Reliability Analysis for k/n(G) System under Poisson Shock

In this paper, a k/n(G) system (i.e. k-out-of-n: G system) under Poisson shock is studied. Assume that the number of the shock arrivals forms a Poisson process with parameter \lambda, and the shock value submits to certain distribution. When a shock arrives, all working components in this system will independently produce a random effect. Assume further that the failure probability of the working component under the shock is the function of the shock value, and each shock will independently produce the system loss until the system failure happen when the number of working components in this system is less than k. Under these assumptions, we can obtain the system reliability function and the system average working time. Further, if the system is repairable, and there is a repairman in this system. We can assume that repair rule is "first in first out", and each failure component after repair can be "as good as new". When the time of repairs is an exponential distribution, the state transfer of the system submits to Markov process. Thereafter, we can establish the state transfer equations of the system, and obtain some reliability indices such as the system availability and the system average working time, the system average stopping time and the system failure frequency under the steady state. Finally, a simple example is given to illustrate the model proposed.