<abstract xmlns="http://www.w3.org/1999/xhtml">In this paper we present limit theorems for lifetime distributions connected with network’s reliability as distributions of random variables(r.v.) min(<italic>Y</italic>1, <italic>Y</italic>2,..., <italic>YM</italic>) and max(<italic>Y</italic>1, <italic>Y</italic>2,..., <italic>YM</italic> ), where <italic>Y</italic>1, <italic>Y</italic>2,..., are independent, identically distributed random variables (i.i.d.r.v.), <italic>M</italic> being Power Series Distributed (PSD) r.v. independent of them and, at the same time, <italic>Yk</italic>, <italic>k</italic> = 1, 2, ..., being a sum of non-negative, i.i.d.r.v. in a Pascal distributed random number.</abstract>

In this paper we present limit theorems for lifetime distributions connected with network’s reliability as distributions of random variables(r.v.) min(Y1, Y2,..., YM) and max(Y1, Y2,..., YM ), where Y1, Y2,..., are independent, identically distributed random variables (i.i.d.r.v.), M being Power Series Distributed (PSD) r.v. independent of them and, at the same time, Yk, k = 1, 2, ..., being a sum of non-negative, i.i.d.r.v. in a Pascal distributed random number.

Lifetime Distributions and their Approximation in Reliability of Serial/Parallel Networks

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

In this paper we present limit theorems for lifetime distributions connected with network’s reliability as distributions of random variables(r.v.) min(Y1,...

Lifetime Distributions and their Approximation in Reliability of Serial/Parallel Networks

Published Online: Sep 22, 2020

Page range: 161 - 172

Received: May 20, 2019

Accepted: Sep 24, 2019

DOI: https://doi.org/10.2478/auom-2020-0025

Keywords
lifetime distributions, survival functions, PSD distributions, series and parallel network systems

© 2020 Alexei Leahu et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Lifetime Distributions and their Approximation in Reliability of Serial/Parallel Networks

Published Online: Sep 22, 2020

Page range: 161 - 172

Received: May 20, 2019

Accepted: Sep 24, 2019

DOI: https://doi.org/10.2478/auom-2020-0025

Keywordslifetime distributions, survival functions, PSD distributions, series and parallel network systems

© 2020 Alexei Leahu et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
lifetime distributions, survival functions, PSD distributions, series and parallel network systems