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WROCŁAW UNIVERSITY
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Contents of PMS, Vol. 41, Fasc. 2,
pages 347 - 358
DOI: 10.37190/0208-4147.41.2.8
Published online 14.9.2021
 

On a conjecture about the comparability of parallel systems with respect to the convex transform order

Idir Arab
Milto Hadjikyriakou
Paulo~Eduardo Oliveira

Abstract:

We study the comparability of the lifetimes of heterogeneous parallel systems with independent exponentially distributed components. It is known that the order statistics of systems composed of two types of components may be comparable with respect to the star transform order. On what concerns the stronger convex transform order, results have been obtained only for the sample maxima assuming that one of the systems is homogeneous. We prove, under the same assumptions as for the star transform ordering, that the lifetimes of heterogeneous parallel systems are not comparable with respect to the convex transform order.

2010 AMS Mathematics Subject Classification: Primary 60E15; Secondary 60E05, 62N05.

Keywords and phrases: star transform order, convex transform order, failure rate, sign variation.

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