An optimal repair–replacement policy for a cold standby system with use priority

Abstract In this paper, the maintenance problem for a cold standby system consisting of two dissimilar components and one repairman is studied. Assume that both component 1 and component 2 after repair follow geometric process repair and component 1 is given priority in use when both components are workable. Under these assumptions, using geometric process repair model, we consider a replacement policy N under which the system is replaced when the number of failures of component 1 reaches N. Our purpose is to determine an optimal replacement policy N∗ such that the average cost rate (i.e. the long-run average cost per unit time) of the system is minimized. The explicit expression for the average cost rate of the system is derived and the corresponding optimal replacement policy N∗ can be determined analytically or numerically. Finally, a numerical example is given to illustrate some theoretical results and the model applicability.

[1]  Sebastian Martorell,et al.  Age-dependent reliability model considering effects of maintenance and working conditions , 1999 .

[2]  Qun Liu,et al.  A geometric process model for M , 2006, Eur. J. Oper. Res..

[3]  Sheldon M. Ross,et al.  Stochastic Processes , 2018, Gauge Integral Structures for Stochastic Calculus and Quantum Electrodynamics.

[4]  Ming Jian Zuo,et al.  Reliability analysis for a circular consecutive-2-out-of-n: F repairable system with priority in repair , 2000, Reliab. Eng. Syst. Saf..

[5]  Yeh Lam.  A maintenance model for two-unit redundant system , 1997 .

[6]  Yuan Lin Zhang.  An optimal geometric process model for a cold standby repairable system , 1999 .

[7]  G. J. Wang,et al.  Replacement problems for a cold standby repairable system , 2006, Int. J. Syst. Sci..

[8]  R. Barlow,et al.  Optimum Preventive Maintenance Policies , 1960 .

[9]  John A. Buzacott.  Availability of Priority Standby Redundant Systems , 1971 .

[10]  A. D. Jerome Stanley,et al.  On geometric processes and repair replacement problems , 1993 .

[11]  Y. Lam,et al.  Analysis of a two-component series system with a geometric process model , 1996 .

[12]  T. H. Savits,et al.  Age Dependent Minimal Repair. , 1985 .

[13]  Ming J. Zuo,et al.  Optimal replacement policy for a multistate repairable system , 2002, J. Oper. Res. Soc..

[14]  Maxim Finkelstein.  A scale model of general repair , 1993 .

[15]  Yuan Lin Zhang.  An optimal replacement policy for a three-state repairable system with a monotone process model , 2004, IEEE Trans. Reliab..

[16]  Yuan Lin Zhang.  A geometrical process repair model for a repairable system with delayed repair , 2008, Comput. Math. Appl..

[17]  Lam Yeh,et al.  Analysis of a parallel system with two different units , 1996 .

[18]  Toshio Nakagawa,et al.  Stochastic behaviour of a two-unit priority standby redundant system with repair , 1975 .

[19]  Leung Kit-Nam Francis.  OPTIMAL REPLACEMENT POLICIES DETERMINED USING ARITHMETICO-GEOMETRIC PROCESSES , 2001 .

[20]  Y. M. Lee,et al.  Using geometric processes to study maintenance problems for engines , 1998 .

[21]  Yeh Lam,et al.  Repairable consecutive‐k‐out‐of‐n: F system with Markov dependence , 2000 .

[22]  Shey-Huei Sheu,et al.  Opportunity-based age replacement policy with minimal repair , 1999 .

[23]  Yeh Lam,et al.  Reliability of consecutive-k-out-of-n: G repairable system , 1998, Int. J. Syst. Sci..

[24]  G. J. Wang,et al.  A shock model with two-type failures and optimal replacement policy , 2005, Int. J. Syst. Sci..

[25]  Inmaculada Torres Castro,et al.  Reward optimization of a repairable system , 2006, Reliab. Eng. Syst. Saf..

[26]  Shey-Huei Sheu,et al.  A Bayesian perspective on age replacement with minimal repair , 1999 .

[27]  Yuan Lin Zhang,et al.  A geometric process repair model for a series repairable system with k dissimilar components , 2007 .

[28]  Ming Jian Zuo,et al.  Optimal replacement policy for a deteriorating production system with preventive maintenance , 2001, Int. J. Syst. Sci..

[29]  L. Yeh.  A note on the optimal replacement problem , 1988, Advances in Applied Probability.

[30]  M. Kijima.  SOME RESULTS FOR REPAIRABLE SYSTEMS WITH GENERAL REPAIR , 1989 .

[31]  Lin Ye.  Geometric processes and replacement problem , 1988 .

[32]  John Yuan,et al.  Optimal maintenance policy for a Markovian system under periodic inspection , 2001, Reliab. Eng. Syst. Saf..

[33]  R. I. Phelps.  Replacement Policies under Minimal Repair , 1981 .

[34]  R. Jiang,et al.  Age replacement policy: a multi-attribute value model , 2002, Reliab. Eng. Syst. Saf..

[35]  Yuan Lin Zhang.  A geometric-process repair-model with good-as-new preventive repair , 2002, IEEE Trans. Reliab..

[36]  Zehui Li,et al.  An extended extreme shock maintenance model for a deteriorating system , 2008, Reliab. Eng. Syst. Saf..

[37]  Y. Zhang.  A bivariate optimal replacement policy for a repairable system , 1994 .

[38]  Wolfgang Stadje,et al.  Optimal strategies for some repair replacement models , 1990 .

[39]  Kyung S. Park.  Optimal Number of Minimal Repairs before Replacement , 1979, IEEE Transactions on Reliability.