Eryilmaz, S.Kan, C.2025-06-052025-06-0520250951-832010.1016/j.ress.2025.1112292-s2.0-105005869605https://doi.org/10.1016/j.ress.2025.111229https://hdl.handle.net/20.500.14411/10614It is important in many respects to have information about the number of failed components in the system when or before a system fails. This paper investigates the mean number of failed components at or before the failure time of the linear consecutive k-out-of-n:F system which is a useful structure to model various engineering systems such as transportation and transmission systems. In particular, closed form expressions for the mean number of failed components within the system that have discretely distributed components lifetimes are obtained. The results are used to estimate the unknown parameter of the components’ lifetime distribution and to find the optimal replacement cycle that minimizes the expected cost per unit of time under a certain age-based replacement policy. © 2025 Elsevier Ltdeninfo:eu-repo/semantics/closedAccessAge ReplacementConsecutive K-Out-Of-N:F SystemDiscrete DistributionEstimationArticleQ1Q1263