Planning time-between-events Shewhart control charts

Shewhart charts for counts are widely used in statistical process control. Usually, they are designed with, as observation to be monitored, the number or the proportion of counts occurring in sampling intervals. However, in many production and administrative processes, as well as in health management and other applied areas, it may be more convenient to monitor the arrival time between successive counts. A unified methodology for planning one-sided and two-sided time-betweenevents Shewhart-type charts is presented. It can be readily applied to any underlying distribution of the counts, and shows how to select the control limits and evaluate the sensitivity of the chart. The procedure is illustrated in a situation of practical relevance in which the time-between-events is exponentially distributed. A numerical example is also given.