PRESERVATION PROPERTIES OF STOCHASTIC ORDERS BY
TRANSFORMATION TO HARRIS FAMILY
Mohammad Hossein Alamatsaz
Abstract: Stochastic comparisons of lifetime characteristics of reliability systems and their
components are of common use in lifetime analysis. In this paper, using Harris family
distributions, we compare lifetimes of two series systems with random number of
components, with respect to several types of stochastic orders. Our results happen to enfold
several previous findings in this connection. We shall also show that several stochastic orders
and ageing characteristics, such as IHRA, DHRA, NBU, and NWU, are inherited by
transformation to Harris family. Finally, some refinements are made concerning related
existing results in the literature.
2010 AMS Mathematics Subject Classification: Primary: 60E15; Secondary:
Keywords and phrases: Ageing intensity order, Marshall–Olkin distribution,
proportional stochastic order, shifted stochastic order, shifted proportional stochastic order,
usual stochastic order.