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Exponentially Weighted Moving Average Control Chart Based on Trimmed Mean for Skewed Distributions
Muhammad Haider, Hafiz Zain Pervaiz
Abstract:
Conventional control charts usually assume that the process data is normally distributed. In practice, though, especially in the contemporary production and service context, data is often skewed, contain outliers, and other anomalies that may compromise the accuracy of conventional checking methods. To counter such challenges, this paper offers a modified exponentially weighted moving average (EWMA) control chart anointed with the trimmed mean as a strong location estimator. The suggested chart has more resistance to distributional asymmetry and contamination by removing extreme values. We obtain analytical control limits of the trimmed-mean EWMA chart and analyze its performance based on a comprehensive simulation based on a variety of non-normal distributions, such as, lognormal, exponential and gamma distribution. The comparative outcomes are on average run length (ARL) measures whereby the proposed approach is always superior to the traditional EWMA mean chart especially when identifying minute changes with skewed noise levels. These results indicate the trimmed-mean EWMA chart is not just more sensitive to the fine changes, but much more robust to non-Gaussian, which is why it is a viable quality control tool in the contexts where the data normality cannot be assumed.
Keywords:
EWMA, Average run length (ARL), Skewness, Trimmed mean, Gamma
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