Journal of Quality Engineering and Management

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

Document Type : Original Article

Authors

Farnoosh Shiravani
Mohammad Bamanimoghadam
Reza Pourtaheri

Department of Statistics, Faculty of Statistics, Mathematics and Computer Science, Allameh Tabatabaei University, Tehran, Iran.

https://doi.org/10.48313/jqem.2024.214758
Abstract
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.

Keywords

Realistic economic-statistical design
Control chart X ̄
Multiple assignable causes
Burr-XII shock model
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Journal of Quality Engineering and Management
Volume 14, Issue 2
Summer 2024
Pages 127-144

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