Consider a process whose specifications on a quality characteristic are 100 ± 15. You know that the standard deviation of this normally distributed quality characteristic is 5. Where should you center the process to minimize the fraction defective produced? Now suppose that the mean shifts to 105, and you are using a sample size of 4 on an X̅ chart.

(a) What is the probability that such a shift is detected on the first sample following the shift?

(b) What is the average number of samples until an out-of-control point occurs? Compare this result to the average number of observations until a defective occurs (assuming normality).