644 CHAPTER 16 STATISTICAL QUALITY CONTROLinfluence the number of defective units produced. To answer this question, we must collect
data on the process and see how the system reacts to changes in the process variables.
Statistical methods, including the SPC and experimental design techniques in this book, can
contribute to this knowledge.16-43. The diameter of fuse pins used in an aircraft engine
application is an important quality characteristic. Twenty-five
samples of three pins each are shown as follows:SUPPLEMENTAL EXERCISES(e) To make this process a six-sigma process, the variance
would have to be decreased such that PCRk2.0. What
should this new variance value be?
(f) Suppose the mean shifts to 64.01. What is the probability
that this shift will be detected on the next sample? What is
the ARL after the shift?
16-44. Rework Exercise 16-43 with and Scharts.
16-45. Plastic bottles for liquid laundry detergent are
formed by blow molding. Twenty samples of n100 bottles
are inspected in time order of production, and the fraction de-
fective in each sample is reported. The data are as follows:X^2(a) Set up and Rcharts for this process. If necessary, revise
limits so that no observations are out-of-control.
(b) Estimate the process mean and standard deviation.
(c) Suppose the process specifications are at 64 0.02.
Calculate an estimate of PCR. Does the process meet a
minimum capability level of PCR1.33?
(d) Calculate an estimate of PCRk. Use this ratio to draw con-
clusions about process capability.XSample
Number Diameter
1 64.030 64.002 64.019
2 63.995 63.992 64.001
3 63.988 64.024 64.021
4 64.002 63.996 63.993
5 63.992 64.007 64.015
6 64.009 63.994 63.997
7 63.995 64.006 63.994
8 63.985 64.003 63.993
9 64.008 63.995 64.009
10 63.998 74.000 63.990
11 63.994 63.998 63.994
12 64.004 64.000 64.007
13 63.983 64.002 63.998
14 64.006 63.967 63.994
15 64.012 64.014 63.998
16 64.000 63.984 64.005
17 63.994 64.012 63.986
18 64.006 64.010 64.018
19 63.984 64.002 64.003
20 64.000 64.010 64.013
21 63.988 64.001 64.009
22 64.004 63.999 63.990
23 64.010 63.989 63.990
24 64.015 64.008 63.993
25 63.982 63.984 63.995Sample Fraction Defective
1 0.12
2 0.15
3 0.18
4 0.10
5 0.12
6 0.11
7 0.05
8 0.09
9 0.13
10 0.13
11 0.10
12 0.07
13 0.12
14 0.08
15 0.09
16 0.15
17 0.10
18 0.06
19 0.12
20 0.13(a) Set up a Pchart for this process. Is the process in statisti-
cal control?
(b) Suppose that instead of n100, n200. Use the data
given to set up a Pchart for this process. Revise the con-
trol limits if necessary.
(c) Compare your control limits for the Pcharts in parts (a) and
(b). Explain why they differ. Also, explain why your assess-
ment about statistical control differs for the two sizes of n.c 16 .qxd 5/8/02 9:58 PM Page 644 RK UL 6 RK UL 6:Desktop Folder: