New Cumulative Sum Control Chart for Monitoring Poisson Processes

The cumulative sum (CUSUM) control charts are widely used for measurement control of continuous processes. However, the quality characteristics of interest in many production processes, follows a sequence of discrete counts for non-conformities often modeled using a Poisson distribution. This paper introduces new CUSUM control chart design structure to monitor the location of a Poisson parameter. The proposed two-sided scheme is based on ranked set sampling, a more well-structured data collection method than the traditional random sampling. Extensive simulations were used to compute the average, standard deviation and percentiles of the run-length distribution for the new Poisson CUSUM charts. Relative run-length performances achieved were compared with the classical schemes for monitoring improvements or deteriorations in a Poisson process. Consequently, it turns out that the new scheme has greatly enhanced the sensitivity of the classical chart in detecting changes in Poisson processes. The practical application of the new Poisson CUSUM chart is illustrated through a numerical example.