Using CUSUM control schemes for monitoring quality levels in compound Poisson production environment: The geometric Poisson process

摘要

The CUSUM control scheme is considered to be one of the efficient reference tools in detecting a small structure change in a process. However, too often the assumption is made that the defects follow a Poisson distribution. In practice, the process is more complex and the distributions of defects are more appropriately modeled by the compound Poisson distribution. Here the underlying distribution is the geometric Poisson distribution, a Poisson distribution compounded by a geometric distribution, and the CUSUM based on this is addressed. An effective CUSUM control scheme can provide an adequate average run length (ARL) that can be obtained from the probability transition matrix for the Markov chain. With proper ARL selected, the geometric Poisson CUSUM control scheme is developed for process control.