Control Charts Based on the Exponential Distribution: Adapting Runs Rules for the t Chart

In this article we present a probabilistic-based method to construct a t chart to monitor the stability of a process. Assuming that the time between events can be modeled with an exponential distribution, we show how to apply the supplementary runs rules to identify whether the process is out of control. We compare the exact average run length (ARL) when the process is stable and under control, as well as the ability of this chart to identify a shift in the process to other charts currently used to monitor the same type of processes. Similar charts are applied in health care to monitor the rate of infections and other adverse events. However, some existing methods provide undesirable behavior when attempting to detect shifts and may hide or incorrectly demonstrate the nature of such shifts.