Economic and Economic Statistical Designs for MEWMA Control Charts

Abstract

This paper proposes methods for determining the optimal choice of design parameters (including control limits, sample size, exponential weights for past observations, and sampling interval) for the multivariate exponentially weighted moving average (MEWMA) control chart. Extending the Lorenzen-Vance flexible cost model (Lorenzen and Vance (1986)) to develop economic designs for MEWMA control chart parameters, we then add statistical constraints to obtain economic statistical designs. The choice of parameters is dependent on the average run length (ARL) when the process is in control and out of control. Evaluating the ARL values for the MEWMA chart through simulation, we determine optimal chart parameters given cost information. Results are presented on model sensitivity (in terms of expected cost and out-of-control ARL) to misspecification of the size of the shift in the process mean vector. We also consider the impact of perturbing the sampling interval on expected cost.

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