The Replacement Policy For Some Repairable System And Its Reliability Research

In repair-replacement problem, it is usually assumed that the system afterrepair is “as good as new”. This is very perfect repair model. However, it is notalways true in practice, most repairable system are deteriorative because of theenvironment influences, the repair equipment effect and the repair horizontalinfluences. By using the geometric process and the renewal process, therepair-replacement policy for some repairable system are considered. Theexplicit expression of the long-run average cost per unit time is obtained. Anumerical example is given to illustrate the uniqueness of the optimalreplacement policy, the sensitivity analysis the influence of the importantparameters of the model for the optimal replacement policy and average cost.Firstly, we consider the replacement policy of one-component repairablesystem with one repairman, who can have two vacation parameters. When thesystem is working, the repairman will taking vacation pattern one with aprobability p, in contrast, the repairman will taking vacation pattern two with aprobability1-p.We consider a replacement policy N based on the number of thefailures of the system. The expression for the average cost of the system isderived. A numerical example is given to analysis the average cost andreplacement policy of the system. Secondly, the optimal replacement policy for a warm-standby systemconsisting of two dissimilar components is studied. Assume that eachcomponent after repair is not “as good as new” and component1has priority inuse, the component2can repair “as good as new” after warm-standby failures.The system will be replaced if the repair times of component1reachN, Theexplicit expression of the average cost is derived, and the corresponding optimalreplacement policy can be determined analytically or numerically.Finally, a shock maintenance model for a two-component series systemwith preventive repair is considered. Assume that the interarrival time of theshocks a truncated normal distribution. When the shock has been arrived, thesystem will be interrupted and the preventive repair for component1isexecuted at once. An optimal replacement policy N1, N2is studied, based onthe number of the failures of component1and component2. The explicitexpression of the average cost is derived, and the corresponding optimalreplacement policy can be determined analytically or numerically. Finally, anumerical example is given to illustrate the existing of the replacement policyand the sensitivity analysis for the average cost with respect to parameters.