Journal of Systems Science and Complexity

, Volume 31, Issue 6, pp 1541–1553 | Cite as

The Ordering and Replacement Policy for the System with Two Types of Failures

  • Qiaoqiao GaoEmail author
  • Dequan Yue
  • Bing Zhao


In this paper, the optimal maintenance policy is investigated for a system with stochastic lead time and two types of failures. The system has two types of failures, one type is repairable, when the repairable failure occurs, the system will be repaired by repairman, and the system after repair is not “as good as new”. The other type of failure is unrepairable, and when the unrepairable failure occurs the system must be replaced by a new and identical one. The spare system for replacement is available only by order, and the lead time for delivering the spare system is stochastic. The successive survival times of the system form a stochastically decreasing geometric process, the consecutive repair times after failures of the system form a renewal process. By using the renewal process theory and geometric process theory, the explicit expression of the long-run average cost per unit time under ordering policy (N − 1) is derived, and the corresponding optimal can be found analytically. Finally, the numerical analyses are given.


Failure repair geometric process ordering policy renewal process replace 


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Copyright information

© Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Economics and ManagementShanxi UniversityTaiyuanChina
  2. 2.College of ScienceYanshan UniversityQinhuangdaoChina

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