On the quantile past lifetime of the components of the parallel systems

ABSTRACT

Let T_{1: n} ⩽ T_{2: n} ⩽ ⋅⋅⋅ ⩽ T_{n: n} be ordered lifetimes of components of a parallel system. In this article, the α-quantile past lifetime from the failure of the component with lifetime T_{r: n} provided that the system has failed at or before time t has been introduced. Then, some properties of this measure have been studied.

KEYWORDS:

• Parallel system
• Quantile past lifetime function
• Reversed hazard rate function

MATHEMATICS SUBJECT CLASSIFICATION:

• 90B25