A Mathematical Model for Maintenance Planning based on the Information of Control Charts Using Markov Chains Approach

Document Type : Research Paper

Authors

1 Assistant Professor, Department of Engineering, University of Kurdistan, Sanandaj, Iran

2 M.A. Industrial Engineering, Department of Engineering, University of Kurdistan, Sanandaj, Iran

10.22084/ier.2024.5571

Abstract

Statistical process control (SPC) and maintenance are two key elements for controlling production systems while the aim of both is improving quality and reducing operational costs. Hence, studying integrated models of maintenance and SPC has recently attracted attentions of researchers. The principal goal of these models is to coordinate the decisions of maintenance and quality control so that the integrated models provide better performance in comparison with stand-alone maintenance/quality control models. In this paper, a production system with two operational states plus a failure state is considered. It is assumed assignable causes only affect variance of the process and mean does not affect.  Based on Markov chains properties, a mathematical model is derived to minimize the joint costs of maintenance and quality control.  The model optimally determines the parameters of the control chart, i.e., sample size, time interval of sampling and coefficient of control chart, in order to minimize the expected cost per time unit. While in most previous integrated models of maintenance and quality control, it was assumed that process deterioration and occurrence of assignable causes only affect the process mean, in this paper, assignable cause changes the process variance. The numerical examples and sensitivity analyses reveal that the proposed model optimaly determines the control chart parameters so that the costs of maintenance and quality can be minimized, and the control chart has suitable statistical properties.

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References

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Journal of Industrial Engineering Research in Production Systems
Volume 11, Issue 23
March 2024
Pages 161-173

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