A control chart based on likelihood ratio test for monitoring process mean and variability

Changliang Zou · Zhaojun Wang

73 citations0/0 files storedQuality and Reliability Engineering International

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

Abstract

Abstract Recently, monitoring the process mean and variance simultaneously by using a single chart has drawn more and more attention. In this paper, we propose a new single chart that integrates the EWMA procedure with the generalized likelihood ratio (GLR) test statistics for jointly monitoring both the process mean and variance. It can be easily designed and constructed, and its average run length can be evaluated by a two‐dimensional Markov chain model. Owing to the good properties of the GLR test and EMWA, computation results show that it provides quite a robust and satisfactory performance in various cases, including the detection of the decrease in variability and the individual observation at the sampling point, which are very important in many practical applications but may not be well handled by the existing approaches in the literature. The application of our proposed method is illustrated by a real data example from chemical process control. Copyright © 2009 John Wiley & Sons, Ltd.

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References

1990Exponentially Weighted Moving Average Control Schemes: Properties and Enhancements 1992A Multivariate Exponentially Weighted Moving Average Control Chart 1972An Approach to the Probability Distribution of Cusum Run Length 1989Economic Statistical Control-Chart Designs With an Application to and R Charts 2007Monitoring General Linear Profiles Using Multivariate Exponentially Weighted Moving Average Schemes 2001Monitoring Process Mean and Variability with One EWMA Chart 2006A Reference-Free Cuscore Chart for Dynamic Mean Change Detection and a Unified Framework for Charting Performance Comparison 1991Some Omnibus Exponentially Weighted Moving Average Statistical Process Monitoring Schemes

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2012On monitoring process variability under double sampling scheme 2009Self-starting control chart for simultaneously monitoring process mean and variance 2013Control Charts for Simultaneous Monitoring of Unknown Mean and Variance of Normally Distributed Processes 2017A progressive approach to joint monitoring of process parameters 2013A new multivariate EWMA scheme for monitoring covariance matrices

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