Conventional control charts in statistical process control are designed based on the presumption that the underlying process adheres to normal distribution. In practical scenarios, real-world processes often exhibit skewed distributions, such as the gamma distribution, leading to suboptimal performance of the standard control charts. This research proposes the variable sampling interval (VSI) exponentially weighted moving average (EWMA) \(\overline{X}\) chart specifically designed for the gamma distribution. Performance measures, including the average time to signal and standard deviation of the time to signal, are evaluated through the Monte Carlo simulations. Findings reveal significant performance deteriorations when the VSI EWMA \(\overline{X}\) chart is designed under the normal distribution model for monitoring the gamma process. New charting parameters are specially derived under the gamma distribution to ensure stable in-control performance and faster detection of mean shifts in gamma processes. A practical illustration is employed to demonstrate the implementation of the proposed chart.

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Using Variable Sampling Intervals in EWMA Control Charts for Effective Gamma Process Monitoring

  • Kai Le Goh,
  • Wei Lin Teoh,
  • Kai Lin Ong,
  • Laila El-Ghandour,
  • Zhi Lin Chong,
  • Ming Ha Lee

摘要

Conventional control charts in statistical process control are designed based on the presumption that the underlying process adheres to normal distribution. In practical scenarios, real-world processes often exhibit skewed distributions, such as the gamma distribution, leading to suboptimal performance of the standard control charts. This research proposes the variable sampling interval (VSI) exponentially weighted moving average (EWMA) \(\overline{X}\) chart specifically designed for the gamma distribution. Performance measures, including the average time to signal and standard deviation of the time to signal, are evaluated through the Monte Carlo simulations. Findings reveal significant performance deteriorations when the VSI EWMA \(\overline{X}\) chart is designed under the normal distribution model for monitoring the gamma process. New charting parameters are specially derived under the gamma distribution to ensure stable in-control performance and faster detection of mean shifts in gamma processes. A practical illustration is employed to demonstrate the implementation of the proposed chart.