Reliability of Linear Consecutive- k -Out-of- n Systems With Two Change Points

Linear consecutive-k-out-of-n systems are frequently used to model vacuum systems, telecommunication networks, oil pipeline systems, and the photographing of nuclear accelerators. Substantial research has been devoted to analyzing the reliability of such systems, using many different approaches and assumptions. Nevertheless, existing reliability formulas may not be suitable for all real systems. This paper therefore proposes a nonrecursive closed-form expression for a consecutive-k-out-of-n system that is made up of three types of nonidentical components. The corresponding dynamic survival function and mean time to failure are derived for the suggested system, and numerical experiments are carried out to illustrate its application.