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In this paper, sufficient conditions are presented for comparing the residual lifetimes and inactivity times of dependent random variables at different fixed times, with respect to hazard rate, mean residual life and likelihood ratio orders. The stochastic comparisons of residual lifetimes at different random times are discussed next. Several examples are presented to illustrate the established results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the optimal number of redundant allocation to n -component coherent systems consisting of heterogeneous dependent components. We assume that the system is built up of L groups of different components, $L\geq 1$ , where there are $n_i$ components in group i , and $\sum_{i=1}^{L}n_i=n$. The problem of interest is to allocate $v_i$ active redundant components to each component of type i , $i=1,\dots, L$. To get the optimal values of $v_i$ we propose two cost-based criteria. One of them is introduced based on the costs of renewing the failed components and the costs of refreshing the alive ones at the system failure time. The other criterion is proposed based on the costs of replacing the system at its failure time or at a predetermined time $\tau$ , whichever occurs first. The expressions for the proposed functions are derived using the mixture representation of the system reliability function based on the notion of survival signature. We assume that a given copula function models the dependency structure between the components. In the particular case that the system is a series-parallel structure, we provide the formulas for the proposed cost-based functions. The results are discussed numerically for some specific coherent systems. [ABSTRACT FROM AUTHOR]

This paper is a study on comparison between coherent systems with independent and heterogeneous components. Specifically, we consider 3-component coherent systems composed of two different types of components where we assume that component lifetimes follow the well-known proportional hazards model. We stochastically compare such systems under different situations and based on some assumptions on the parameters of proportionality. [ABSTRACT FROM AUTHOR]

This paper discusses stochastic comparisons for the residual and past lifetimes of coherent systems with dependent and identically distributed (d.i.d.) components under random monitoring in terms of the hazard rate, the reversed hazard rate, and the likelihood ratio orders. Some stochastic comparisons results are also established on the residual lifetimes of coherent systems under random observation times when all of the components are alive at that time. Sufficient conditions are established in terms of the aging properties of the components and the distortion functions induced from the system structure and dependence among components lifetimes. Numerical examples are provided to illustrate the theoretical results as well. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of stochastic comparisons between the lifetimes of two coherent systems with active redundancy. For this purpose, we consider both the active redundancy at the system level and the redundancy at the component level. We assume that the original components are identically distributed and possibly dependent. It is also assumed that for each component, there are m redundant components with possibly different lifetime distributions which follow the proportional hazards (reversed hazards) model. Under some conditions on the domination function of the system, we compare the lifetimes of the systems based on majorization orders between the parameter vectors of the proportionality of the component lifetimes. We also give sufficient conditions under which adding more redundant components imply the system improvement. [ABSTRACT FROM AUTHOR]

We consider a coherent system consisting of n components where the component lifetimes are assumed to be random variables following a probabilistically exchangeable joint distribution function, where the probability distribution does not change with any permutation of the components. We study stochastic properties of the residual lifetime of live components of the system, under different conditions. The number of failed components of the system are explored, under the assumption that the system is operating at time t. We also study the probability that the ith component failure in the system causes the system failure, given that the system is operating at time t. The results of the paper extend some of the existing results in the literature. [ABSTRACT FROM PUBLISHER]