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Article Citation - WoS: 15Citation - Scopus: 16Residual Lifetime of Consecutive k-out-of-n< Systems Under Double Monitoring(Ieee-inst Electrical Electronics Engineers inc, 2012) Eryilmaz, Serkan; Bayramoglu, KonulThe consecutive k-out-of-n systems are important structures in reliability engineering due to their applications in various real life situations. In this paper, we study the residual lifetime of these systems under the condition that the total number of failed components at time is, and at time t(2) (t(2) > t(1)) the system is still working. We obtain explicit expressions for the survival function of the corresponding residual life when the components are exchangeably dependent. We also obtain a signature-based mixture representation for a coherent system satisfying a certain property.Article Citation - WoS: 18Citation - Scopus: 17Reliability of Combined m-consecutive-k< and Consecutive kc< Systems(Ieee-inst Electrical Electronics Engineers inc, 2012) Eryilmaz, SerkanA combined m-consecutive-k-out-of-n:F & consecutive-k(c)-out-of-n:F system consists of linearly ordered components, and fails iff there exist at least k(c) consecutive failed components, or at least m non-overlapping runs of k consecutive failed components. This structure has applications for modeling systems such as infrared detecting and signal processing, and bank automatic payment systems. In this paper, we derive a combinatorial equation for the number of path sets of this structure including a specified number of working components. This number is used to derive a reliability function, and a signature based survival function formulae, for the system consisting of i.i.d. components. We also obtain a combinatorial equation for the reliability of a system with Markov dependent components.
