ANALYTICAL APPROXIMATIONS FOR DETECTION OF A CHANGE- POINT IN CASE OF LIGHT-TAILED DISTRIBUTIONS

Soawanit Sukparungsee · Alexander A. Novikov

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

Abstract

We derive analytic approximations for the expectation of exit times of Exponentially Weighted Moving Average (EWMA) procedure by using the martingale technique. Based on this technique, martingale approach is able to adapt to monitoring of changes of light-tailed distributions such as Gaussian, Poisson and Bernoulli distributions. Simple procedures are addressed for obtaining the optimal design of EWMA. A comparison with Monte Carlo simulation is also presented.

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1954CONTINUOUS INSPECTION SCHEMES 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 1995Detection of Abrupt Changes: Theory and Applications.1998Cumulative Sum Charts and Charting for Quality Improvement 1985Optimal Detection of a Change in Distribution 1987A Simple Method for Studying Run – Length Distributions of Exponentially Weighted Moving Average Charts

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