A generalized multivariate beta distribution: control charting when the measurements are from an exponential distribution

K. Adamski (), S. Human and A. Bekker

Statistical Papers, 2012, vol. 53, issue 4, 1045-1064

Abstract: In Statistical Process Control (SPC) there exists a need to model the run-length distribution of a Q-chart that monitors the process mean when measurements are from an exponential distribution with an unknown parameter. To develop exact expressions for the probabilities of run-lengths the joint distribution of the charting statistics is needed. This gives rise to a new distribution that can be regarded as a generalized multivariate beta distribution. An overview of the problem statement as identified in the field of SPC is given and the newly developed generalized multivariate beta distribution is proposed. Statistical properties of this distribution are studied and the effect of the parameters of this generalized multivariate beta distribution on the correlation between two variables is also discussed. Copyright Springer-Verlag 2012

Keywords: Multivariate beta; Chi-squared; Statistical Process Control; Run-length; Shewhart; Hypergeometric functions; Correlation; Primary 62E15; 62H10; Secondary 62P30; 62F86 (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s00362-011-0407-0

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