. An X chart is used to maintain current control of a process. The cost parame-

ters are d = $0.50, a2 = $0.10, ag = $25, a3 = $50, and a; = $100. A single assignable cause of magnitude 6 = 2 occurs, and the duration of the process in control is an exponential random vari-

able with mean 100 h. Sampling and testing require 0.05 h, and it takes 2 h to locate the assignable cause, Assume that equation 9-31 is the appropriate process model.

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

#=1.

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

(c) Determine the economically opti-

mum design.