A near‐optimal CUSUM‐t$t$ chart

Abstract

AbstractA robust tool for monitoring the process mean in the presence of abrupt changes or estimation errors in the process standard deviation is the cumulative sum (CUSUM)‐ chart. However, optimizing the existing CUSUM‐ chart to minimize the out‐of‐control average run‐length value often involves intricate Markov chain techniques. This complexity prompted the development of a near‐optimal CUSUM‐ chart, presented in this paper, which simplifies the determination of the chart's reference parameter. The reference parameter calculation is based on a predefined shift size in the mean, allowing for swift detection. Meanwhile, the chart's decision interval can be derived through Monte Carlo simulations. Interestingly, both the newly devised near‐optimal CUSUM‐ chart and the established CUSUM‐ chart yield similar out‐of‐control average run‐length values for identical shift sizes and sample sizes. Consequently, the former can serve as a practical alternative to the latter, considering its ease of optimization and implementation.