Optimal Replacement Policy for Multi-State System Under Imperfect Maintenance

Yu Liu, Hong-Zhong Huang
2010 IEEE Transactions on Reliability  
A multi-state system (MSS) has more than two discrete states corresponding to different performance rates. Usually, MSS is viewed as in a failure state once its performance rate falls below user demand, and maintenance is carried out immediately. Generally, the repaired system cannot be regarded as good as new, and oftentimes the system restoration is stochastic. We introduce an optimal replacement policy for MSSs, called policy . Under this policy, a MSS is replaced whenever its failure number
more » ... reaches . We assess the dynamic element state probabilities of each aging multi-state element (MSE) using a stochastic process model which is identified as a non-homogeneous continuous time Markov model (NHCTMM), and we evaluate the state distribution of the entire MSS via the combination of the stochastic process, and the universal generating function (UGF). To quantify the quality of imperfect maintenance, a quasi-renewal process is used to describe the stochastic behavior of each individual MSE after repair. Moreover, we derive an explicit expression of the long-run expected profit per unit time, and determine the optimal failure number to replace the entire system. The proposed models are demonstrated via an illustrative case, followed by some comparative studies. Index Terms-Imperfect maintenance, maintenance policy, multi-state systems, non-homogeneous continuous time Markov model, quasi-renewal process, universal generating function. ACRONYMS MSS multi-state system MSE multi-state element MTTF mean time to failure UGF universal generating function NHCTMM non-homogeneous continuous time Markov model NOTATION Number of the -independent element in the MSS Number of possible states for element Performance rate of element in state Set of all possible performance rates of element Random variable representing the performance rate of element at time Manuscript
doi:10.1109/tr.2010.2051242 fatcat:fcxqcaduofgypmjofrdg3jvnt4