Process Monitoring for Correlated Gamma-Distributed Data Using Generalized-Linear-Model-Based Control Charts

Duangporn Jearkpaporn; Douglas Montgomery; George Runger; Connie M. Borror

doi:10.1002/qre.521

Process Monitoring for Correlated Gamma-Distributed Data Using Generalized-Linear-Model-Based Control Charts

Duangporn Jearkpaporn, Douglas Montgomery, George Runger, Connie M. Borror

Industrial, Systems and Operations Engineering

Research output: Contribution to journal › Review article › peer-review

56 Scopus citations

Abstract

A model-based scheme is proposed for monitoring multiple gamma-distributed variables. The procedure is based on the deviance residual, which is a likelihood ratio statistic for detecting a mean shift when the shape parameter is assumed to be unchanged and the input and output variables are related in a certain manner. We discuss the distribution of this statistic and the proposed monitoring scheme. An example involving the advance rate of a drill is used to illustrate the implementation of the deviance residual monitoring scheme. Finally, a simulation study is performed to compare the average run length (ARL) performance of the proposed method to the standard Shewhart control chart for individuals.

Original language	English (US)
Pages (from-to)	477-491
Number of pages	15
Journal	Quality and Reliability Engineering International
Volume	19
Issue number	6
DOIs	https://doi.org/10.1002/qre.521
State	Published - Nov 1 2003

Keywords

Correlated gamma-distributed data
Generalized linear model
Model-based control chart

ASJC Scopus subject areas

Safety, Risk, Reliability and Quality
Management Science and Operations Research

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10.1002/qre.521

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title = "Process Monitoring for Correlated Gamma-Distributed Data Using Generalized-Linear-Model-Based Control Charts",

abstract = "A model-based scheme is proposed for monitoring multiple gamma-distributed variables. The procedure is based on the deviance residual, which is a likelihood ratio statistic for detecting a mean shift when the shape parameter is assumed to be unchanged and the input and output variables are related in a certain manner. We discuss the distribution of this statistic and the proposed monitoring scheme. An example involving the advance rate of a drill is used to illustrate the implementation of the deviance residual monitoring scheme. Finally, a simulation study is performed to compare the average run length (ARL) performance of the proposed method to the standard Shewhart control chart for individuals.",

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AU - Jearkpaporn, Duangporn

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AU - Runger, George

AU - Borror, Connie M.

PY - 2003/11/1

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N2 - A model-based scheme is proposed for monitoring multiple gamma-distributed variables. The procedure is based on the deviance residual, which is a likelihood ratio statistic for detecting a mean shift when the shape parameter is assumed to be unchanged and the input and output variables are related in a certain manner. We discuss the distribution of this statistic and the proposed monitoring scheme. An example involving the advance rate of a drill is used to illustrate the implementation of the deviance residual monitoring scheme. Finally, a simulation study is performed to compare the average run length (ARL) performance of the proposed method to the standard Shewhart control chart for individuals.

AB - A model-based scheme is proposed for monitoring multiple gamma-distributed variables. The procedure is based on the deviance residual, which is a likelihood ratio statistic for detecting a mean shift when the shape parameter is assumed to be unchanged and the input and output variables are related in a certain manner. We discuss the distribution of this statistic and the proposed monitoring scheme. An example involving the advance rate of a drill is used to illustrate the implementation of the deviance residual monitoring scheme. Finally, a simulation study is performed to compare the average run length (ARL) performance of the proposed method to the standard Shewhart control chart for individuals.

KW - Correlated gamma-distributed data

KW - Generalized linear model

KW - Model-based control chart

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JF - Quality and Reliability Engineering International

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Process Monitoring for Correlated Gamma-Distributed Data Using Generalized-Linear-Model-Based Control Charts

Abstract

Keywords

ASJC Scopus subject areas

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