On Asymptotic Insensitivity of Reliability Function of a 2-out-of-n Model Under Quick Recovery of Its Components

In some previous papers, closed-form representations for the reliability characteristics of k-out-of-n models with an exponential distribution of components lifetimes and arbitrary distributions of their repair times have been found. In those investigations, the markovization method was applied for calculation of the main reliability characteristics, including the reliability function in terms of Laplace transform. In the recent paper, the reliability function is calculated for a repairable 2-out-of-n model in the same assumptions about life and repair times distributions. The problem of its sensitivity in case of quick recovery of system’s components and exponentially distributed repair time is discussed with the same example. It is proved that the reliability function in scale of its mean time to failure is an exponential one. An estimation of convergence rate is also obtained. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.