Abstract
In this paper, we consider the replacement of a single unit with catastrophic failure mode. Besides replaced at a preset time, the unit is also replaced at failure time or if it encounters a production wait and its age has reached a threshold. The joint preventive maintenance interval and threshold optimization problem are formulated with the objective of minimizing the expected cost per unit time in long run. A numerical example is presented to illustrate the applicability of the model.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Abbreviations
- C f :
-
Average cost of a failure replacement
- C p :
-
Average cost of an age replacement
- C w :
-
Average cost of a replacement at production wait
- C(T, τ):
-
The long run cost per unit time
- E[C]:
-
The expected renewal cycle cost
- E[Z]:
-
The expected renewal cycle length
- f X (t):
-
Probability density function of X, t ∈ (τ, T]
- F X (t):
-
Cumulative distribution function (CDF) of X
- N(t):
-
The number of production waits that occur during [0, t]
- T :
-
The planned replacement time which ranges over [0,∞)
- X :
-
The random variable denoting the age of the unit with PDF f X (t) and CDF F X (t) = P{X ⩽ t}
- Y :
-
The random arrival time of the nearest production wait that occurs after time τ
- Z :
-
The random length of a renewal cycle
- λ :
-
The arrival rate of the production wait
- τ :
-
The age threshold representing the minimum age requirement for replacing the unit at production wait
References
Nakagawa T. Maintenance theory of reliability [M]. London: Springer-Verlag, 2005.
Wang W B. An overview of the recent advances in delay-time-based maintenance modelling [J]. Reliability Engineering and System Safety, 2012, 106: 165–178.
Barlow R E, Proschan F. Mathematical theory of reliability [M]. New York: John Wiley & Sons Ltd., 1965.
Dohi T, Kaio N, Osaki S. Maintenance, modeling and optimization [M]. Boston: Kluwer Academic Publishers, 2000.
Kaio N, Dohi T, Osaki S. Stochastic models in reliability and maintenance [M]. New York: Springer-Verlag, 2002.
Dohi T, Kaio N, Osaki S. Handbook of reliability engineering [M]. London: Springer-Verlag, 2003.
Wang W B. Models of inspection, routine service, and replacement for a serviceable one-component system [J]. Reliability Engineering and System Safety, 2013, 116: 57–63.
Wang W. Delay time modelling, in complex system maintenance handbook [M]. Amsterdam: Springer-Verlag, 2008.
Wang W B, Zhao F, Peng R. A preventive maintenance model with a two-level inspection policy based on a three-stage failure process [J]. Reliability Engineering and System Safety, 2014, 121: 207–220.
Ross S M. Introduction to probability models [M]. New York: Elsevier, 2007.
Wang W, Christer A H. Solution algorithms for a nonhomogeneous multicomponent system inspection model [J]. Computer and Operations Research, 2003, 30: 19–34.
Author information
Authors and Affiliations
Corresponding author
Additional information
Foundation item: the National Natural Science Foundation of China (Nos. 11426084, 11001005, 71231001, 71301009 and 71420107023), the China Postdoctoral Science Foundation Funded Project (No. 2013M530531), the Natural Science Foundation of Hebei Province (No. A2014208133), the Foundation of Hebei Education Department (No. QN2014132) and the Ministry of Education Doctor of Philosophy Supervisor Fund (No. 20120006110025)
Rights and permissions
About this article
Cite this article
Wang, Wb., Li, P. & Peng, R. Optimal preventive maintenance policy with consideration of production wait. J. Shanghai Jiaotong Univ. (Sci.) 20, 322–325 (2015). https://doi.org/10.1007/s12204-015-1630-y
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12204-015-1630-y