In Statistical Process Control (SPC) there exists a need to model the runlengthdistribution of a Q-chart that monitors the process mean when measurementsare from an exponential distribution with an unknown parameter. To develop exactexpressions for the probabilities of run-lengths the joint distribution of the chartingstatistics is needed. This gives rise to a new distribution that can be regarded as ageneralized multivariate beta distribution. An overview of the problem statement asidentified in the field of SPC is given and the newly developed generalized multivariatebeta distribution is proposed. Statistical properties of this distribution are studied andthe effect of the parameters of this generalized multivariate beta distribution on thecorrelation between two variables is also discussed.
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