Shewhart‐type Phase II control charts for monitoring times to an event with a guaranteed in‐control and good out‐of‐control performance

Monitoring time to event (failure) data is important in many applications. Proper monitoring and control can make the production process more efficient and provide economic advantages. In this paper, we consider the efficacy of a class of Shewhart‐type control charts for monitoring time to event data following an exponential distribution with an unknown mean, which is estimated from a class of estimators. An estimator is chosen within this class, so that the in‐control performance is maximized with respect to a number of popular criteria in the recent literature, and the proposed optimal charts are compared on the basis of their in‐control and out‐of‐control performance. The comparisons include the traditional Phase II exponential Shewhart chart using the maximum likelihood estimator. Improved in‐control and out‐of‐control performances of these charts can enhance the quality and productivity of manufacturing processes. Since no chart is best under all the criteria, a ranking system is used to choose a chart to use in practice with a good overall performance. Two illustrative examples using real data are given; summary and conclusions are offered.