Realistic economic-statistical design of X ̄ control chart based on Lorenzen and Vance model in the presence of independent multiple assignable causes under the burr-XII shock model

The main goal of this study is to propose a realistic and practical model for the economic-statistical design of X ̄control charts in the presence of multiple independent assignable causes under the Burr Type XII shock model. The model aims to minimize underestimation of the actual cost per unit time of the quality cycle.

This research utilizes the Burr Type XII distribution as a shock model to develop the RED model for optimal design of X ̄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.

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, emphasizing the importance of considering this probability in E(A) calculations.

 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.