Preservation properties of stochastic orders by transformation to Harris family

摘要

Stochastic comparisons of lifetime characteristics of reliability systems andtheir components are of common use in lifetime analysis. In this paper, using Harrisfamily distributions, we compare lifetimes of two series systems with random numberof components, with respect to several types of stochastic orders. Our results happento enfold several previous findings in this connection. We shall also show that severalstochastic orders and ageing characteristics, such as IHRA, DHRA, NBU, and NWU,are inherited by transformation to Harris family. Finally, some refinements are madeconcerning related existing results in the literature.