The Maintenance Replacement Policy Of Some Reliability Models For Deteriorating Systems

In maintenance problem, it is often to assume that a failed system after repair will be'as good as new'. This is a perfect repair model. However, it is not always true in practice.Most systems are deteriorating because of the ageing effect and the accumulated wearing.Consequently, the successive operating times after repair are stochastically decreasing whilethe consecutive repair times after failure are stochastically increasing. Therefore, the studyof the reliability and the optimal maintenance and replacement policy have great theoreticaland practical significance.Based on the theory of geometric process, the reliability and the optimal maintenanceand replacement policy are analyzed in several new reliability and maintenance replacementmodels of deteriorating system. We derive some important reliability indices using thesupplementary variable method. Using renewal process theory, the explicit expression ofthe long-run expected cost per unit time of the system is derived. The optimal maintenanceand replacement policies which minimize the long-run expected cost per unit time of thesystem are given numerically. Some comparisons and analysis with existing policies arealso discussed by numerical methods.Firstly, we study the optimal replacement policy of series system with a cold standbycomponent. Assume that the system is consisting of three components and one repairman,where the component 1 and component 2 series and component 3 is standby unit as com-ponent 2. Adopting the replacement policy which based on the number of failures of thecomponent 1 and component 2, we derive the explicit expression of the long-run expectedcost per unit time of the system. The optimal replacement policy which minimize the ex-pected cost is provided numerically.Secondly, the optimal maintenance and replacement policy of the multistate deterioratesystem with preventive maintenance is discussed. Assume that the system has k + 1 dif-ferent states, including one working state and k failure states. The work will be interruptedand the preventive repair will be executed as soon as the system reliability reaches to anundetermined constant. By using a bivariate maintenance and replacement policy (R,N),the explicit expression of the long-run expected cost per unit time is derived. The deterio- rate multistate system with preventive maintenance is equivalent to the geometric processmodel with preventive repair for a two-state system. We also considered a special case,the optimal replacement policy of the two-failure-state deteriorate system with preventivemaintenance. The preventive repair will be executed as soon as the hazard rate reachesto an critical value. The explicit expression of the long-run expected cost per unit time isdetermined. The corresponding optimal mixed policy can be determined numerically. Wealso provide numerically some comparisons with two maintenance policies which are theperiodic preventive maintenance policy and the preventive maintenance policy based on re-liability. The result shows that the preventive maintenance policy based on the hazard rateis the optimal.Subsequently, we studied a simple repairable system with delayed repair and a replace-ment repair-facility. There is a delayed time before each repair and the repair-facility is notcompletely reliable. Using supplementary variable method, we derive some important reli-ability indices, for example, availability, reliability and MTTFF. Adopting the replacementpolicy N, we derive some important reliability indices and the explicit expression of thelong-run expected cost per unit time of the system. The optimal replacement policy whichminimize the expected cost is provided numerically.Then, the optimal replacement policy of a two-component cold standby system sub-jected toδ-shocks. We generalized the single-unit system subjected toδ-shocks. Assumethat the random shocks arrive according to a Poisson process. Whenever inerarrival times ofsuccessive shocks are less then a threshold which relates to the number of repairs, the work-ing component will fail. Using supplementary variable method, we derive some importantreliability indices. The explicit expression of the long-run expected cost per unit time isderived. We further determine numerically the optimal policy. Sensitivity analysis is alsoprovided.Finally, a simple repairable system with its repairman having multiple delayed vaca-tions is studied. There is a random waiting time before an formal vacation. Using sup-plementary variable method, we derive some important reliability indexes, for example,availability, reliability and MTTFF. Adopting replacement policy N which based on thenumbers of the failure, we give the explicit express of the long-run expected cost per unit time. The optimal replacement policy is provide numerically. Sensitivity analysis is alsoprovided.