INSTRUCTOR PROBLEMS
Problem 9.80
What is the difference between quality control and quality assurance?
Problem 9.81
If a batch of parts is rejected for SPC, does that mean it does not meet the tolerances?
Problem 9.82
SPC control charts have upper and lower control limits that are three times the standard deviation from the
mean. Why?
Problem 9.83
If the SPC UCL and LCL were increased to six sigma would more parts be rejected? Explain.
Problem 9.84
Why does the actual production mean value differ from the specified dimension and tolerance?
Problem 9.85
Why would C
p
and C
pk
have different values?
Problem 9.86
The data in the table were measured over a two-week period for a 1.000″ shaft with a tolerance of ±0.010″.
(a) Draw accurate X– control charts.
(b) Determine C
p
and C
pk.
(c) What would the tolerance have to be if we required six sigma quality?
1.0093
0.9938
1.0079
1.0064
0.9957
0.9974
0.9935
1.0034
0.9972
0.9986
1.0054
1.0038
1.0001
0.9973
0.9923
0.9993
0.9997
1.0034
0.9990
1.0000
1.0031
1.0045
1.0067
0.9998
0.9992
0.9976
0.9943
0.9965
0.9999
1.0025
1.0009
0.9934
0.9987
1.0101
1.0011
0.9945
0.9969
1.0011
1.0031
1.0000
1.0002
1.0001
Samples
1.0034
0.9997
1.0001
1.0064
0.9982
0.9946
1.0033
1.0086
0.9997
0.9912
1.0013
1.0027
1.0002
0.9956
Date
Nov., 1, 2021
Nov., 2, 2021
Nov., 3, 2021
Nov., 4, 2021
Nov., 5, 2021
Nov., 6, 2021
Nov., 7, 2021
Nov., 8, 2021
Nov., 9, 2021
Nov., 10, 2021
Nov., 11, 2021
Nov., 12, 2021
Nov., 13, 2021
Nov., 14, 2021
1.0058
1.0002
0.9946
mean
1.001225
0.998825
1.00215
1.0024
0.9979
1.000525
1.00025
1.00275
1.000125
0.997675
1.00225
1.001025
0.9987
0.997375
Date
Nov., 1, 2021
Nov., 2, 2021
Nov., 3, 2021
Nov., 4, 2021
Nov., 5, 2021
Nov., 6, 2021
Nov., 7, 2021
Nov., 8, 2021
Nov., 9, 2021
Nov., 10, 2021
Nov., 11, 2021
Nov., 12, 2021
Nov., 13, 2021
Nov., 14, 2021
X’’ = 1.0002
SD = 0.00186
UCL = 1.0058
LCL = 0.9946
b)
a)
C
P
U L–
6σ
––––––––––––– 1.010 0.990–
6 0.00186( )
––––––––––––––––––––––––––––––––– 1.79= = =
C
PK
U X–
3σ
––––––––––––––ORX L–
3σ
––––––––––––– 1.010 1.0002–
3 0.00186( )
––––––––––––––––––––––––––––––––––––OR1.0002 0.990–
3 0.00186( )
–––––––––––––––––––––––––––––––––––– 1.76OR1.83 1.76= = = =
Problem 9.87
Draw a curve that shows the relationship between customer satisfaction and precision.
Inst. Ans. 9.87
Problem 9.88
A distillation tower is used to separate benzene recycled chemical waste. The mean benzene purity is 96.5%
with a standard deviation of 0.8%. What is the C
p
value if a customer orders
(a) 97%±1%, (b) 95%±2%, (c)
96.5%±3%?
Inst. Ans. 9.88
Unsatisfied
Crude Precise
Satisfied
C
P
U L–
6σ
––––––––––––– U L–
6 0.8( )
–––––––––––––––
= =
a)
b)
c)
C
P
98 96–
6 0.8( )
–––––––––––––––––– 0.417= =
C
P
2 2–( )–
6 0.8( )
–––––––––––––––––––– 0.833= =
C
P
3 3–( )–
6 0.8( )
–––––––––––––––––––– 1.25= =
marginally acceptable
Problem 9.89
Find and summarize legal cases for the following situations. The summaries should include the defendants, a
brief summary of the issue, the judgment, and the penalty.
(a) A company violating air-quality regulations
(b) An engineer criminally negligent for water pollution
(c) A company found criminally negligent for environmental contamination
Problem 9.90
Research and list the laws and regulations for your geographical area that deal with the use and disposal of
potassium fluoride.