Morvarid Derakhshan Andisheh Journal of Quality Engineering and Management 3134-0849 14 2 2024 08 22 Realistic economic-statistical design of control chart based on the Lorenzen and Vance model in the presence of independent multiple assignable causes under the burr-XII shock model Realistic economic-statistical design of control chart based on the Lorenzen and Vance model in the presence of independent multiple assignable causes under the burr-XII shock model 127 144 214758 10.48313/jqem.2024.214758 FA Farnoosh Shiravani Department of Statistics, Faculty of Statistics, Mathematics and Computer Science, Allameh Tabatabaei University, Tehran, Iran. Mohammad Bamanimoghadam Department of Statistics, Faculty of Statistics, Mathematics and Computer Science, Allameh Tabatabaei University, Tehran, Iran. 0000-0003-1324-8024 Reza Pourtaheri Department of Statistics, Faculty of Statistics, Mathematics and Computer Science, Allameh Tabatabaei University, Tehran, Iran. Journal Article 2023 07 15 Purpose: The main goal of this study is to propose a realistic and practical model for the economic-statistical design of control charts in the presence of multiple independent assignable causes under the Burr Type XII shock model. The model aims to minimize the underestimation of the actual cost per unit time of the quality cycle. Methodology: This research utilizes the Burr Type XII distribution as a shock model to develop the RED model for optimal design of control charts. The Lorenz and Van cost function is also extended to account for multiple assignable causes, and a numerical example is provided to demonstrate the solution approach. Findings: Numerical results reveal that the proposed model outperforms existing models in accurately estimating the real cost per unit time of the quality cycle. Furthermore, an increase in the shock probability leads to a non-decreasing trend in the average cost, underscoring the importance of accounting for this probability in E(A) calculations. Originality/Value: This is the first study to employ the Burr Type XII distribution as a shock model in the economic-statistical design of control charts. By extending existing cost models, the paper introduces a novel and realistic approach to designing control charts in the presence of multiple independent shocks. Purpose: The main goal of this study is to propose a realistic and practical model for the economic-statistical design of control charts in the presence of multiple independent assignable causes under the Burr Type XII shock model. The model aims to minimize the underestimation of the actual cost per unit time of the quality cycle. Methodology: This research utilizes the Burr Type XII distribution as a shock model to develop the RED model for optimal design of control charts. The Lorenz and Van cost function is also extended to account for multiple assignable causes, and a numerical example is provided to demonstrate the solution approach. Findings: Numerical results reveal that the proposed model outperforms existing models in accurately estimating the real cost per unit time of the quality cycle. Furthermore, an increase in the shock probability leads to a non-decreasing trend in the average cost, underscoring the importance of accounting for this probability in E(A) calculations. Originality/Value: This is the first study to employ the Burr Type XII distribution as a shock model in the economic-statistical design of control charts. By extending existing cost models, the paper introduces a novel and realistic approach to designing control charts in the presence of multiple independent shocks.

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