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Some New Results on Uncertain Age Replacement Policy

  • Zhang, Chunxiao ;
  • Guo, Congrong
  • Received : 2012.09.03
  • Accepted : 2013.03.06
  • Published : 2013.03.31

Abstract

Age replacement policy is a commonly policy in maintenance management of spare part. It means that a spare part is always replaced at failure or fixed time after its installation, whichever occurs first. An optimal age replacement policy of spare parts concerns with finding the optimal replacement time determined by minimizing the expected cost per unit time. The age of the part was generally assumed to be a random variable in the past literatures, but in many situations, there are few or even no observed data to estimate the probability distribution of part's lifetime. In order to solve this phenomenon, a new uncertain age replacement policy has been proposed recently, in which the age of the part was assumed to be an uncertain variable. This paper discusses the optimal age replacement policies by dealing with the parts' lifetimes as different distributed uncertain variables. Several results on the optimal age replacement time are provided when the lifetimes are described by the uncertain linear, zigzag and lognormal distributions.

Keywords

Age Replacement Policy;Uncertain Renewal Process;Optimal Replacement Time;Uncertainty Distribution

References

  1. Barlow, R. E. and Hunter, L. C. (1960), Optimum preventive maintenance policy, Operation Research, 8(1), 90-100. https://doi.org/10.1287/opre.8.1.90
  2. Brown, M. and Proschan, F. (1983), Imperfect repair, Journal of Applied Probability, 20(4), 851-859. https://doi.org/10.2307/3213596
  3. Kahneman, D. and Tversky, A. (1979), Prospect theory: an analysis of decision under risk, Econometrica, 47(2), 263-292. https://doi.org/10.2307/1914185
  4. Lin, Y. (1988), Geometric processes and replacement problem, Acta Mathematicae Applicatae Sinica, 4 (4), 366-377. https://doi.org/10.1007/BF02007241
  5. Liu, B. (2007), Uncertainty Theory (2nd ed.), Springer-Verlag, Berlin.
  6. Liu, B. (2008), Fuzzy process, hybrid process and uncertain process, Journal of Uncertain Systems, 2(1), 3-16.
  7. Liu, B. (2009), Some research problems in uncertainty theory, Journal of Uncertain Systems, 3(1), 3-10.
  8. Liu, B. (2010), Uncertainty Theory: A Branch of Mathematics for Modeling Human Uncertainty, Springer-Verlag, Berlin.
  9. Liu, B. (2013), Uncertainty Theory (4th ed.), Uncertainty Theory Laboratory, Beijing.
  10. Tilquin, C. and Cleroux, R. (1975), Periodic replacement with minimal repair at failure and adjustment costs, Naval Research Logistics Quarterly, 22(2), 243-254. https://doi.org/10.1002/nav.3800220204
  11. Yao, K. and Ralescu, D. A. (2013), Age replacement policy in uncertain environment, Iranian Journal of Fuzzy Systems, 10(2), 29-39.
  12. Zhang, Y. L. (1994), A bivariate optimal replacement policy for a repairable system, Journal of Applied Probability, 31(4), 1123-1127. https://doi.org/10.2307/3215336