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In many physical systems, reliability evaluation, such as ones encountered in telecommunications, the design of integrated circuits, microwave relay stations, oil pipeline systems, vacuum systems in accelerators, computer ring networks, and spacecraft relay stations, have had applied consecutive  k -out-of- n  system models. These systems are characterized as logical connections among the components of the systems placed in lines or circles. In literature, a great deal of attention has been paid to the study of the reliability evaluation of consecutive  k -out-of- n  systems. In this paper, we propose a new method to compute the reliability of consecutive  k -out-of- n :F systems, with  n  linearly and circularly arranged components. The proposed method provides a simple way for determining the system failure probability. Also, we write R-Project codes based on our proposed method to compute the reliability of the linear and circular systems which have a great number of components.

A new method for computing the reliability of consecutive k -out-of- n :F systems