Age replacement with Markovian opportunity process. (December 2021) - Zheng, Junjun; Okamura, Hiroyuki; Dohi, Tadashi
Abstract: This paper focuses on the age replacement problems under the assumption that the arrival of opportunities follows a stochastic point process. The opportunity is a chance to make the replacement, and one can replace a unit with a low cost at the opportunity. In this paper, the opportunity-based age replacement models by Dekker and Dijkstra (1992) and Zhao and Nakagawa (2012) are extended in the environment where the opportunity process is in accordance with a Markovian arrival process (MAP). The MAP is one of the general point processes, and involves a Poisson process and some renewal process classes. This work introduces the generalization of the arrival process of the preventive replacement problems with opportunities. Furthermore, a comprehensive evaluation of the opportunity-based age replacement policies by Dekker and Dijkstra (1992) and Zhao and Nakagawa (2012) in the generalized modeling framework is carried out. Highlights: Generalizing the opportunity arrival process for age replacement using MAP. Providing explicit formulas of the long-run average cost for replacement policies. Evaluating and comparing existing policies in our generalized modeling framework. Investigating the effect of opportunity process's characteristic on optimal policy. Revealing that Dekker and Dijkstra's policy was effective in most cases.