Generalized Control Charts for Non-Normal Data Using g-and-k Distributions

Haynes, Michele, Mengersen, Kerrie and Rippon, Paul (2008) Generalized Control Charts for Non-Normal Data Using g-and-k Distributions. Communications in Statistics - Simulation and Computation, 37 9: 1881-1903. doi:10.1080/03610910802255170


Author Haynes, Michele
Mengersen, Kerrie
Rippon, Paul
Title Generalized Control Charts for Non-Normal Data Using g-and-k Distributions
Formatted title
Generalized Control charts for Non-Normal Data Using g-and-k Distributions
Journal name Communications in Statistics - Simulation and Computation   Check publisher's open access policy
ISSN 0361-0918
1532-4141
Publication date 2008-11-01
Year available 2008
Sub-type Article (original research)
DOI 10.1080/03610910802255170
Open Access Status
Volume 37
Issue 9
Start page 1881
End page 1903
Total pages 23
Editor N Balakrishnan (Editor-in-Chief)
Place of publication London
Publisher Taylor & Francis
Language eng
Subject C1
010401 Applied Statistics
970101 Expanding Knowledge in the Mathematical Sciences
Abstract Statistical control charts are often used in industry to monitor processes in the interests of quality improvement. Such charts assume independence and normality of the control statistic, but these assumptions are often violated in practice. To better capture the true shape of the underlying distribution of the control statistic, we utilize the g-and-k distributions to estimate probability limits, the true ARL, and the error in confidence that arises from incorrectly assuming normality. A sensitivity assessment reveals that the extent of error in confidence associated with control chart decision-making procedures increases more rapidly as the distribution becomes more skewed or as the tails of the distribution become longer than those of the normal distribution. These methods are illustrated using both a frequentist and computational Bayesian approach to estimate the g-and-k parameters in two different practical applications. The Bayesian approach is appealing because it can account for prior knowledge in the estimation procedure and yields posterior distributions of parameters of interest such as control limits.
Keyword Average run length (ARL)
Bayesian Estimation
Control chart
g-and-k distributions
Non-normality
Robustnesss
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: 2009 Higher Education Research Data Collection
School of Social Science Publications
Social Research Centre Publications
 
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Created: Fri, 27 Mar 2009, 20:44:40 EST by Margaret Gately on behalf of School of Social Science