Power approximations in the economic design of control charts

Abstract

A new approximate method is proposed for the economic design of control charts based on an estimate of the power of the control chart at optimality. Multiple linear regression is employed for the derivation of the approximate formula expressing the power of the control chart as a function of the model parameters. A simple optimization procedure is then used to determine the economic design of the control chart for the predicted value of the chart's detection power. The application of the new approach is illustrated through Duncan's models for variables control charts for processes subject to single and multiple assignable causes. Evaluation of the performance of the approximate method indicates that the approximate control chart design is very close to the exact optimum while its implementation requirements are reduced.