An x bar chart is used to maintain current control of a process. The cost parameters are a1 = $0.50, a2 = $0.10, a3 = $25, a'3 = $50, and a4 = $100. A single assignable cause of magnitude d = 2 occurs, and the duration of the process in control is an exponential random variable with mean 100 h. Sampling and testing require 0.05 h, and it takes 2 h to locate the assignable cause. Assume that equation 10.31 is the appropriate process model.

(a) Evaluate the cost of the arbitrary control chart design n = 5, k = 3, and h = 1.

(b) Evaluate the cost of the arbitrary control chart design n = 5, k = 3, and h = 0.5.

(c) Determine the economically optimum design.