A Preventive Replacement Policy for a System Subject to Bivariate Generalized Polya Failure Process

Hyunju Lee, Ji Hwan Cha and Maxim Finkelstein
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Hyunju Lee: Department of Statistics, Hankuk University of Foreign Studies, Yongin 17035, Korea
Ji Hwan Cha: Department of Statistics, Ewha Womans University, Seoul 03760, Korea
Maxim Finkelstein: Department of Mathematical Statistics, University of the Free State, Bloemfontein 9300, South Africa

Mathematics, 2022, vol. 10, issue 11, 1-15

Abstract: Numerous studies on preventive maintenance of minimally repaired systems with statistically independent components have been reported in reliability literature. However, in practice, the repair can be worse-than-minimal and the components of a system can be statistically dependent. The existing literature does not cover this important in-practice setting. Therefore, our paper is the first to deal with these issues by modeling dependence in the bivariate set up when a system consists of two dependent parts. We employ the bivariate generalized Polya process to model the corresponding failure and repair process. Relevant stochastic properties of this process have been obtained in order to propose and further discuss the new optimal bivariate preventive maintenance policy with two decision parameters: age and operational history. Moreover, introducing these two parameters in the considered context is also a new feature of the study. Under the proposed policy, the long-run average cost rate is derived and the optimal replacement policies are investigated. Detailed numerical examples illustrate our findings and show the potential efficiency of the obtained results in practice.

Keywords: dependent failure process; bivariate generalized Polya process; dependent worse-than-minimal repair process; optimal replacement policy (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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