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Article Citation - WoS: 6Citation - Scopus: 8The Mean Number of Failed Components in Discrete Time Consecutive K-Out F System and Its Application To Parameter Estimation and Optimal Age-Based Preventive Replacement(Elsevier Sci Ltd, 2025) Eryilmaz, Serkan; Kan, CihangirIt 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.Article Citation - Scopus: 1The Distribution of Wind Power from a Dispersed Array of Wind Turbine Generators and Its Reliability Based Applications(Elsevier, 2026) Eryilmaz, Serkan; Kan, Cihangir; Devrim, YilserIn this paper, the probability distribution of wind power from a dispersed array of wind turbine sites is studied considering forced outage rates of wind turbines. The wind speeds at distinct sites are assumed to be dependent and the dependence is modeled by copulas. In particular, the probability distribution of the aggregate power from two sites is exactly derived. The probability distribution of the aggregate power is also derived under the particular case when site 1 consists of n1 identical wind turbines of type 1 and site 2 consists of n2 identical wind turbines of type 2. Numerical results are presented to illustrate the theoretical findings for a chosen copula function.