Optimal allocation of relevations in coherent systems

In this paper we study the allocation problem of relevations in coherent systems. The optimal allocation strategies are obtained by implementing stochastic comparisons of different policies according to the usual stochastic order and the hazard rate order. As special cases of relevations, the load-sharing and minimal repair policies are further investigated. Sufficient (and necessary) conditions are established for various stochastic orderings. Numerical examples are also presented as illustrations.

On the Dynamic Cumulative Past Quantile Entropy Ordering

In many society and natural science fields, some stochastic orders have been established in the literature to compare the variability of two random variables. For a stochastic order, if an individual (or a unit) has some property, sometimes we need to infer that the population (or a system) also has the same property. Then, we say this order has closed property. Reversely, we say this order has reversed closure. This kind of symmetry or anti-symmetry is constructive to uncertainty management. In this paper, we obtain a quantile version of DCPE, termed as the dynamic cumulative past quantile entropy (DCPQE). On the basis of the DCPQE function, we introduce two new nonparametric classes of life distributions and a new stochastic order, the dynamic cumulative past quantile entropy (DCPQE) order. Some characterization results of the new order are investigated, some closure and reversed closure properties of the DCPQE order are obtained. As applications of one of the main results, we also deal with the preservation of the DCPQE order in several stochastic models.

Further Results of the TTT Transform Ordering of Order n

To compare the variability of two random variables, we can use a partial order relation defined on a distribution class, which contains the anti-symmetry. Recently, Nair et al. studied the properties of total time on test (TTT) transforms of order n and examined their applications in reliability analysis. Based on the TTT transform functions of order n, they proposed a new stochastic order, the TTT transform ordering of order n (TTT-n), and discussed the implications of order TTT-n. The aim of the present study is to consider the closure and reversed closure of the TTT-n ordering. We examine some characterizations of the TTT-n ordering, and obtain the closure and reversed closure properties of this new stochastic order under several reliability operations. Preservation results of this order in several stochastic models are investigated. The closure and reversed closure properties of the TTT-n ordering for coherent systems with dependent and identically distributed components are also obtained.

Optimal allocation of a coherent system with statistical dependent subsystems

This paper studies the optimal allocation policy of a coherent system with independent heterogeneous components and dependent subsystems, the systems are assumed to consist of two groups of components whose lifetimes follow proportional hazard (PH) or proportional reversed hazard (PRH) models. We investigate the optimal allocation strategy by finding out the number $k$ of components coming from Group A in the up-series system. First, some sufficient conditions are provided in the sense of the usual stochastic order to compare the lifetimes of two-parallel–series systems with dependent subsystems, and we obtain the hazard rate and reversed hazard rate orders when two subsystems have independent lifetimes. Second, similar results are also obtained for two-series–parallel systems under certain conditions. Finally, we generalize the corresponding results to parallel–series and series–parallel systems with multiple subsystems in the viewpoint of the minimal path and the minimal cut sets, respectively. Some numerical examples are presented to illustrate the theoretical findings.

A Bayesian Mixture Modelling of Stop Signal Reaction Time Distributions: The Second Contextual Solution for the Problem of Aftereffects of Inhibition on SSRT Estimations

The distribution of single Stop Signal Reaction Times (SSRT) in the stop signal task (SST) has been modelled with two general methods: a nonparametric method by Hans Colonius (1990) and a Bayesian parametric method by Dora Matzke, Gordon Logan and colleagues (2013). These methods assume an equal impact of the preceding trial type (go/stop) in the SST trials on the SSRT distributional estimation without addressing the relaxed assumption. This study presents the required model by considering a two-state mixture model for the SSRT distribution. It then compares the Bayesian parametric single SSRT and mixture SSRT distributions in the usual stochastic order at the individual and the population level under ex-Gaussian (ExG) distributional format. It shows that compared to a single SSRT distribution, the mixture SSRT distribution is more varied, more positively skewed, more leptokurtic and larger in stochastic order. The size of the results’ disparities also depends on the choice of weights in the mixture SSRT distribution. This study confirms that mixture SSRT indices as a constant or distribution are significantly larger than their single SSRT counterparts in the related order. This result offers a vital improvement in the SSRT estimations.

Residual Probability Function for Dependent Lifetimes

In this paper, the residual probability function is applied to analyze the survival probability of two used components relative to each other in the case when their lifetimes are dependent. The expression of the function by copulas has been derived along with some examples of particular copulas. The behaviour of the residual probability function in terms of the underlying dependence is also discussed. The residual probability order is also considered in the dependent case. In the class of Archimedean survival copulas, we prove that the residual probability order implies the usual stochastic order in the reversed direction, and the hazard rate order concludes the residual probability order.

Varma Quantile Entropy Order

We give a stochastic order for Varma residual entropy and study several properties of it, like closure, reversed closure and preservation of this order in some stochastic models.