An x 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 δ = 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.
 = 0.01/hr or 1/ = 100hr; δ = 2.0
a1 = $0.50/sample; a2 = $0.10/unit; a'3 = $50; a3 = $25; a4 = $100/hr
g = 0.05hr/sample; D = 2hr
(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.