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:

(a) Set up XÌ… and R charts 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 that the process specifications are at 64 ± 0.02. Calculate an estimate of PCR. Does the process meet a minimum capability level of PCR ‰¥ 1.33?

(d) Calculate an estimate of PCR_k. Use this ratio to draw conclusions about process capability.

(e) To make this process a 6-sigma process, the variance σ² would have to be decreased such that PCR_k = 2.0. What should this new variance value be?

(f) Suppose that the mean shifts to 64.01. What is the probability that this shift is detected on the next sample? What is the ARL after the shift?

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Sample Number Diameter 1 64.030 64.002 64.019 2 63.995 63.992 64.001 64.021 63.988 64.024 64.002 63.996 63.993 63.992 64.007 64.015 63.994 63.997 64.009 63.995 64.006 63.994 64.003 63.993 8. 63.985 63.995 64.008 64.009 10 63.998 74.000 63.990 63.994 11 63.998 63.994 12 64.004 64.000 64.007 64.002 13 63.983 63.998 64.006 63.994 14 63.967 64.012 15 64.014 63.998 64.000 63.984 64.005 16 64.012 17 63.994 63.986 64.006 64.010 18 64.018 63.984 64.003 64.002 20 64.000 64.010 64.013 64.001 64.009 21 63.988 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 63.995