On the Percentile Residual Lifetime of Parallel Systems

Abstract

In this paper, we consider a parallel system consisting of n components. Then, the percentile residual lifetime of the system given survival of at least n − r + 1, r = 1, 2, …, n component(s) has been introduced, and some properties of this measure have been investigated. We show that the system accommodates decreasing percentile residual lifetime function, provided the components have increasing hazard rate functions. Different parallel systems have been compared with each other in terms of the introduced measure. Furthermore, behavior of the percentile residual lifetime of the system and the components have been compared in terms of some reliability notions. Also, a characterization result has been presented.

Keywords:

• Parallel system
• Percentile residual lifetime
• Reliability measure

Mathematics Subject Classification:

• Primary 62E10
• Secondary 60E05