Abstract:
The traditional (frequentist) tr -chart is a Shewhart-type chart useful for monitoring times between events
(interarrival times) following an exponential distribution. This problem often arises in high-yield processes
where the defect rate is low and hence the conventional attribute charts such as the c-chart and the u-chart
are often ine↵ective. We consider this problem under the Bayesian framework and propose a Bayesian tr -
chart when the exponential rate parameter is unknown. The Bayesian tr -chart is a Shewhart-type chart that
incorporates parameter uncertainty via a prior and a posterior distribution, unlike the traditional tr -chart.
The control limits are constructed from the predictive distribution of a plotting statistic. The performance
of the proposed chart is evaluated and comparisons are made with the traditional tr -chart. The Bayesian
chart is seen to be advantageous in certain situations. An illustrative example is given and a summary and
conclusions are o↵ered.
