Numerical Approximations of Average Run Length for AR(1) on Exponential CUSUM

Jaruchat Busaba

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

Abstract

We study the Cumulative Sum (CUSUM) procedure when observations are from a first order autoregressive model with exponential white noise. The objective of this paper is to present a numerical integration method for evaluating 0 ARL and 1 ARL , where 0 ARL is the average run length when the process is in control and 1 ARL is the average run length when the process is out of control. The integrals in the Integral Equation (IE) method for the CUSUM procedure are approximated by using the Gauss-Legendre rule for numerical integration. The results obtained from the numerical integration method are compared with results obtained from explicit formulae. We have shown that the results obtained from the two methods are in excellent agreement.

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1954CONTINUOUS INSPECTION SCHEMES 1932Economic Control of Quality of Manufactured Product.1990Exponentially Weighted Moving Average Control Schemes: Properties and Enhancements 2000Control Chart Tests Based on Geometric Moving Averages 1998Cumulative Sum Charts and Charting for Quality Improvement 1988Time-Series Modeling for Statistical Process Control 1991Some Statistical Process Control Methods for Autocorrelated Data 1987A Simple Method for Studying Run – Length Distributions of Exponentially Weighted Moving Average Charts

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2020The exact solution of the average run length on a modified EWMA control chart for the first-order moving-average process 2017Multivariate copulas on the MCUSUM control chart

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