Economic-statistical design of EWMAj2 control charts for monitoring process variability

摘要

This article presents an economic-statistical model for the minimum cost design of EWMA_(x~2) charts with time-varying control limit for detecting increases in the process standard deviation. A nonlinear programming model is developed to minimize the expected total cost per unit time for soling the optimal decision variables including sample size, sampling interval, control limit width and smoothing constant of EWMA. The objective function of this model is based on Duncan's cost model, subject to additional statistical constrains on average run length (ARL). Some useful guidelines of designing EWMA_(x~2) charts are obtained from the results of optimal solutions. Given that the in-control ARL is fixed, it is shown that the minimum cost value would be certainly found out from the optimal solutions of the statistical design model with the minimum out-of-control ARL.