Refer to Exercise 21.12.
a. Find the probability that the x chart does not detect a shift of 1.5 standard deviations on the first sample after the shift occurs.
b. Compute the probability that the x chart will not detect the shift for the first eight samples after the shift.

In exercise 21.12

The operations manager is unsatisfied with the current sampling plan. He changes it to samples of size 2 every half hour. What is the average number of units produced until the chart indicates that the process is out of control when it is not?

A production facility produces 100 units per hour and uses an x chart to monitor its quality. The control limits are set at 3 standard errors from the mean. When the process goes out of control, it usually shifts the mean by 1.5 standard deviations. Sampling is conducted once per hour with a sample size of 3.