On the conditional residual life and inactivity time of coherent systems (original) (raw)

Conditional residual lifetimes of coherent systems

Statistics & Probability Letters, 2013

In this paper, we derive mixture representations for the reliability function of the conditional residual lifetime of a coherent system with n independent and identically distributed (i.i.d.) components under the condition that at least j and at most k − 1 (j < k) components have failed by time t. Based on these mixture representations, we then discuss stochastic comparisons of the conditional residual lifetimes of two coherent systems with independent and identical components.

A note on the conditional residual lifetime of a coherent system under double monitoring

Communications in Statistics - Theory and Methods, 2018

In this note, we derive some mixture representations for the reliability function of the conditional residual lifetime of a coherent system with n independent and identically distributed (i.i.d.) components under the condition that at time t 1 the jth failures has occurred and at time t 2 the kth failures (j < k) have not occurred yet. Based on the mixture representations, we then discuss the stochastic comparisons of the conditional residual lifetimes of two coherent systems with i.i.d. components.

Conditional residual lifetimes of coherent systems under double monitoring

Communications in Statistics, 2016

Stochastic comparisons of residual lifetimes and inactivity times of coherent systems

Journal of Applied Probability, 2013

Under the assumption of independent and identically distributed (i.i.d.) components, the problem of the stochastic comparison of a coherent system having used components and a used coherent system has been considered. Necessary and sufficient conditions on structure functions have been provided for the stochastic comparison of a coherent system having used/inactive i.i.d. components and a used/inactive coherent system. As a consequence, for r-out-of-n systems, it has been shown that systems having used i.i.d. components stochastically dominate used systems in the likelihood ratio ordering.

Mixture representations of residual lifetimes of used systems

Journal of Applied Probability, 2008

The representation of the reliability function of the lifetime of a coherent system as a mixture of the reliability function of order statistics associated with the lifetimes of its components is a very useful tool to study the ordering and the limiting behaviour of coherent systems. In this paper, we obtain several representations of the reliability functions of residual lifetimes of used coherent systems under two particular conditions on the status of the components or the system in terms of the reliability functions of residual lifetimes of order statistics.

On the residual lifelengths of the remaining components in a coherent system

Metrika, 2013

In this note, we consider a coherent system with the property that, upon failure of the system, some of its components remain unfailed in the system. Under this condition, we study the residual lifetime of the live components of the system. Signature based mixture representation of the joint and marginal reliability functions of the live components are obtained. Various stochastic and aging properties of the residual lifetime of such components are investigated. Some characterization results on exponential distributions are also provided.

Erratum to: Mixture representations of residual lifetimes of used systems

Journal of Applied Probability, 2015

On conditional residual lifetime and conditional inactivity time of k-out-of-n systems

In designing structures of technical systems, the reliability engineers often deal with the reliability analysis of coherent systems. Coherent system has monotone structure function and all components of the system are relevant. This paper considers some particular models of coherent systems having identical components with independent lifetimes. The main purpose of the paper is to study conditional residual lifetime of coherent system, given that at a fixed time certain number of components have failed but still there are some functioning components. Different aging and stochastic properties of variables connected with the conditional residual lifetimes of the coherent systems are obtained. An expression for the parent distribution in terms of conditional mean residual lifetime is provided. The similar result is obtained for the conditional mean inactivity time of the failed components of coherent system. The conditional mean inactivity time of failed components presents an interest in many engineering applications where the reliability of system structure is important for designing and constructing of systems. Some illustrative examples with given particular distributions are also presented.

Reliability and mean residual life functions of coherent systems in an active redundancy

Naval Research Logistics (NRL), 2017

In this article, the reliability and the mean residual life (MRL) functions of a system with active redundancies at the component and system levels are investigated. In active redundancy at the component level, the original and redundant components are working together and lifetime of the system is determined by the maximum of lifetime of the original components and their spares. In the active redundancy at the system level, the system has a spare, and the original and redundant systems work together. The lifetime of such a system is then the maximum of lifetimes of the system and its spare. The lifetimes of the original component and the spare are assumed to be dependent random variables.

Some stochastic comparisons of conditional coherent systems

Applied Stochastic Models in Business and Industry, 2008

This paper investigates coherent systems with independent and identical components. Stochastic comparison on the residual life and the inactivity time of two systems with stochastically ordered signatures is conducted.

On the conditional residual life and inactivity time of coherent systems (original) (raw)

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