Abstract:
In Statistical Process Control (SPC) there exists a need to model the runlength
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.
