Cold Standby Repairable Deteriorating System With Single Repairman Vacation

Cold standby system which composed of two-units is one of the most classicaland important models in the theory and application of reliability models.There aremany scholars has been studied on this topic extensively and obtained a lot ofachievements. But their reseaches only separately consider the failure units can berepaired as good as new.or repairman vacations However,because of the system isaging and wearing out, and sometimes in order to keeping the repairman highworking efficiency ,or for the purpose of increase system income and letting himengaged in other work,so, it is more suitable to consider these two factors togetherOn the basis of the predecessors, through the use of Markov process theory,monotonous process the supplementary variable technique , and the Laplacetransform method ,this paper will give a comprehensive study in the following twosituations:1. Assmed that each component of the system is not‘as good as new’after repair,and the components’lifetimes and the components’repair times constitute ageometrical process, vacation times of the repairman are exponentiallydistributed,and two components lifetimes from the same distributed. By usinggeometric process, the supplementary variable method and the LaplaceTransform tool, we derive the Laplace transform formulas of some mainreliability indices of the system, such as the availability, MTTFF and theasymptotic failure frequency etc. Furthermore, we have a study on a special caseτ=∞，a = b=1,λ₁ =λ₂ =λ.2. In practice, as the lifetimes of the system become shorter and the repair timesbecome longer, vacation times of the repairman will gradually reduction. Basedon this consideration, we continue to assumed that the components’lifetimesand the components’repair times and vacation times of the repairman are allconstitute monotonous process, and each component is not‘as good as new’afterrepair. The Laplace transform expressions of some main reliability indices of thesystem are obtained, such as the reliability, the availability，MTTFFand theasymptotic failure frequency etc. Furthermore, we disscuss a special case : τ=∞, a = b = c = 1,β_n¹（ y ）=μ₁,β_n ² （ y ）=μ₂,α_n¹ （ x ） =λ₁（ x ）,α_n²（ x ） =λ₂（ x）...