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Stochastic orders are useful to compare the lifetimes of two systems. We discuss both active redundancy as well as standby redundancy. We show that redundancy at the component level is superior to that at the system level with respect to different stochastic orders, for different types of systems. © 1963-2012 IEEE.

Department of Mathematics

World University root node

IEEE Transactions on Reliability

Component redundancy versus system redundancy in different stochastic orderings

We study the system (series/parallel) where the components are randomly chosen from two different batches. We assume that one batch is more reliable than the other in some stochastic sense. In the case of series systems we show that, under certain conditions, lifetime of one system dominates that of the other in different stochastic orders viz. hazard rate, down shifted hazard rate and likelihood ratio orders. Further, we show that the same principle holds for the reversed hazard rate and the likelihood ratio orders in the case of parallel systems. © 2014 Elsevier B.V. All rights reserved.

Operations Research Letters

Some results on series and parallel systems of randomized components

In this article, we study aging properties of parallel and series systems with a random number of components. We show that the decreasing likelihood ratio property is closed under the formation of random minima. We also show, by counterexamples, that other aging properties are not closed under the formation of random minima or maxima. Some mistakes in the literature are corrected. © 2014 Wiley Periodicals, Inc.

Naval Research Logistics

Some aging properties of parallel and series systems with a random number of components

Optimum lifetime of a series system with active spares always depends on the allocation of spares at component /system level. We prove that under some sufficient conditions, component redundancy offers greater reliability than the system redundancy in likelihood ratio ordering for n-component matching spares. We also show that this principle holds under some sufficient conditions in likelihood ratio ordering for 2-component non-matching spares of iid components and iid spares. Further, we give some sufficient conditions under which reversed hazard rate order does not exist between two 2-component systems of matching spares. © 2013 Elsevier B.V. All rights reserved.

Some results on active redundancy at component level versus system level

One of the widely discussed in the literature and relevant in practice shock models is the delta-shock model that is described by the constant time of a system's recovery after a shock. However, in practice, as time progresses and due to deterioration of a system, this recovery time is gradually increasing. This important phenomenon was not discussed in the literature so far. Therefore, in this paper, we are considering a time-dependent delta-shock model, i.e., the recovery time becomes an increasing function of time. Moreover, we assume that shocks occur according to the generalized Polya process that contains the homogeneous Poisson process, the non-homogeneous Poisson process and the Polya process as particular cases. For the defined survival model, we derive the corresponding survival function and the mean lifetime and study the related optimal replacement policy along with some relevant stochastic properties.