Efficient Monitoring of a Parameter of Non-Normal Process Using a Robust Efficient Control Chart: A Comparative Study

Aamir Majeed Chaudhary, Aamir Sanaullah (), Muhammad Hanif, Mohammad M. A. Almazah, Nafisa A. Albasheir and Fuad S. Al-Duais
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Aamir Majeed Chaudhary: Department of Statistics, National College of Business Administration and Economics, Lahore 54660, Pakistan
Aamir Sanaullah: Department of Statistics, COMSATS University Islamabad, Lahore Campus, Lahore 54000, Pakistan
Muhammad Hanif: Department of Statistics, National College of Business Administration and Economics, Lahore 54660, Pakistan
Mohammad M. A. Almazah: Department of Mathematics, College of Sciences and Arts (Muhyil), King Khalid University, Muhyil 61421, Saudi Arabia
Nafisa A. Albasheir: Department of Mathematics, College of Sciences and Arts (Majardah), King Khalid University, Magardah 61937, Saudi Arabia
Fuad S. Al-Duais: Mathematics Department, College of Humanities and Science, Prince Sattam Bin Abdulaziz University, Al Aflaj 16278, Saudi Arabia

Mathematics, 2023, vol. 11, issue 19, 1-30

Abstract: The control chart is a fundamental tool in statistical process control (SPC), widely employed in manufacturing and construction industries for process monitoring with the primary objective of maintaining quality standards and improving operational efficiency. Control charts play a crucial role in identifying special cause variations and guiding the process back to statistical control. While Shewhart control charts excel at detecting significant shifts, EWMA and CUSUM charts are better suited for detecting smaller to moderate shifts. However, the effectiveness of all these control charts is compromised when the underlying distribution deviates from normality. In response to this challenge, this study introduces a robust mixed EWMA-CUSUM control chart tailored for monitoring processes characterized via symmetric but non-normal distributions. The key innovation of the proposed approach lies in the integration of a robust estimator, based on order statistics, that leverages the generalized least square (GLS) technique developed by Lloyd. This integration enhances the chart’s robustness and minimizes estimator variance, even in the presence of non-normality. To demonstrate the effectiveness of the proposed control chart, a comprehensive comparison is conducted with several well-known control charts. Results of the study clearly show that the proposed chart exhibits superior sensitivity to small and moderate shifts in process parameters when compared to its predecessors. Through a compelling illustrative example, a real-life application of the enhanced performance of the proposed control chart is provided in comparison to existing alternatives.

Keywords: CUSUM; EWMA; mixed control chart; average run length; generalized least square estimation; order statistics; Lloyd’s estimator (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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