ECONOMIC STATISTICAL DESIGN OF X̄ CONTROL CHARTS FOR SYSTEMS WITH WEIBULL IN-CONTROL TIMES

This paper considers the economic statistical design of X̄ control charts with Weibull failure properties. A Weibull failure model is appropriate for many systems in electrical and mechanical industries. The economic statistical control chart design model is developed and illustrated by two examples. It is shown that for some situations, the increase in costs associated with the improved statistical performance may not be significant compared to the economic design. A sensitivity analysis is performed to examine the cost effect of changing the controlled properties: Type I error rate, power, average time to signal (ATS); the expected process shift to be detected; and the Weibull scale and shape parameters. Results show that cost is relatively insensitive to improvement in Type I and Type II error rates, but is highly sensitive to changes in smaller upper bounds on ATS. Mis-specification of the underlying Weibull failure distribution parameters also may have significant economic consequences. © 1997 Elsevier Science Ltd