Question

In-control procedure has upper specification of (USL=62), lower specification of (LSL=38). A size sample (n=20) from this procedure reveals that the process mean is centered approximately at the midpoint of the specification interval, and that the sample standard deviation is found to be (s=1.75) Calculate the 95% confidence interval on (Cp)

Answer 1

Here we have given that,

USL=Upper specification limit=62

LSL=Lower specification limit=38

n= sample size =20

S=sample standard deivation=1.75

Now,

we want to find the 95% confidence interval for the

Formula is as follows,

first we find Cp

=2.29

Now, we find the Critical value

c= confidence level = 0.95

= level of significance = 1-c = 1-0.95 = 0.05

degress of freedom = n-1 = 20-1=19

we get,

10.12

32.85

Now,we find the CI

Lower limit =1.671

Upper Limit =3.011

INterpretations:

We are 95% confidnent that the Cp values lies wtihin this interval