Drift Change Point Estimation in Multistage Processes Using MLE

Abstract

Usually the time a control chart shows an out-of-control signal is not the exact time at which a change happens; instead, the change has started before this time. The exact time the change starts is called the change point. Although many manufacturing processes are of a multistage type, most of change point estimations in the literature focused on processes with a single stage. In this research, a multistage process with a single quality characteristic monitored in each stage is first modeled using both a first-order autoregressive (AR(1)) and an autoregressive moving average (ARMA(1, 1)) model. Then, a maximum likelihood estimator is derived to estimate the change points, i.e., the sample number and the stage number, at which a drift change occurs in the location parameter of the multistage processes. To monitor the process, cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) control charts are used and the performance of the proposed estimator is compared with the ones of CUSUM and EWMA approach in terms of the average and the standard deviation of the sample number and the number of wrong stages. The results of several simulation experiments indicate that the MLE estimator has a good performance to estimate drift change-point in multistage process.