Intuitively, activating the standby of a k-out-of-n:G system to the working state at the last moment fully utilizes the redundancy and hence would result in a more reliable system; however, this is not always true as shown in a counterexample. This paper presents several scenarios under which,...

Ordering properties on order statistics from heterogeneous observations have been paid lots of attention. This article devotes to investigating the ordering properties on order statistics from statistically dependent observations. We build the likelihood ratio order and the (reversed) hazard...

For heterogeneous Weibull samples with a common shape parameter and weakly majorized scale parameters, we study the likelihood ratio order and the stochastic order between minimums of independent and dependent samples, respectively. Also, an application in fabric strength is presented.

We study here extremes of residuals of the bivariate lifetime and the residual of extremes of the two lifetimes. In the case of generalized Marshall–Olkin model and the total time transformed exponential model, we first present some sufficient conditions for the extremes of residuals to be...

This paper studies the tail behavior of the Poisson shot-noise processes with interdependent and heavy-tailed random shocks. In the presence of statistical dependence between the shock and its arrival time we establish the asymptotic behavior of the tail probability. Two examples are presented...

This note studies the allocation of an active redundant component in a series system. We mainly conduct a stochastic comparison between random lives of a series system with two components under two allocation choices. The case with a standby redundancy and when the system is parallel are...

NBUC class life distributions are dealt with in this paper. Firstly, a lower bound of the reliability function based upon mean and variance (both assumed finite) is presented. It is shown that the bound effectively improves "known bounds" for NBU life distributions. Secondly, a sufficient...

This paper studies the multivariate mixed proportional reversed hazard rate model having dependent mixing variables. Stochastic comparison as well as aging properties in this model are investigated, and stochastic monotone properties of the population vector with respect to the mixing vector are...

This paper deals with the reversed hazard rate of general mixture models. Dependence and monotone properties of the reversed hazard rate are studied. Some lower bounds of the expected inactivity time of the overall population are presented with an application. Finally, preservation of DRHR under...