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On distributions of order statistics for absolutely continuous copulas with applications to reliability

Piotr Jaworski, Tomasz Rychlik (2008)

Kybernetika

Performance of coherent reliability systems is strongly connected with distributions of order statistics of failure times of components. A crucial assumption here is that the distributions of possibly mutually dependent lifetimes of components are exchangeable and jointly absolutely continuous. Assuming absolute continuity of marginals, we focus on properties of respective copulas and characterize the marginal distribution functions of order statistics that may correspond to absolute continuous...

On generalized conditional cumulative past inaccuracy measure

Amit Ghosh, Chanchal Kundu (2018)

Applications of Mathematics

The notion of cumulative past inaccuracy (CPI) measure has recently been proposed in the literature as a generalization of cumulative past entropy (CPE) in univariate as well as bivariate setup. In this paper, we introduce the notion of CPI of order α and study the proposed measure for conditionally specified models of two components failed at different time instants, called generalized conditional CPI (GCCPI). Several properties, including the effect of monotone transformation and bounds of GCCPI...

On goodness-of-fit for the absence of memory model

Vilijandas Bagdonavičius, Rüta Levulienė (2001)

Kybernetika

Logrank-type and Kolmogorov-type goodness-of-fit tests for the absence of memory model are proposed when the accelerated experiments are done under step-stresses. The power of the test against the approaching alternatives is investigated. The theoretical results are illustrated with simulated data.

On preservation under univariate weighted distributions

Salman Izadkhah, Mohammad Amini, Gholam Reza Mohtashami Borzadaran (2015)

Applications of Mathematics

We derive some new results for preservation of various stochastic orders and aging classes under weighted distributions. The corresponding reversed preservation properties as straightforward conclusions of the obtained results for the direct preservation properties, are developed. Damage model of Rao, residual lifetime distribution, proportional hazards and proportional reversed hazards models are discussed as special weighted distributions to try some of our results.

On reliability analysis of consecutive k -out-of- n systems with arbitrarily dependent components

Ebrahim Salehi (2016)

Applications of Mathematics

In this paper, we consider the linear and circular consecutive k -out-of- n systems consisting of arbitrarily dependent components. Under the condition that at least n - r + 1 components ( r ≤ n ) of the system are working at time t , we study the reliability properties of the residual lifetime of such systems. Also, we present some stochastic ordering properties of residual lifetime of consecutive k -out-of- n systems. In the following, we investigate the inactivity time of the component with lifetime T r : n at the system...

On univariate and bivariate aging for dependent lifetimes with Archimedean survival copulas

Franco Pellerey (2008)

Kybernetika

Let 𝐗 = ( X , Y ) be a pair of exchangeable lifetimes whose dependence structure is described by an Archimedean survival copula, and let 𝐗 t = [ ( X - t , Y - t ) | X > t , Y > t ] denotes the corresponding pair of residual lifetimes after time t , with t ≥ 0 . This note deals with stochastic comparisons between 𝐗 and 𝐗 t : we provide sufficient conditions for their comparison in usual stochastic and lower orthant orders. Some of the results and examples presented here are quite unexpected, since they show that there is not a direct correspondence between univariate...

Optimal mean-variance bounds on order statistics from families determined by star ordering

Tomasz Rychlik (2002)

Applicationes Mathematicae

We present optimal upper bounds for expectations of order statistics from i.i.d. samples with a common distribution function belonging to the restricted family of probability measures that either precede or follow a given one in the star ordering. The bounds for families with monotone failure density and rate on the average are specified. The results are obtained by projecting functions onto convex cones of Hilbert spaces.

Currently displaying 101 – 120 of 181