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- Title
Dynamic probability control limits for the adaptive multivariate EWMA chart.
- Authors
Haq, Abdul
- Abstract
Effective monitoring of the control charts requires the establishment of appropriate control limits. Various methods have been proposed to determine the fixed control limits (FCLs) based on a specified in‐control average run‐length value, such as Markov chains, integral equations, and Monte Carlo simulations.With the FCLs, the conditional false alarm rate (CFAR) of a control chart varies over time in an unexpected and undesirable way, where the CFAR refers to the probability of a false alarm at a particular time given no previous false alarm. To address this issue, dynamic probability control limits (DPCLs) can be employed to keep the CFAR constant over time. In this study, we determine the DPCLs using fixed and time‐varying sample sizes for the adaptive multivariate EWMA chart when the underlying process is assumed to follow a multivariate normal distribution. The DPCLs are designed to automatically adjust to changes in the probability distribution of the sample size, while maintaining a consistent CFAR. This results in a closely matched run‐length performance for an in‐control process compared to that of the geometric distribution.
- Subjects
MARKOV chain Monte Carlo; DISTRIBUTION (Probability theory); GEOMETRIC distribution; ADAPTIVE control systems; MONTE Carlo method; QUALITY control charts
- Publication
Quality & Reliability Engineering International, 2024, Vol 40, Issue 4, p2067
- ISSN
0748-8017
- Publication type
Article
- DOI
10.1002/qre.3509