modern research physics

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Monitoring process mean and variance simultaneously in a single control chart simplifies
the process monitoring. If in addition, a simultaneous control chart is capable of
recognizing the source of contamination, this capability leads to additional simplicity.
These are the reasons why simultaneous control charts have attracted many researchers and
manufacturers.
Recently, in the statistical process control literature some control charts have been
introduced which are based on the idea of Bayesian predictive density. This type of control
charts, not only brings into account the uncertainty concerning the estimation of unknown
parameters, but also do not need extensive simulations for computation of control limits.
These control charts have been introduced for mean and variance in both univariate and
multivariate situations.
Up to now, no simultaneous control chart has been introduced based on Bayesian predictive
density. In this paper, using the idea of Bayesian predictive density, we introduce a new
simultaneous control chart for monitoring univariate mean and variance. We illustrate the
important capabilities of this new chart through simulated data.
This new chart is applicable when parameters are unknown. In other words, it brings into
account the uncertainty concerning the unknown parameters. This chart is able to recognize
the source of contamination and is sensitive to small changes in the mean and variance. In
this chart the control limits, needless of simulation, can simply be obtained from normal
table.