Exact solution of the average run length for the cumulative sum chart for a moving average process of order q

Kanita Petcharat · Saowanit Sukparungsee · Yupaporn Areepong

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

Abstract

In this paper we use a Fredholm integral equation approach to derive an explicit formula for the average run length (ARL) of a cumulative sum (CUSUM) chart for random observations described by a moving average process of order q (MA(q)) with exponential white noise.We compare the computational times required for calculating the ARL from our exact formula with the computational times required for solving the Fredholm integral equations using a Gauss-Legendre numerical scheme.We find that the computational times are approximately 1 s for the explicit formula and approximately 13 min for the numerical integration scheme.

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References

1954CONTINUOUS INSPECTION SCHEMES 1990Exponentially Weighted Moving Average Control Schemes: Properties and Enhancements 1972An Approach to the Probability Distribution of Cusum Run Length 1987A Simple Method for Studying Run – Length Distributions of Exponentially Weighted Moving Average Charts 1993Performance of CUSUM Control Schemes for Serially Correlated Observations 2009Control charts, Cusum techniques and funnel plots. A review of methods for monitoring performance in healthcare 2002Evaluating environmental performance using statistical process control techniques 2013The computation of average run length and average time to signal: an overview

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