Economic and Economic-Statistical Designs for MEWMA Control Charts

Abstract


Designing Multivariate Exponentially Weighted Moving Average (MEWMA) control charts means making rational decisions about several parameters: the upper control limit, the sample size, the time interval between samples, and the exponential smoothing constant. Extending the Lorenzen-Vance flexible cost model 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 when it is 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. This presentation is the result of joint work with Kevin Linderman, Department of Operations and Management Science, University of Minnesota. A paper on the subject will appear in the Journal of Quality Technology.

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