Investigation of the repairable consecutive k-out-of-n: F system

The consecutive k-out-of-n:F system is defined as a system which consists of n components such that the system breakdowns if and only if at least k consecutive components fail. Another special type of system related to the consecutive k-out-of-n:F system is the consecutive k-out-of-n:G system. A consecutive k-out-of-n:G system is an ordered sequence of n components such that the system works if and only if at least k consecutive components work. If we consider that components are repairable, then consecutive k-out-of-n systems are called a repairable systems. In this study, we will examine the repairable consecutive k-out-of-n:F system and try to determine its reliability at any time t for situations where the system is linear and circular.