On the profust reliabilities of consecutive k-out-of-n systems

System reliability concept is a very popular topic among scientific research areas. Systems may be classified based on their structures such as linear and circular, based on their evaluation characteristics such as fuzzy and nonfuzzy states and based on working principles such as F and G systems. Linear and circular system distinction is originated from ordering difference of components. System and/or component states can be evaluated as fuzzy and nonfuzzy. If system and component states are both evaluated as nonfuzzy, then the reliability of such a system is considered as conventional reliability. On the contrary, if system or component states are evaluated as fuzzy, then reliability of such a system is considered as fuzzy reliability. While the working principle is defined with respect to the number of failed components for an F system, it is defined with respect to the number of working components for a G system. A consecutive k-out-of-n:F system composes of a sequence of n ordered components such that the system is failed if and only if at least k consecutive components in the system are failed. Similarly, consecutive k-out-of-n:G system composes of a sequence of n ordered components such that the system works if and only if at least k consecutive components in the system work. In this study, we research the profust (states of components are evaluated as nonfuzzy and state of system is evaluated as fuzzy) reliabilities of consecutive k-out-of-n:F and G systems considering both linear and circular sequence of n components. The reliabilities of these systems are evaluated for independent and identically distributed components. Easy-to-use formulas for the reliabilities of these systems are obtained using the distribution of some run statistics. In order to use these formulas, the working probability of a component at any time is sufficient. Some numerical results and figures are also presented to acquire some information about the reliabilities of related systems and to compare performance differences between conventional and profust reliabilities of systems considered in this study. © 2013 IMechE.