A predictive Bayesian approach to EWMA and CUSUM charts for time-between-events monitoring

ABSTRACT

This article introduces Bayesian predictive monitoring of time-between-events using Cumulative Sum (CUSUM) and Exponentially Weighted Moving Average (EWMA) control charts with predictive control limits. It is shown that the proposed methodology not only overcomes the requirement of a large Phase-I data set to establish control limits, but also feasible for online process monitoring. In addition to Bayesian memory-type charts with dynamic control limits, a comparison of the frequentist sequential charts, designed by using the unbiased and biased estimator of the process parameter, is also given in this article. For the performance evaluation of the predictive TBE chart in the presence of practitioner-to-practitioner variability, we use the average of the in-control average run length (AARL) and the standard deviation of the in-control run length (SDARL).

Keywords:

• Average run length (ARL)
• Bayesian process monitoring
• Bayesian CUSUM
• Bayesian EWMA
• poisson process
• predictive control limits
• sequential process monitoring
• self-adaptive control charts
• time-between-events control charts

Disclosure statement

No potential conflict of interest was reported by the author(s).