Reliability Analysis Of The Voting Repairable System And Interrelated Issue

The voting repairable system is one of the most basis and important systems in the theory and the application of reliability models. It has a wide range of applications in integrate circuit design, the satellite relay communications system and other engineering fields. Much of the previous works on this topic have studied, but they suppose that components of the system are repaired immediately after fail and the failure units can be repaired as good as new.In this paper, by using Markov process theory, the supplementary variable technique, the Laplace transform and the geometric process, we will give a comprehensive study in the following respects:1. A k out of n cold standby repairable system with a repairman single vacation is considered. Assume that the components'lifetimes are exponentially distributed, repair times of the components and vacation times of repairman are both generally distributed, and every component is as good as a new one upon repair completion. By using the supplementary variable technique and the tool of Laplace transform, we derive the Laplace transform formulas of some main reliability indices of the system, such as MTTFF, the reliability, the steady state failure frequency etc. Furthermore, suppose repair times of the components Y Erlang ( 2,α), vacation times of repairman Z Erlang ( 2,β), we give an example of 2 out of 4 system to illustrate the sensitivity of the system.2. A k out of n cold standby repairable system with multiple delay vacations is studied. Assume that the components'lifetimes and the delay vacation time of the repairman are exponentially distributed, and repair times of the components and vacation times of repairman are both generally distributed. By using the supplementary variable technique and the tool of Laplace transform, we derive the Laplace transform formulas of some main reliability indices of Laplace transform of the system, such as MTTFF, the steady state availability, the asymptotic failure frequency etc. At last, an example is taken as to illustrate the gained conclusions.3. A two-dissimilar-unit cold standby repairable deteriorating system with single repairman vacation is considered. In practice, the lifetimes of the system become shorter and the repair times become longer with age and usage. For this problem, assumed that the components'consecutive lifetimes and the components'consecutive repair times form geometrical process, vacation times of the repairman are exponentially distributed, and each component is not'as good as new'after repair. The Laplace transform expressions of some main reliability indices of the system are obtained, such as the reliability, the availability and the asymptotic failure frequency etc. Furthermore, we have a study on a special caseÏ„=∞,a = b= 1,λ₁ =λ₂ =λ. The results of the system are more general than existing results in previous literatures.