Refer to Exercise 21.19.
a. Find the probability that the x chart does not detect a shift of .75 standard deviation on the first sample after the shift occurs.
b. Compute the probability that the x chart will not detect the shift for the first four samples after the shift.

In exercise 21.19

The company is considering changing the sampling plan so that 20 components are sampled every 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 firm that manufactures notebook computers uses statistical process control to monitor all its production processes. For one component, the company draws samples of size 10 every 30 minutes. The company makes 4,000 of these components per hour. The control limits of the x chart are set at 3 standard errors from the mean. When the process goes out of control, it usually shifts the mean by .75 standard deviation.