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Control Chart for Exponential Processes Using a Percentile Based Modified Capability Index
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AI
DOI：10.1007/s41096-026-00286-8.png)
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Abstract
En 中文
Classical process capability indices such as C-pk and respective control charts are derived assuming normality of the underlying process. When the process is not normal, i.e., it is skewed. In particular, in many reliability and time-between-events problems, an exponential process is observed. Such indices and respective control charts may not capture process capability and thus may not detect any shifts in the process in a timely fashion. To this end, a modified capability index, namely C-pk(& lowast;), is proposed. Specifically, this index is based on percentiles of the process distribution, which provide a robust estimation of process spread and location. If this index is considered as a function of time, then a respective control chart is proposed with control limits determined to meet a desired in-control ARL. Simulation experiments are conducted to compare the performance of the proposed chart with that of classical C-pk chart under various subgroup sizes and values of the rate parameter. It is demonstrated that the proposed chart detects any shifts in the process faster compared to classical chart while it exhibits similar in-control performance. Specifically, it is shown that proposed method results in significantly smaller values of out-of-control ARL and reduced variability in performance. For instance, when a moderate value of 0.8 is assumed in the rate parameter, it is demonstrated that ARL is reduced from 63.73 to 19.06 when a moderate shift value of 0.8 is assumed in the rate parameter. Moreover, the proposed method is applied to a real dataset of inter-arrival times of coal-mining disasters, and it is demonstrated that it detects any deviations in the process faster compared to classical method.
Keywords:
Exponential process monitoring
Percentile-based capability analysis
Modified Cpk
Average run length (ARL)
Skewed distribution quality control
Industrial reliability and quality assurance
Journal
J
IF:
0.6
Papers:
38
Citations:
0