On the dependability function of a system. Part I. Analytical results

The paper aims to study the primary dependability characteristics of restorable k-out-of-n systems with arbitrary distributions of failure-free time and time to component repair, as well as the total number of repair units. A k-out-of-n system is a system consisting of n components that fails when k out of its (k≤n) components fail. l repair devices are available for restoring failed components. Such a system is denoted as <GI k≤n |GI|l>. The research employed marked Markov processes and the theory of order statistics. Using the proposed approach, a mathematical system model was constructed, marks transformations were mapped and analytic expressions for calculating their distributions were given. In the following part of the paper, using the proposed method, a simulation algorithm will be defined for the purpose of assessing the key dependability characteristics. It will not only enable a numerical study of such systems, but will also help analyse the sensitivity of the dependability characteristics to the initial system parameters.