A Mixed CUSUM-EWMA Chart for Monitoring a Weibull Process with Type-I Censoring

摘要

Process quality can be controlled and improved by monitoring reliability data using control charts. With this objective, Shewhart type and exponentially weighted moving average (EWMA) charts based on the conditional expected value and a cumulative sum (CUSUM) chart based on the likelihood ratio have been proposed to monitor the mean shift of a Weibull process with type-I censoring. The approach is based on the assumption that monitoring the scale parameter of the Weibull distribution is equivalent to monitoring its mean when the shape parameter is fixed. In this paper, we propose a mixed CUSUM-EWMA chart for earlier detection of smaller shifts in the scale parameter. We employ a Monte Carlo simulation approach to set the control limits and compute the average run length (ARL) and standard deviation of run lengths (SDRLs). The ARL and SDRL are utilized as two performance measures. The proposed chart has shown better performance as compared to the existing control charts in detecting smaller shifts in most cases. We provide an example based on a real data to illustrate the application of the proposed chart.