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Shock models with NBUFR and NBAFR survivals.

A. M. Abouammoh, M. I. Hindi, A. N. Ahmed (1988)

Trabajos de Estadística

The life distribution H(t) of a device subject to shocks governed by a Poisson process and pure birth process is considered as a function of probabilities Pk of not surviving the first k shocks. It is shown that some properties of a discrete distribution {P'k} are reflected on properties of the continuous life distribution H(t). In particular, if Pk has the discrete NBUFR properties, then H(t) has the continuous NBUFR and NBAFR properties. The NBUFR and NBAFR life distributions are obtained under...

Some examples of non-monotonicities in a two-unit redundant system

Antonín Lešanovský (1984)

Aplikace matematiky

A cold-standby redundant sytem with two identical units and one repair facility is considered. Units can be in three states: good ( I ) , degraded ( I I ) , and failed ( I I I ) . It is supposed that only the following state-transitions of a unit are possible: I I I , I I I I I , I I I , I I I I . The paper deals with the comparison of some initial situations of the system and with a stochastical improvement of units (stochastical increase of time of work in state I and/or stochastical decrease of times of repairs of the types I I I and/or I I I I ) and...

Some stochastic comparison results for series and parallel systems with heterogeneous Pareto type components

Lakshmi Kanta Patra, Suchandan Kayal, Phalguni Nanda (2018)

Applications of Mathematics

We focus on stochastic comparisons of lifetimes of series and parallel systems consisting of independent and heterogeneous new Pareto type components. Sufficient conditions involving majorization type partial orders are provided to obtain stochastic comparisons in terms of various magnitude and dispersive orderings which include usual stochastic order, hazard rate order, dispersive order and right spread order. The usual stochastic order of lifetimes of series systems with possibly different scale...

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