Joint Monitoring of Process Location and Dispersion Based on CUSUM Procedure and Generalized Likelihood Ratio in the Presence of Measurement Errors

Abstract

In this paper, we propose a new methodology based on the combination of cumulative sum procedure and generalized likelihood ratio statistic for joint monitoring of the process location and dispersion. Then, we explore the effect of measurement errors on detecting ability of the proposed control chart when (i) the variance of measurement error is constant (ii) the variance of measurement error increases linearly as the level of the process mean increases. We also utilize multiple measurements on each sample point in order to decrease the adverse effects of measurement errors on the performance of the proposed control charts. Two numerical examples based on simulation studies are given to evaluate the ability of the proposed methods in terms of average run length, median run length, standard deviation of run length, and the first and third quantile points of the run length distribution (Q1 and Q3). Finally, a real life example is given to illustrate the application of the proposed method. Copyright © 2017 John Wiley & Sons, Ltd.

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