An Optimal Replacement Policy For The Repair System Under ?-power Process

Study on the maintenance policy is an important content in the theory of reliability,which is widely used in the engineering application.It is important practical significance to research the optimal replacement strategy.In the past,many papers are assumed to be perfect maintenance to repair a repairable system,namely the repair is "as good as new",but in fact,system failure after the repair is not "as good as new" which is a deteriorating repairable system.Based on existing research results,the optimal replacement policy is studied for more in-depth research and application in this thesis.To simulate the components process operation state by using the a-power and the renewal process theory.We derived the explicit expressions of the expected cost rate by using the extended maintenance policy N,and through the analysis and numerical simulation,we verified the existence and uniqueness of the optimal replacement policy.In this thesis,the main work is listed as follows:?1?Under Poisson shock,a one-component repairable system is considered.The system after repair is not "as good as new".The system's failure may be due to external shocks or intrinsic factors.The shocks arrive according to a Poisson process.Assume that the successive threshold values follow a non-decreasing geometrical process after repair and the repair time of the system is a-power process.Using the theory of renewal process,the explicit expression of the expected long run cost rate is derived and the corresponding optimal policy can be determined analytically or numerically.And the existence and uniqueness of the optimal replacement policy N*is proved.Finally,several numerical examples are given to visualize some theory results in this model.?2?On the basis of the past chapter' shock model,considering the system failure is may caused by many different factors,we assume that the system has two types of failures when it fails and the repair systems with delay repair characteristics.Using extended repair policy N,the shock model was established by using the theory of renewal process and a-power process,the expression of the average loss of the system after long-run operation in unit time is obtained.Finally a numerical example is given to illustrate the existence and uniqueness of the optimal replacement policy.?3?Based on the theory of downtime,the cold standby repairable system with delayed repair optimization model is been considered.The system consists of two different units and one repairman,and the system after repair is not "as good as new".Under the?-power process,the explicit expression of the long-run expected cost rate and downtime rate on the replacement policy under the bivariate policy?N₁,N₂?are derived.The optimal replacement policy with minimizing the expected down-time rate subject to an appropriate cost rate can be got.Finally,a numerical example is given to illustrate some theoretical result in this thesis.