Question

1. For each of the following processes, a sample of size 400 is collected in order to estimate the process mean and variability.

Process	Mean	Sample Standard Deviation (s or σ)	Lower Spec	Upper Spec
A	29.3	0.74	26.8	31.8
B	119.6	2.56	115.5	132.5

1. Indicate which measure of process capability (Cpvs.Cpk) appears the more appropriate to use for each process, and state why.
2. Compute the appropriate measure of process capability for each process.

Answer 1

Process	Mean	Sample Standard Deviation (s or σ)	Lower Spec	Upper Spec	a. appropriate measure
A	29.3	0.74	26.8	31.8	Cp	0.62
B	119.6	2.56	115.5	132.5	Cpk	3.50
sample size, n	400
Cp is appropriate when the process is centered, i.e. mean lies somewhere between the upper and lower spec, whereas Cpk is more apt for situations where the process is not centered, i.e. the mean tends to shift towards upper or lower spec.
in process A, the mean lies between the lower and upper spec, hence, Cp will be a more appropriate measure of process capability
in process B, the mean is towards the lower spec, and hence, Cpk will the appropriate measure of process capability
Cp= (USL-LSL)/6s
Cpk=min [{(USL-mean)/3s}, {(mean-LSL)/3s}]

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