Reliability and optimal age-based replacement policy for consecutive 2-out-of-n:G system equipped with protection blocks

Abstract

This paper concerns the reliability evaluation and optimal age-based replacement policy for the linear consecutive 2-out-of-$n$:G system whose two consecutive components are protected by a block that has its own failure rate. Two alternative methods are proposed to compute the reliability of the system. The first method is based on direct probabilistic approach and uses the reliability of the ordinary consecutive 2-out-of-$n$:G system. The second method is based on the concept of survival signature. Closed form equations for the system reliability and the mean number of failed components within the system are obtained. The optimal age-based replacement policy is also defined and studied. Extensive numerical results are presented to illustrate the findings.