Reliability Analysis Of A Special System

Reliability applications in military technology has extended to the national economy in many areas since the eighties of the last century's research, while the consecutive-k-out-of-n system and related systems has progressed very rapidly and achieved a great deal of results. Up to the present, research in this area has not yet stopped. This system is widely found in engineering practice in a class of systems, such as street lighting systems, microwave towers, which can use consecutive-k-out-of-n: F systems to describe. There are many articles in different conditions, using different methods to estimate the bounds for the reliability of the consecutive-k-out-of-n: F system, this paper also used different methods to make some research.We do the following research in this paper:Firstly, on the assumption that each component is independent but has different distributions, to the un-repairable consecutive-k-out-of-n F system, On the one hand we give a precise formula to compute the reliability of the consecutive- k- out-of-n: F system using consecutive minimal cut sets. On the other hand we give the upper and lower bounds for the consecutive-k-out-of-n: F system by using the associated property of random variable.Secondly, we consider a linear consecutive-k-out-of-n: F repairable system with one repair man. Assume that the working time and the repair time of the components in the system are both exponentially distributed, and each component after repair is `as good as new'. By using the generalized transition probability, the state transition probabilities in the system are derived.Thirdly, we consider a circular consecutive-2-out-of-3: F repairable system with one repair man. Assume that the working time and the repair time of the components in the system are both exponentially distributed, and each component after repair is'as good as new'. Finally we get the Laplace transformation of the system's reliability and the MTTFF. And then using the generalized transition probability, the state transition probabilities in the complicated consecutive-k-out-of-n: F system are derived.Finally, we study of the consecutive-k-out-of-n: F system under Poisson shock. Assume that the number of the shock arrivals forms a Poisson process with parameterλ, and the shock value submits of certain distribution. Each component is independent, and the repair time of the components in the system are both exponentially distributed. The system has one repairable man, by using the generalized transition probability, the state transition probabilities in the system are derived, and then we obtain some reliability indices such as the system availability and the system average working time.