Realistic economic design of Shewhart control charts in the presence of multiple independent assignable causes using Burr-XII shock model

Document Type : Original Scientific Paper

Authors

Department of Statistics‎, ‎Allameh Tabataba'i University‎, ‎Tehran‎, ‎Iran

Abstract

This study proposes a novel framework for the realistic economic design of Shewhart control charts, addressing a critical yet overlooked limitation in traditional economic design models. Unlike classical approaches, the realistic economic design model explicitly incorporates the probability that no new assignable causes arise after the first assignable cause appears within a quality cycle an event previously assumed to be deterministic, despite its unrealistic nature in dynamic industrial environments. By integrating the flexible Burr-XII shock model, which accommodates various hazard rate behaviors (increasing, decreasing, constant, unimodal, and U-shaped), the proposed model offers a more accurate and practical tool for economic decision-making in process monitoring. The approach extends the widely cited Lorenzen and Vance (1986) framework, enabling a more comprehensive analysis of control chart performance under multiple independent assignable causes. Numerical results demonstrate that models such as that of Saadatmelli et al. (2018), based on Duncan (1971) assumptions and Burr-XII failure times, substantially underestimate the average cost per unit time. This discrepancy highlights the importance of using more realistic frameworks like our model to ensure cost-effective quality control.

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Journal of Statistical Modelling: Theory and Applications
Volume 6, Issue 1
January 2025
Pages 1-27

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History

  • Receive Date: 07 June 2025
  • Revise Date: 10 August 2025
  • Accept Date: 28 August 2025

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