A manager is contemplating using Rules 1 and 4 for determining out-of-control conditions. Suppose that the manager constructs 3σ limits.
(a) What is the overall type I error probability assuming independence of the rules?
(b) On average, how many samples will be analyzed before detecting a change in the process mean? Assume that the process mean is now at 110 mm (having moved from 105 mm) and that the process standard deviation is 6 mm. Samples of size 4 are selected from the process.