Statistically Constrained Economic Design of the EWMA Control Chart

Abstract

This paper presents a statistically constrained economic model for the optimal design of an exponentially weighted moving average (EWMA) control chart for controlling process means. The optimum design parameters include the sample size, control limit width, sampling interval, and EWMA weight. The parameters are obtained by minimizing a total cost function proposed by Lorenzen and Vance, subject to additional statistical constraints on average run length (ARL) or average time-to-signal (ATS). Sensitivity analysis of the minimum costs as they are affected by various ATS bounds shows that the cost is more sensitive to smaller out-of-control bounds on ATS or ARL, but relatively insensitive to larger bounds. Investigation of economic statistical design for the EWMA chart reveals that adding constraints does not significantly increase the cost and does provide better protection against shift sizes other than those expected. Cost comparisons between optimal economic designs and optimal economic statistical designs show no significant cost increase when imposing statistical constraints on the cost model.

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