Chapter 10.4, Problem 1E

Refer to Exercise 3 in Section 10.2.

1. a. Delete any samples necessary to bring the process variation under control. (You did this already if you did Exercise 3 in Section 10.2.)
2. b. Use $\bar{R}$ to estimate ${\sigma }_{\bar{x}}$ ( ${\sigma }_{\bar{x}}$ is the difference between $\overline{\stackrel{¯}{X}}$ and the 1σ control limit on an $\bar{X}$ chart).
3. c. Construct a CUSUM chart, using $\overline{\stackrel{¯}{X}}$ for the target mean μ, and the estimate of ${\sigma }_{\bar{x}}$ found in part (b) for the standard deviation. Use the values k = 0.5 and h = 4.
4. d. Is the process mean in control? If not, when is it first detected to be out of control?
5. e. Construct an $\bar{X}$ chart, and use the Western Electric rules to determine whether the process mean is in control. (You did this already if you did Exercise 3 in Section 10.2.) Do the Western Electric rules give the same results as the CUSUM chart? If not, how are they different?