A control chart for the Gamma distribution as a model of time between events

TLDR: In this article, a random-shift model for calculating the out-of-control average time to signal (ATS) of the Gamma chart is developed, which is shown to be much more accurate than the conventional method based on a fixed shift model through comparing with Monte Carlo simulation.

Abstract: In this paper, control charts for monitoring exponentially distributed time between events (TBE) are studied. In particular, a Gamma chart which monitors the time until the rth event is proposed and investigated. A new method based on a random-shift model for calculating the out-of-control average time to signal (ATS) of the Gamma chart is developed. It is shown to be much more accurate than the conventional method based on a fixed-shift model through comparing with Monte Carlo simulation. A comparison is also made among the exponential, the Gamma and the exponential CUSUM charts, which shows that the Gamma chart is more sensitive than the exponential chart and the performance of a Gamma chart with r = 4 is comparable with that of an exponential CUSUM optimally designed. However, the advantage of the Gamma chart is the ease involved in the design, evaluation and implementation. The use of the Gamma chart is illustrated with two real and one simulated examples.