The length of industrial filters is a quality characteristic ofinterest. Thirty samples,each of size 5, are chosen from theprocess. The data yields an average length of
110 mm, with the process standarddeviation estimated to be 4 mm.
(a) Find the warning limits for acontrol 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 112mm, what are the chances of detecting this shift
by the third sample drawn after theshift?
(d) What is the chance of detectingthe shift for the first time on the second sample
point drawn after the shift?
(e) What is the ARL for a shift in theprocess mean to 112 mm? How many samples,
on average, would it take to detect achange in the process mean to 116 mm?
