Using geometric Poisson exponentially weighted moving average control schemes in a compound Poisson production environment

In this study, the variable to be controlled over time is the number of defects. Meanwhile, the underlying distribution of defects is the geometric Poisson distribution, a Poisson distribution compounded by a geometric distribution. For production process control, the exponentially weighted moving average (EWMA) control scheme based on the geometric Poisson process is addressed. Performance of the EWMA control scheme is assessed not only by both in-control and out-of-control average run lengths (ARL’s), but also by higher moments of the run length (RL) distribution. The run length distribution properties can be obtained from the probability transition matrix and implemented using the computer programs developed in this study. With proper ARL and variance of RL selected, any small shift in mean can be detected via the geometric Poisson EWMA control scheme.