A process has mean 11 and standard deviation 2.5. The process ismonitored by taking samples of size 5 at regular intervals. Theprocess is declared to be out of control if a point plots outsidethe 3σ control limits on a chart.
17a.) If the process mean shifts to 14, what is the averagenumber of samples that will be drawn before the shift is detectedon a X⎯⎯⎯X¯ chart?
17b.) An upward shift to what value will be detected with an ARLof 4?
17c.) If the sample size remains at 5, to what value must thestandard deviation be reduced to produce an ARL of 4 when theprocess mean shifts to 14?
17d.) If the standard deviation remains at 2.5, what sample sizemust be used to produce an ARL of no greater than 4 when theprocess mean shifts to 14? Round up the answer to the nearestinteger.
