Defective Parts Can Not Be Repaired, Such As The New Alignment Adjacent N Continuous K System Reliability Analysis

Consecutive-k-out-of-n system is widely applied in engineering .For example, street-lamp system and microwave system may be generalized by it. The dependability of consecutive-k-out-of-n system has been investigated by many researchers so far, but they suppose that the system is not repairable or the failure units can be repaired as good as new.In this paper, we shall study the dependability of consecutive-n-1-out-of-n: G repairable system under the following respective assumptions :Firstly, it is assumed that the life distribution and the repair distribution of each component are exponential distributions. Under this assumption, the failure units can not be repaired as good as new and key components have higher priority for repair. By introducing supplementary variable Ii(t) which is the period of the component / at time t ,we construct a generalized Markov process {N(t),Ii(t),...,In(t),t 0}and give L transforms of some reliability indices such as availability, reliability and MTTFF .Secondly, propose that the life distribution of each component is exponential distribution and the repair distribution of each component is general distribution. Under this assumption, the failure units can not be repaired as good as new and are to be repaired by "first in first out" rule.By inducting supplementary variable Ii(t) which is the period of the component i at time t and the repair time Yi (t) that has been spent on the being repaired component i in the Ii(t)th period ,we construct a generalized Markov process and derive L transforms of some reliability indices such as availability, reliability and MTTFF. What's more, we draw a conclusion that if the life distribution and the repair distribution of each component are exponential distributions, the repair rules have no effect on reliability and MTTFF.Thirdly, we give an example to illustrate applications of conclusions obtained above .Finally, suppose that failure units of 2-out-of-n: F system can not be repaired as good as new, L transforms of some reliability indices of this system are attained.