• Insert the paddle into the bead mixture.
• Raise the paddle at a 20 degree angle so that as
many depressions as possible will hold a bead.
Gently angel to one side so excess production
beads fall off. We want to produce 21 beads per
shift (worker).
• Inspectors count the beads independently and
record the counts. Count both defectives and total
beads produced.
The Great Blue Bead Company
• The chief inspector checks the counts and
announces the results, which are written
down by the recorder.
• The chief inspector dismisses the worker.
• When all six willing workers have produced
the days quota, the foreman evaluates the
results.
ZERO DEFECTS
Name
Ihab
Jesse
Matthew
Natalie
Sahar
Cameron
Round 1
# Reds
p
3
0.143
6
0.286
3
0.143
7
0.333
6
0.286
2
0.095
Statistics
p bar =
Round 2
Cumuilative 2 Rounds
# Reds
p
# Reds
p
2
0.095
5
0.119
2
0.095
8
0.190
2
0.095
5
0.119
2
0.095
9
0.214
5
0.238
11
0.262
8
0.381
10
0.238
0.214
0.167
Round 3
Cumuilative 3 Rounds
# Reds
p
# Reds
p
4
0.190
9
0.143
5
0.238
13
0.206
6
0.286
11
0.175
5
0.238
14
0.222
4
0.190
15
0.238
4
0.190
14
0.222
0.222
0.201
0.190
Round 4
Cumuilative 4 Rounds
# Reds
p
# Reds
p
5
0.238
14
0.167
4
0.190
17
0.202
4
0.190
15
0.179
3
0.143
17
0.202
6
0.286
21
0.250
4
0.190
18
0.214
0.206
0.202
Name
Ihab
Jesse
Matthew
Natalie
Sahar
Cameron
Round 1
# Reds
p
3
0.143
6
0.286
3
0.143
7
0.333
6
0.286
2
0.095
Statistics
p bar =
Round 2
Cumuilative 2 Rounds
# Reds
p
# Reds
p
2
0.095
5
0.119
2
0.095
8
0.190
2
0.095
5
0.119
2
0.095
9
0.214
5
0.238
11
0.262
8
0.381
10
0.238
0.214
0.167
Round 3
Cumuilative 3 Rounds
# Reds
p
# Reds
p
4
0.190
9
0.143
5
0.238
13
0.206
6
0.286
11
0.175
5
0.238
14
0.222
4
0.190
15
0.238
4
0.190
14
0.222
0.222
0.201
0.190
Round 4
Cumuilative 4 Rounds
# Reds
p
# Reds
p
5
0.238
14
0.167
4
0.190
17
0.202
4
0.190
15
0.179
3
0.143
17
0.202
6
0.286
21
0.250
4
0.190
18
0.214
0.206
0.202
Run Chart of Fraction of Red Beads
Produced
UCL = .47
DAY 1
Fraction of Red
Beads
0.400
DAY 2
DAY 3
DAY 4
0.300
Mean =.21
0.200
0.100
LCL = 0.00
0.000
0
10
20
Trials
30
Red Bead Experiment- Lessons
for Managers
• Variation exists in systems and, if stable,
can be predicted.
– Although the exact number of red beads in any
particular paddle is not predictable, we can
describe statistically what we expect from the
system.
Adapted from the Management and Control of QUALITY, 4th ed. by Evans and Lindsay, SouthWestern
Red Bead Experiment- Lessons
for Managers
• All the variation in the production of red
beads, and the variation from day to day of
any willing worker, came entirely from the
process itself.
– Neither motivation nor threats had any
influence.
– Many managers believe that all variation is
controllable and place blame on those who
cannot do anything about it.
Adapted from the Management and Control of QUALITY, 4th ed. by Evans and Lindsay, SouthWestern
Red Bead Experiment- Lessons
for Managers
• Numerical goals are often meaningless.
– Merit pay and probation actually reward or
penalize the system and lead to worker
frustration.
– There is no basis for assuming that the best
willing workers of the past will be the best in
the future.
Adapted from the Management and Control of QUALITY, 4th ed. by Evans and Lindsay, SouthWestern
Red Bead Experiment- Lessons
for Managers
• Management is responsible for the system.
The experiment shows bad management.
– Procedures are rigid.
– Willing workers have no say in improving the
process.
– Management is responsible for the incoming
material, but did not work with the supplier to
improve the inputs to the system.
Adapted from the Management and Control of QUALITY, 4th ed. by Evans and Lindsay, SouthWestern
Red Bead Experiment- Lessons
for Managers
– Management designed the system and decided
to rely on inspection to control the process.
Three inspectors are probably as costly as the
six workers and add practically no value to the
input.
Adapted from the Management and Control of QUALITY, 4th ed. by Evans and Lindsay, SouthWestern
Chapter 12
Statistical Applications in Quality and
Productivity Management
Chapter Objectives
• Introduction to the History of Quality
• Deming’s 14 Points of Management
• Common Cause Variation and Special Cause
Variation
• Control Charts for the Proportion of
Nonconforming Items
• Control Charts for the Range and Mean
Chapter 12
Statistical Quality Management
Chapter Homework
• Read sections 12.1 through 12.4 and 12.6 (skip
12.5)
• Do quick results 12.4e and 12.6e
• Do problems 12.5 and 12.17 – use excel for the
charts, but double check the control limits by
hand
Quality Management
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Focus on process improvement
System, not individual
Teamwork
Customer satisfaction
Organizational transformation
No fear
Requires investment, saves money
Dr. W. Edwards Deming
• B.S. in Electrical Engineering
University of Wyoming, 1921
• M.S. Mathematics and
Mathematical Physics
University of Colorado, 1925
• Ph.D. from Yale University,
1928
http://www.deming.org/
Control Charts
• Sequential collection of variable data
• Control Chart to monitor variation
– Focus on time
– Study nature of variability
• Causes of Variation
– Special or Assignable
– Chance or Common
Control Limits
• Used to evaluate variation for:
– Variation outside established control limits
– Patterns over time
• Process Average + 3 standard deviations
– Upper Control Limit (UCL)
= process average + 3 standard deviations
– Lower Control Limit (LCL)
= process average – 3 standard deviations
Control Chart Patterns
Special or Assignable Cause Variation
This is a “signal.”
Train Arrival Tim e
0.3
Outside Control
Limit
Proportion Late
0.25
0.2
UCL
0.15
pBar
0.1
LCL
0.05
0
0
2
4
6
8
10
Days
12
14
16
18
20
Control Chart Patterns
Pattern over Time
Unacceptable Cans of Soda
Proportion Defective
0.02
0.018
UCL
0.016
0.014
pBar
0.012
Increasing Trend
0.01
LCL
0.008
0.006
0.004
The magic number is 8!
0.002
0
0
5
10
15
Trial or sample
20
25
Control Chart Patterns
Common Cause Variation
“Static” vs. a “Signal”
Within Control Limits
The p Chart
• Attribute Control Chart
– For Proportion of Non-Conforming Items
• Control Limits

p 1 p
p3
n

The p Chart
Obtaining Upper and Lower Control Limits

p 1 p
UCL  p  3
n

p 1 p
LCL  p  3
n


p is the average proportion
n is the average subgroup size
Example: 12.3 Pg. 740
n  235
2.2894
p
 .1145
20
.11451  .1145
UCL  .1145 3
 .1768
235
.11451  .1145
LCL  .1145 3
 .0522
235
Example: 12.3 cont.
Summary
The p Chart
• Control Chart for the Proportion
• Used to determine whether special or common
• Control Limits:

p 1 p
p3
n

p is the average proportion
n is the average subgroup size
Control Charts for the
Range and Mean
• Used when characteristic is measured
numerically – called Variables Control
Charts
• More sensitive than p chart
• Two charts
– Variation in a process (range)
– Process Average (mean)
• Interpret variation chart first (range)
The R Chart
•Must be examined first
Out of control variation could cause
misinterpretation of the mean chart
Control Limits for the Range
d3
R  3R
d2
From table E.9, page E-18
d3 represents the relationship
between the standard
deviation and the standard
error
d2 represents the relationship
between the standard
deviation and range
Control Limits for the R Chart
d3
UCL  R  3R
d2
d3
LCL  R  3R
d2
Sum of the Ranges
R
Number of Subgroups
Control Limits for the R Chart
The “Simple” Way
UCL  D4 R
LCL  D3 R
Control Limits for the R Chart
The “Simple” Way
d3
UCL  R  3R
d2

 d 3 
 R1  3  
 d 2 

 d3 
D 4  1  3 
 d2 
d3
LCL  R  3R
d2

 d 3 
 R1  3  
 d 2 

 d3 
D3  1  3 
 d2 
Control Limits for the R Chart
The “Simple” Way
UCL  D4 R
LCL  D3 R
The X Chart
•If the Range is in Control
•Measures the variability of the mean
Subgroups of size n
Control Limits for the Mean Chart X is the average of the
subgroup averages
X 3
R
d2 n
OR
X  A2 R
Example 12.15 Page 756-757
Control Limits for the Range
sum of the ranges
8147
R

 271.57
number of subgroups
30
UCL  D4 R  2.114271.57  574 .09
LCL  D3 R  0271.57  0

d3
 .864  
LCL  R  3R  271.57  3 271.57
   31.06
d2
 2.326  

Example 12.15 cont.
The R Chart
Units Handled
700
600
UCL
500
400
300
RBar
200
100
0
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
LCL
31
32
Example 12.15 cont.
Control Limits for the Mean
Sum of theMeans
5960
X

 198.67
Number of Subgroups
30
.577
271(.271
57 .57)  355.37
UCL  X  A2 RR  198
.
67

0

 198 .67  3
UCL  X  3
d2 n

355
.
31
 
 2.326 5 


LCL  X  A2 R  198.67  0.577(271.57)  41.97
 271 .57 
R
  41.93
 198 .67  3
LCL  X  3



2
.
326
5
2 n Equations

Use dThese
Example 12.15 cont.
The Mean Chart
Units Handled
400
UCL
350
300
250
200
XBar
150
100
50
LCL
0
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
Summary
Control Charts for the Range
and Mean
• Two charts
– Variation in a process
– Process Average
• Interpret variation chart first (range)
• Control Limits for the Range:
UCL  D4 R LCL  D3 R
Sum of the Ranges
R
Number of Subgroups
Summary
Control Charts for the Range
and Mean
• Interpret mean chart second
• Control Limits for the Range:
X 3
R
d2 n
X  A2 R
Subgroups of size n
X is the average of the
subgroup averages

p 1 p
p3
n





p 1 p
UCL  p  3
n
p 1 p
LCL  p  3
n
d3
R  3R
d2
d3
UCL  R  3R
d2
OR
d3
LCL  R  3R
d2
OR
UCL  D4 R
LCL  D3 R
X 3
R
d2 n
UCL  X  3
LCL  X  3
R
d2 n
R
d2 n
or X  A2 R
or X  A2 R