Linear Consecutive k-out-of-n Unrepairable System

Abstract

The consecutive  k-out-of-n repairable system has always been very populer models in reliability mathematics. It has been used to model various engineering systems, such as street-lamp system, microwave stations of a telecom network, oil pipeline system, and other engineering fields. This paper researched a linear consecutive k-out-of-n  unrepairable system. Assuming the system has no repairman, and the working time of each component is negative exponentially distributed and independent of each other. Firstly, study the liner consecutive four out of eight fail system in the particular example. Then we discuss two kinds of three and two units out of eight units fail, the system cannot work. Finally, according to the relationship of the n and k, the system will be discussed three cases to obtain failed probability and reliability by using total probability formula.

Key words: k-out-of-n, unrepairable system, key component.