Preventive Maintenance Strategy Of Several Types Of Reliability Systems Under The Shock Model

Shock model which is one of the important contents in the mathematical theory of reliability,are used for describing systems that are subject to shocks of random magnitudes in a stochastic environment.The lifetime distribution and maintenance strategy of the shock model have important research significance.In this paper,based on the reliability of system,we studied two different types of the shock model and discuss their preventive maintenance strategies.In the first model,this paper considers a cumulative damage model under ran-dom threshold and formulates preventive maintenance strategy.Different from previ-ous article system threshold is not constant,but is randomized.Under the condition of preventive maintenance,system fails only when the total damage exceeds a ran-dom threshold level L at some shock and is replaced before failure at time T,at shock N,or at damage Z.The expected cost rates of three replacement policies are ob-tained.Optimal preventive maintenance strategy which minimize the expected cost is discussed and some numerical examples are presented to illustrate application of the method.In the second model,system is subjected to external shocks which occur ac-cording to nonhomogeneous poisson process and shocks causes two different types of effects on the system Type ? shock,which causes system to fail and changes system failure rate,can be rectified by a general repair,while type ? shock results in a non-repairable failure and must,be fixed by a replacement.The occurrence of a particular type of shock is dependent on the arrival time of shocks since the last replacemen-t.The objective of this paper is to determine the optimal preventive maintenance strategy T before replacement that minimizes the expected cost rate.A numerical example is presented to validate the theoretical result.