The availability of a system with dependent units is obtained in the case where the system fails when one of the essential units fails. Markov model is assumed. The system considered consists of dependent units of which units are essential units. A unit is said to be essential if its failure causes the system to fail. The mean and variance of time to system failure are given. Unit reliability is also discussed.
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...
A cold-standby redundant sytem with two identical units and one repair facility is considered. Units can be in three states: good , degraded , and failed . It is supposed that only the following state-transitions of a unit are possible: , , , . 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 and/or stochastical decrease of times of repairs of the types and/or ) and...
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...
In this paper, we introduce a new stochastic order between continuous non-negative random variables called the PLR (proportional likelihood ratio) order, which is closely related to the usual likelihood ratio order. The PLR order can be used to characterize random variables whose logarithms have log-concave (log-convex) densities. Many income random variables satisfy this property and they are said to have the IPLR (increasing proportional likelihood ratio) property (DPLR property). As an application,...