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The aim of the present work is to investigate the performances of a specificBayesian control chart used to compare two processes. The chart monitors theratio of the percentiles of a key characteristic associated with the processes.The variability of such a characteristic is modeled via the Weibulldistribution and a practical Bayesian approach to deal with Weibull data isadopted. The percentiles of the two monitored processes are assumed to beindependent random variables. The Weibull distributions of the keycharacteristic of both processes are assumed to have the same and stable shapeparameter. This is usually experienced in practice because the Weibull shapeparameter is related to the main involved factor of variability. However, if achange of the shape parameters of the processes is suspected, the involveddistributions can be used to monitor their stability. We first tested theeffects of the number of the training data on the responsiveness of the chart.Then we tested the robustness of the chart in spite of very poor priorinformation. To this end, the prior values were changed to reflect a 50% shiftin both directions from the original values of the shape parameter and thepercentiles of the two monitored processes. Finally, various combinations ofshifts were considered for the sampling distributions after the Phase I, withthe purpose of estimating the diagnostic ability of the charts to signal anout-of-control state. The traditional approach based on the Average Run Length,empirically computed via a Monte Carlo simulation, was adopted.

A first look at the performances of a Bayesian chart to monitor the ratio of two Weibull percentiles