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- Title
A near‐optimal CUSUM‐t$t$ chart.
- Authors
Haq, Abdul; Khoo, Michael B. C.
- Abstract
A 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)‐t$t$ chart. However, optimizing the existing CUSUM‐t$t$ 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‐t$t$ 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‐t$t$ chart and the established CUSUM‐t$t$ 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.
- Subjects
CUSUM technique; MONTE Carlo method; MARKOV processes; STATISTICAL process control; SAMPLE size (Statistics)
- Publication
Quality & Reliability Engineering International, 2024, Vol 40, Issue 4, p2116
- ISSN
0748-8017
- Publication type
Article
- DOI
10.1002/qre.3516