Reliability And Maintennance Replacement Policy Of Cold Standby Systems With Two Units

Cold standby repairable system with two components is an important system inreliability theory. Based on the theory of geometric process, the reliability and theoptimal maintenance and replacement policy are analyzed in cold standby repairablesystem with two units. Some important reliability indexes are derived by applying thesupplementary variable method. Using geometric process and renewal process theory,the explicit expression of the long-run expected cost per unit time of the system isderived. The optimal replacement policy is analyzed through numerical examples.Firstly, the maintenance and replacement policy of a cold standby repairablesystem with two-unit and two-repairman is investigated. Under the condition that thefailure units can’t be repaired as new units, the explicit expressions of the long-runaverage cost per unit time is derived. The optimal replacement policy can be calculatednumerically. Under the optimal replacement policy, two repairmen model and onerepairman model are compared, and some numerical results are obtained.Secondly, the problem of the reliability of cold standby repairable system withtwo components and synchronous multiple vacation is investigated. Assume that thework time and repair time of two units follows exponential distributions and thevacations follows general distribution. The repair for component1is geometric andthe repair for component2is as good as new. Under these assumptions, using thegeometric process theory and Laplace transformation, some important reliabilityindexes of the system are obtained.Finally, the problem of the maintenance and replacement policy of cold standbyrepairable system of two components with multiple synchronous and delay vacation isinvestigated. Assume that the work time, the repair time, the vacation time and thedelay time of two repairmen follow exponential distributions. Under the condition thatthe failure units can’t be repaired as new units. The explicit expressions of the long-runaverage cost per unit time is derived by using the geometric process and the renewalreward theorem. The optimal replacement policy is calculated numerically. Under each replacement policy, the multiple synchronous vacation model and non-vacation modelare compared, and some numerical results are obtained. Finally the influence of someimportant parameters for the optimal average cost and the replacement policy arediscussed.