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.
Bibliographical noteFunding Information:
Funding: The work of the first author was supported by Hankuk University of Foreign Studies Research Fund of 2022 and the National Research Foundation of Korea (NRF) grant funded by the Korea Government (Ministry of Science of ICT) (no. 2021R1F1A1048037). The work of the second author was also supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (grant no. 2019R1A6A1A11051177).
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- bivariate generalized Polya process
- dependent failure process
- dependent worse-than-minimal repair process
- optimal replacement policy