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313828

Stochastic Partial Orders, With Applications to Reliability

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Last updated: 28 Dec 2024

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Abstract

Suppose each of two devices is subjected to shocks occurring randomly as events in a Poisson process with constant intensity . Let Pkdenote the probability that the first device will survive the first k shocks and Qkdenote such a probability for the second device. Let H1 (t) and H2 (t) denote the survival functions of the first and second device respectively. In this paper, we show that some new partial ordering, namely dual (D), dual stochastic (DST), dual weak likelihood ratio (DWLR), increasing failure rate (IFR), dual mean residual lives (DMRL) and dual convex (DC) ordering between the shock survival probabilities Pk and Qkare preserved by the corresponding survival functions H1 (t) and H2 (t). We also obtain sufficient conditions under which the above-mentioned relations between the discrete distributions are verified in some commutative damage shock models.

DOI

10.21608/esju.2000.313828

Keywords

Stochastic Partial Orders - Namely Dual - Dual Stochastic, DWLR, DMRL, iFR, DC

Volume

44

Article Issue

1

Related Issue

43031

Issue Date

2000-06-01

Publish Date

2000-06-01

Page Start

112

Page End

120

Print ISSN

0542-1748

Online ISSN

2786-0086

Link

https://esju.journals.ekb.eg/article_313828.html

Detail API

https://esju.journals.ekb.eg/service?article_code=313828

Order

10

Type

Original Article

Type Code

1,914

Publication Type

Journal

Publication Title

The Egyptian Statistical Journal

Publication Link

https://esju.journals.ekb.eg/

MainTitle

Stochastic Partial Orders, With Applications to Reliability

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Article

Created At

28 Dec 2024