A new approach Spider's web initial solution and data envelopment analysis for solving an $X$-bar control chart

Subject Areas : Statistics

K. Ranjbar ¹ , H. Khaloozadeh ² , A. Heydari ³

1 - Department of Mathematics, Payame Noor University, Tehran, Iran
2 - Department of Systems and Control, K.N.Toosi University of Technology, P.O. Box 16315-1355, Tehran, Iran
3 - Department of Mathematics, Payame Noor University, Tehran, Iran

Received: 2023-10-15 Accepted : 2023-12-17 Published : 2023-12-23

Keywords: Data Envelopment Analysis (DEA), economical control chart design, multi objective optimization problem (MOOP), Spider's web initial solution (SWIS),

Abstract :

$X$-bar control charts are widely used to monitor and control business and manufacturing processes. Design of control charts refers to the selection of parameters, including sample size, control-limit width, and sampling frequency. Many researchers have worked on this issue and have also proposed various solutions. However, despite the numerous advantages, the proposed methods also have their own set of problems. The biggest challenge is the complexity of solving these issues. Due to the fact that optimal design of control charts can be formulated as a multi objective optimization problem, in this paper to solve this problem, we used initial solution Spider's web data envelopment analysis method. In previous methods used multiple algorithms to resolve the issue. But in the proposed method once using Data Envelopment Analysis method and without any other algorithm can solve multi objective problem and this method can yield desirable efficient. Lastly, we compare our method with others and demonstrate its application in a real industrial context.

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