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This article finds that multivariate generalized Marshall-Olkin distributions are of the lack-of-partial-memory property in the sense of residual lifetimes of elder components being independent of those younger ones' ages. Also, we further investigate aging behavior and stochastic dependence of the multivariate residual lifetime of this family of random vectors. [ABSTRACT FROM AUTHOR]

This article studies the parallel system with two component lifetimes following Marshall/Olkin-type distribution. We develop some sufficient conditions for the hazard rate order on the system lifetime, which essentially generalize related results in the literature on lifetime distributions with Marshall–Olkin structure. [ABSTRACT FROM AUTHOR]

This paper studies stochastic comparisons between a population and subpopulations in both multiplicative and additive frailty models. The comparisons between a population and its baseline in stochastic ordering are conducted as a special case. We build equivalent characterizations of some common stochastic orders between a population and a subpopulation, in terms of the frailty of the subpopulation and the first two moments of frailty variable. Some examples and applications are discussed as well. [ABSTRACT FROM AUTHOR]

This paper introduces a cyber security model with imperfect detection, in which one attacker launches multiple attacks against the target with adjusted strength based on the previous attacking outcome. Several sufficient conditions leading to the usual stochastic order on the first time to observe a truly compromised target, to observe a successful attack and to compromise the target are developed, respectively. The probability for the target to be truly compromised before observing some number of successful attacks is proved to increase (decrease) in the attacking (defense) strength. Monte Carlo simulations are also conducted to empirically illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

For two components and one standby redundancy, we develop a characterization on the hazard rate order and the reversed hazard rate order of the redundant system lifetime in the context of mutually independent components lifetimes. Also, the likelihood ratio order is derived on the lifetime of the series system with two components lifetimes and two matched active redundancies lifetimes both following the proportional hazard model. [ABSTRACT FROM AUTHOR]

This paper deals with series and parallel systems of dependent components equipped with starters. We study the hazard rate order, the dispersive order and the usual stochastic order of system lifetimes in the context of component lifetimes having proportional hazard rates. The main results either generalize or extend corresponding conclusions of Joo and Mi (2010) and Da, Ding, and Li (2010). [ABSTRACT FROM AUTHOR]

An increasing generalized failure rate of a lifetime X defines an ageing concept, denoted by IGFR. Another notion, denoted by DRPFR, is defined by the decreasingness of the reversed proportional failure rate. In this article, we provide characterizations for both IGFR and DRPFR absolutely continuous lifetimes, based on monotonicity of quotients of probabilistic functionals and a result by Nanda and Shaked (2001). We derive the necessary conditions for the IGFR notion, based on stochastic orderings of truncated distributions, and we prove that the product of DRPFR lifetimes is also DRPFR; that the IGFR property is preserved by composition with certain risk aversion utility functions; and that the order statistics and the records (and the subsequent order statistic (record)) are IGFR under suitable assumptions, with similar results for DRPFR lifetimes. Also, we provide sufficient conditions for the hazard rate ordering of products and random products of IGFR lifetimes, and similar results for the reversed hazard rate order and DRPFR lifetimes, with a complementary result for the mean residual life order of random products of two families of IGFR lifetimes, we derive the upper and lower bounds for the cumulative distribution function of the product of IGFR lifetimes, and we provide the lower bounds for the risk function of an IGFR lifetime based on the distribution moments, and these bounds are extended for the product of IGFR lifetimes. We discuss extensively the applications of the results in insurance portfolios. [ABSTRACT FROM AUTHOR]

This paper studies the optimal allocation of one active redundancy to a k-out-of-n system in the context of statistically dependent component lifetimes. It is proved that assigning the redundancy to the weakest component is more favorable so as to get a larger system lifetime in terms of both the usual stochastic order and the stochastic preference order. [ABSTRACT FROM AUTHOR]

For random variables with Archimedean copula or survival copula, we develop the reversed hazard rate order and the hazard rate order on sample extremes in the context of proportional reversed hazard models and proportional hazard models, respectively. The likelihood ratio order on sample maximum is also investigated for the proportional reversed hazard model. Several numerical examples are presented for illustrations as well. [ABSTRACT FROM AUTHOR]

This paper deals with bivariate Farlie–Gumbel–Morgenstern distributions. We build the TP2 (RR2) property of the residual lifetime and study the evolution of the dependence of the residual lifetime at large age. Also, we derive the aging property in the sense of the upper orthant order. Furthermore, in the context of IFR (DFR) marginals the residual lifetime at the age above the median is found to be increasing (decreasing) in the upper orthant order. [ABSTRACT FROM AUTHOR]

This article further investigates the allocation of coverage limits and deductibles to multiple independent risks from the viewpoint of policyholders with increasing utility functions. In a more general setup, we develop the usual stochastic orders on the retained loss, which either generalize or supplement the corresponding results due to Lu and Meng (2011) and Hu and Wang (2014). Also, the most unfavorable and favorable allocations of coverage limits and deductibles are developed for multiple risks with dominated reversed hazard rates and hazard rates, respectively. [ABSTRACT FROM AUTHOR]

This paper further studies monotone aging properties of the multivariate random lifetime. We revise the sufficient condition for the negative monotone aging property in terms of the multivariate usual stochastic order in Theorem 3.3 of Rezapour et al. (2013) and derive the condition sufficient to the multivariate monotone aging properties in terms of the upper orthant order. Also we study the upper orthant order of multivariate residual lifetimes and inactivity times from populations sharing a common Archimedean survival copula and Archimedean survival copula, respectively. Two simple applications in multivariate stress-strength and frailty models are presented as well. [ABSTRACT FROM PUBLISHER]

This article recasts the optimal allocations of coverage limits for two independent random losses. Under some regularity conditions on the two concerned probability density functions, we build the sufficient and necessary condition for the existence of the optimal allocation of coverage limits, and derive the optimal allocation whenever they do exist. The results supplement Lu and Meng (2011, Proposition 5.2) and Hu and Wang (2014, Theorem 5.1). [ABSTRACT FROM PUBLISHER]

This paper studies the allocation of independent redundancies with a common life distribution tok-out-of-nsystems of independent components with non identical life distributions. A sufficient condition is found for allocating more active redundancies to the weaker component to gain a larger lifetime fork-out-of-nsystems, and assigning more standby redundancies to the weaker (stronger) components is proved to yield larger lifetime for series (parallel) systems in the sense of the increasing concave (convex) order. Also, the optimal policy is proved to be majorized by all other policies when the system’s components are stochastically ordered. [ABSTRACT FROM PUBLISHER]

In this article, we review some recent results on the stochastic comparison of convolutions from independent and heterogeneous random variables. We highlight the close connections that exist between some classical stochastic orders and majorization-type orders. [ABSTRACT FROM AUTHOR]

This article studies series and parallel systems with two independent components. Optimal allocation of one redundancy to a parallel system and that of two redundancies to a series one are derived, respectively. [ABSTRACT FROM AUTHOR]

Let X1,..., Xn be independent exponential random variables with respective hazard rates λ1,..., λn, and Y1,..., Yn be i.i.d. exponential random variables with common hazard rate λ. It is proved that X2: n, the second order statistic from X1,..., Xn, is larger than Y2: n, the second order statistic from Y1,..., Yn, with respect to the right spread order if and only if [image omitted] with [image omitted] and Λi = Λ(1) - λi, and X2: n is smaller than Y2: n with respect to the right spread order if and only if [image omitted] Further, the case with proportional decreasing hazard rate is also studied, and the results obtained here form nice extensions to some corresponding ones known in the literature. [ABSTRACT FROM AUTHOR]

This article studies allocation of two nonidentical standby redundancies in series and parallel systems. The optimal allocation of two available standby (active) redundancies which are related to the bolstered working components, is also discussed. [ABSTRACT FROM AUTHOR]

This article investigates properties of mixture model of proportional reversed hazard rate. Firstly, the mixing random variable and the overall population variable are proved to be positively likelihood dependent. Secondly, lower bounds for the distribution function as well as the conditional distribution are established in the case that the mixing variable belongs to certain nonparametric classes. Finally, some stochastic orders on the mixing (baseline) variables are proved to be translated to the corresponding overall population variables. [ABSTRACT FROM AUTHOR]

This article deals with the multiple-outlier exponential model. The likelihood ratio order between m-spacings of the combined sample is developed, some results extend the conclusions on simple spacings in Wen et al. (2007). [ABSTRACT FROM AUTHOR]

A new test statistic for testing the strict DMRL property of life distribution is developed. The asymptotic normality is established and the comparison between the test proposed and some other related ones in literature is conducted through evaluating the Pitman's asymptotic relative efficiency. Edge-worth expansion is also employed to improve the accuracy of the convergence rate of the test statistic. Some numerical results are presented as well to demonstrate the performance and the asymptotic normality of the new testing procedure. [ABSTRACT FROM AUTHOR]