Reliability evaluation of m -consecutive- k,l -out-of- n: F system subjected to shocks

In this paper, we propose a shock model for an m-consecutive-k, l-out-of-n: F system. This paper presents a reliability analysis of an m-consecutive-k, l-out-of-n: F system subjected to shocks that destroy a random number of components. One of the main random variables is the number of components affected by successive shocks. Phase-type distributions have been used to model the intervals between successive shocks. The main objective of this study is to show how phase-type distributions can be used to determine the reliability of m-consecutive-k, l-out-of-n: F systems subjected to shocks, which destroy a random number of components. Consideration is given to the optimal replacement time problem, which addresses the minimization of the total long-run average cost per unit time.