Question

9. The length of industrial filters is a quality characteristic of interest. Thirty samples,
each of size 5, are chosen from the process. The data yields an average length of
110 mm, with the process standard deviation estimated to be 4 mm.
(a) Find the warning limits for a control chart for the average length.
(b) Find the 3sigma control limits. What is the probability of a type I error?
(c) If the process mean shifts to 112 mm, what are the chances of detecting this shift
by the third sample drawn after the shift?
(d) What is the chance of detecting the shift for the first time on the second sample
point drawn after the shift?
(e) What is the ARL for a shift in the process mean to 112 mm? How many samples,
on average, would it take to detect a change in the process mean to 116 mm?

Answer 1

Answer:

Here X: Length of industrial filter is a quality characteristic. Given that thirty samples each of size five gave the process average = 110 mm with process standard = 4 mm.