On system reliability under random load of elements

Kopocińska, Ilona; Kopociński, Bolesław

doi:10.4064/am-17-1-5-14

Cited by 10 publications

(3 citation statements)

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“…A sample of applications is given in Section 6. In particular we extend some results of Kopocinska and Kopocinski (1980) and of Schechner (1984) and the model of Ross (1984).…”

Section: Introductionsupporting

confidence: 61%

“…The following model generalizes models of Kopocinska and Kopocinski (1980), Ross (1984) and Schechner (1984). Using different methods of proof, Kopocinska andKopocinski (1980), Corollary 4, andSchechner (1984) Esary and Marshall (1970», the distribution of 1'(T) is NBU (for a discussion on this property see Marshall and Shaked (1986». Proof. From Theorem 6.2 it follows that T is MIHR Is; From Theorem 7.1 of Arjas (1981a) it follows then that Tis MNBU I~.…”

Section: Applicationsmentioning

confidence: 99%

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Multivariate hazard rates and stochastic ordering

Shaked

Shanthikumar

1987

Advances in Applied Probability

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Properties of the conditional hazard rates of X1, · ··, Xn and Y1, · ··, Yn, which imply (X1, · ··, Xn) (Y1, · ··, Yn), are found. These are used to find conditions on the hazard rates of T = (T1, · ··, Tn) which ensure that T has the MIHR | property of Arjas (1981a) and the ‘weakened by failure’ property of Arjas and Norros (1984). Applications for load-sharing model and multivariate imperfect repair are given.

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“…A sample of applications is given in Section 6. In particular we extend some results of Kopocinska and Kopocinski (1980) and of Schechner (1984) and the model of Ross (1984).…”

Section: Introductionsupporting

confidence: 61%

Section: Applicationsmentioning

confidence: 99%

Multivariate hazard rates and stochastic ordering

Shaked

Shanthikumar

1987

Advances in Applied Probability

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“…functions j (t|I; t 1 , … , t |I| ) do not even depend on the calendar time t. Such models can be seen as natural generalizations of the condition of independent and exponentially distributed lifetimes (see, in particular, the work of Norros 8 ). A number of different papers in the literature have been devoted to the reliability analysis of systems under related probability models for the lifetimes of components (see, in particular, other works 11,[13][14][15][16] ).…”

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confidence: 99%

Reliability, signature, and relative quality functions of systems under time‐homogeneous load‐sharing models

Spizzichino

2018

Appl Stoch Models Bus & Ind

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For a coherent binary system made of binary components, we consider the assumption that the components' lifetimes are distributed according to a time‐homogeneous, load‐sharing model. Such models are characterized in terms of the so‐called multivariate conditional hazard rate functions. We aim to point out some related properties of the notions of signature, relative quality functions, and reliability functions. On this purpose, we preliminarily collect all the necessary background and review some related literature. This paper concludes with a discussion, also containing some hints for future work.

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Algorithm of State Stationary Probability Computing for Continuous-Time Finite Markov Chain Modulated by Semi-Markov Process

Andronov

Vishnevsky

2016

Communications in Computer and Information Science

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On system reliability under random load of elements

Cited by 10 publications

References 0 publications

Multivariate hazard rates and stochastic ordering

Multivariate hazard rates and stochastic ordering

Reliability, signature, and relative quality functions of systems under time‐homogeneous load‐sharing models

Algorithm of State Stationary Probability Computing for Continuous-Time Finite Markov Chain Modulated by Semi-Markov Process

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