On Reliability Function of a k-out-of-n Model in Case of Quick Recovery of Its Components

Vladimir Rykov, Nika Ivanova
In some previous works, closed-form representations for reliability characteristics of k-out-of-n model with an exponential distribution of components lifetime and arbitrary distribution of their repair time have been found. In that investigation, the markovization method was applied for calculation of the main reliability characteristics. In the recent paper, reliability function is considered for a repairable k-out-of-n model in the same assumptions about life and repair time distributions. The problem of its sensitivity in case of quick recovery of system’s components is discussed on an example of 2-out-of-n model. It is shown that the reliability function in scale of its mean time to failure is asymptotically exponential.