Evaluatiok of optimum weights and average run lenghts in ewma control schemes

Muni S. Srivastava · Yanhong Wu

31 citations0/0 files storedCommunication in Statistics- Theory and Methods

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Advanced Statistical Process Monitoring Probability and Statistical Research Fault Detection and Control Systems

Abstract

In this paper, a two sided exponentially weighted moving average (EWMA) control scheme of Roberts (1959) is studied. By using a continuous time model, explicit formulae for the average run lengths are obtained. Using these results, a formula for the optimal weight in the EWMA is obtained by minimizing the out of control average run length for a given reference value and in control average run length [ARL 0), which is assumed to be large. These optimunl weights are found to be very close to the optimum weights obtained by Lucas and Saccucci(1990) for the discrete time model using the Markov chain method. It is shown that the EWMA scheme performs almost as well as the CUSUM for moderate ARLO. Another important finding that emerges from this study is that the EWMA scheme is less sensitive to the choice of a reference value as compared to the CUSIJM. We also provide very accurate formulae for the ARL O and ARL μ of the two-sided CUSUM procedure.

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References

1990Exponentially Weighted Moving Average Control Schemes: Properties and Enhancements 1971Procedures for Reacting to a Change in Distribution 2000Control Chart Tests Based on Geometric Moving Averages 1986The Exponentially Weighted Moving Average 1986Optimal Stopping Times for Detecting Changes in Distributions 1985Sequential Analysis 1959Control Chart Tests Based on Geometric Moving Averages 1987A Simple Method for Studying Run – Length Distributions of Exponentially Weighted Moving Average Charts

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2008Comparisons of control schemes for monitoring the means of processes subject to drifts 2015Exact solution of the average run length for the cumulative sum chart for a moving average process of order q 2008ANALYTICAL APPROXIMATIONS FOR DETECTION OF A CHANGE- POINT IN CASE OF LIGHT-TAILED DISTRIBUTIONS 2023Analytical Explicit Formulas of Average Run Length of Homogenously Weighted Moving Average Control Chart Based on a MAX Process 2014A novel gradient approach for optimal design and sensitivity analysis of EWMA control charts

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