  The aim of the present work is to investigate the performances of a specific
Bayesian control chart used to compare two processes. The chart monitors the
ratio of the percentiles of a key characteristic associated with the processes.
The variability of such a characteristic is modeled via the Weibull
distribution and a practical Bayesian approach to deal with Weibull data is
adopted. The percentiles of the two monitored processes are assumed to be
independent random variables. The Weibull distributions of the key
characteristic of both processes are assumed to have the same and stable shape
parameter. This is usually experienced in practice because the Weibull shape
parameter is related to the main involved factor of variability. However, if a
change of the shape parameters of the processes is suspected, the involved
distributions can be used to monitor their stability. We first tested the
effects 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 prior
information. To this end, the prior values were changed to reflect a 50% shift
in both directions from the original values of the shape parameter and the
percentiles of the two monitored processes. Finally, various combinations of
shifts were considered for the sampling distributions after the Phase I, with
the purpose of estimating the diagnostic ability of the charts to signal an
out-of-control state. The traditional approach based on the Average Run Length,
empirically computed via a Monte Carlo simulation, was adopted.
