A maximum likelihood approach to estimate the change point of multistage Poisson count processes

The difference between the signaling time and the real change point of a process is an important monitoring issue. If the exact time at which the change manifests itself into the process is known, then process engineers can identify and eliminate the root causes of process disturbance efficiently and quickly, resulting in considerable amount of time and cost savings. Multistage count processes that are often observed in production environments must be monitored to assure quality products. In this study, multistage Poisson count processes are first introduced. Then, the process is modeled using a first-order integer-valued autoregressive time series (INAR(1)). For out-of-control signals obtained by a combined exponentially weighted moving average (EWMA) and c control chart, Newton’s method is next used to approximate the rate and the dependence parameters. Finally, the maximum likelihood method is employed to estimate the out-of-control sample along with the out-of-control stage. Besides, the accuracy and the precision of the proposed estimators are examined through some Monte Carlo simulation experiments. The results show that the estimators are accurate and promising.