Skip to main content
SpringerLink
Log in

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

  • Published:
Journal of Systems Science and Complexity Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Lam Y, Geometric process and replacement problem, Acta Mathematicae Applicatae Sinica, 1988, 4: 366–377.

    Article  MathSciNet  Google Scholar 

  2. Lam Y, A note on the optimal replacement problem, Advances in Applied Probability, 1988, 20: 479–782.

    Google Scholar 

  3. Jia J S and Wu S M, Optimizing replacement policy for a cold-standby system with waiting repair times, Applied Mathematics and Computation, 2009, 24: 133–141.

    Article  MathSciNet  MATH  Google Scholar 

  4. Zhang Y L and Wang G J, A deteriorating cold standby repairable system with priority in use, European Journal of Operational Research, 2007, 18: 278–295.

    Article  MATH  Google Scholar 

  5. Wang G J and Zhang Y L, Geometric process model for a system with inspections and preventive repair, Computers & Industrial Engineering, 2014, 75: 13–19.

    Article  Google Scholar 

  6. Zong S L, Chai G R, Zhang Z G, et al., Optimal replacement policy for a deteriorating system with increasing repair times, Applied Mathematical Modelling, 2013, 37: 9768–9775.

    Article  MathSciNet  MATH  Google Scholar 

  7. Zhang Y L and Wang G J, An optimal replacement policy for a multistate degenerative simple system, Applied Mathematical Modelling, 2010, 34: 4138–4150.

    Article  MathSciNet  MATH  Google Scholar 

  8. Liu H T, Meng X Y, and Wu WJ, The cold standby system with repair of non-new and repairman vacation, Journal of Computational Information Systems, 2012, 8: 1349–1357.

    Google Scholar 

  9. YuM M, Tang Y H, Liu L P, et al., A phase-type geometric process repair model with spare device procurement and repairman’s multiple vacations, European Journal of Operational Research, 2013, 25: 310–323.

    MathSciNet  MATH  Google Scholar 

  10. Lin D, Zuo M J, and Yam R C M, Sequential imperfect preventive maintenance models with two categories of failure modes, Naval Research Logistics, 2001, 48: 173–183.

    Article  MathSciNet  MATH  Google Scholar 

  11. Kim M J and Makis V, Optimal maintenance policy for a multi-state deteriorating system with two types of failures under general repair, Computers and Industrial Engineering, 2009, 57: 298–303.

    Article  Google Scholar 

  12. Zequeira R I and Brenguer C, Periodic imperfect preventive maintenance with two categories of competing failure modes, Reliability Engineering and System Safety, 2006, 91: 460–468.

    Article  Google Scholar 

  13. Castro I T, A model of imperfect preventive maintenance with dependent failure modes, European Journal of Operational Research, 2009, 16: 217–224.

    Article  MathSciNet  MATH  Google Scholar 

  14. Cheng G Q and Li L, An optimal replacement policy for a degenerative system with two-types of failure states, Journal of Computational and Applied Mathematics, 2014, 21: 139–145.

    Article  MathSciNet  MATH  Google Scholar 

  15. Wang G J and Zhang Y L, Optimal repair-replacement policies for a system with two types of failures, European Journal of Operational Research, 2013, 26: 500–506.

    Article  MathSciNet  MATH  Google Scholar 

  16. Chien Y H, A number-dependent replacement policy for a system with continuous preventive maintenance and random lead times, Applied Mathematical Modelling, 2009, 33: 1708–1718.

    Article  MathSciNet  MATH  Google Scholar 

  17. Chien Y H, Optimal number of minimal repairs before ordering spare for preventive replacement, Applied Mathematical Modelling, 2010, 34: 3439–3450.

    Article  MathSciNet  MATH  Google Scholar 

  18. Chien Y H and Chen J A, Optimal spare ordering policy for preventive replacement under cost effectiveness criterion, Applied Mathematical Modelling, 2010, 34: 716–724.

    Article  MathSciNet  MATH  Google Scholar 

  19. Sheu S H and Chien Y H, Optimal age-replacement policy of a system subject to shocks with random lead-time, European Journal of Operational Research, 2004, 19: 132–144.

    Article  MathSciNet  MATH  Google Scholar 

  20. Tang Y H, Yu M M, Fu Y H, et al., PH deteriorating repairable system with phase-type stochastic lead time and its optimal replacement policy, Journal of Systems Science and Mathematical Sciences, 2010, 30(9): 1222–1235 (in Chinese).

    MathSciNet  MATH  Google Scholar 

  21. Yu M M, Tang Y H, Fu Y H, et al., A deteriorating repairable system with stochastic lead time and replaceable repair facility, Computer & Industrial Engineering, 2012, 62: 609–615.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Economics and Management, Shanxi University, Taiyuan, 030006, China

    Qiaoqiao Gao

  2. College of Science, Yanshan University, Qinhuangdao, 066004, China

    Dequan Yue & Bing Zhao

Authors
  1. Qiaoqiao Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dequan Yue
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Bing Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Qiaoqiao Gao.

Additional information

This paper was recommended for publication by Editor CHEN Youhua.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gao, Q., Yue, D. & Zhao, B. The Ordering and Replacement Policy for the System with Two Types of Failures. J Syst Sci Complex 31, 1541–1553 (2018). https://doi.org/10.1007/s11424-018-6295-9

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11424-018-6295-9

Keywords

Search

Navigation