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Approximate calculations of age-based random replacement times

Author

Listed:
  • Xufeng Zhao
  • Chen Gao
  • Cunhua Qian
  • Toshio Nakagawa

Abstract

It is always difficult to discuss the analytical formulas, in which optimum solutions of replacement policies satisfy, due to the mathematical complexity. This paper proposes several approximate calculations for age-based random replacement policies, such that the unit is replaced at time T, at random time Yj (j=1,2,…) over time T, and at random time YN for Yj (j=1,2,…,N). We use the inequality properties of the formulas and the bounds of the extended failure rate functions to find the approximate calculations of replacement times in analytical ways. It is shown from numerical examples that these approximate calculations would become useful references for the optimum age-based random replacement times.

Suggested Citation

  • Xufeng Zhao & Chen Gao & Cunhua Qian & Toshio Nakagawa, 2020. "Approximate calculations of age-based random replacement times," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(15), pages 3808-3820, August.
    • Handle: RePEc:taf:lstaxx:v:49:y:2020:i:15:p:3808-3820
    DOI: 10.1080/03610926.2019.1710203
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