Residual Lifetime Of Coherent System Research Articles

On conditional residual lifetimes of coherent systems consisting of components with discrete lifetimes

On conditional residual lifetimes of coherent systems consisting of components with discrete lifetimes

ON THE RESIDUAL AND PAST LIFETIMES OF COHERENT SYSTEMS UNDER RANDOM MONITORING

This paper discusses stochastic comparisons for the residual and past lifetimes of coherent systems with dependent and identically distributed (d.i.d.) components under random monitoring in terms of the hazard rate, the reversed hazard rate, and the likelihood ratio orders. Some stochastic comparisons results are also established on the residual lifetimes of coherent systems under random observation times when all of the components are alive at that time. Sufficient conditions are established in terms of the aging properties of the components and the distortion functions induced from the system structure and dependence among components lifetimes. Numerical examples are provided to illustrate the theoretical results as well.

Copula-based representations for the reliability of the residual lifetimes of coherent systems with dependent components

In the context of coherent systems, we obtain representations for the reliability function of the residual lifetime at time t under different assumptions. Specifically, four cases are considered based on system information at time t : the system is working (case 1); all the components of the system are working (case 2); some components have failed at given times t 1 , … , t r < t but the other components and the system are working (case 3); some components have failed at some unknown failure times (case 4). In each of these cases, we obtain a representation for the reliability function of the associated system residual lifetime, based on the copula representation for the component lifetimes and the structure of the system. These representations can be applied to systems with generally dependent components. The representations obtained are also used to compare the respective system residual lifetimes under different stochastic orders. Some illustrative examples are included.

Distribution-free comparisons of residual lifetimes of coherent systems based on copula properties

In this paper a general procedure is proposed to get stochastic comparisons of residual lifetimes of coherent systems. The comparison results obtained are based on the structure of the system and on properties of the copula used to describe the dependence between the component lifetimes. They are distribution-free with respect to the component lifetime distributions. We consider two system residual lifetimes at a given time $$t>0$$ . In the first one, we just assume that the system is working at time t while, in the second one, we assume that all the components are working at time t. We study the main stochastic orderings: hazard rate, stochastic, mean residual life and likelihood ratio orders. Specific results are obtained in the particular case of independent components and in the case of identically distributed components. Some illustrative examples are included. They prove that, in some cases, these system residual lifetimes are not ordered. Even more, surprisingly, sometimes the first residual lifetime is greater (in some stochastic sense) than the second one under a given dependence model.

Conditional residual lifetimes of coherent systems under double monitoring

ABSTRACTIn this paper, we obtain a mixture representation for the reliability function of the conditional residual lifetime of a coherent system with n independent and identically distributed (i.i.d.) components under double monitoring. We suppose that at time t1, j components have failed while at time t2 the system is still alive. Based on these mixture representation, we then study stochastic comparisons of the conditional residual lifetimes of two coherent systems with independent and identical components.

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.

Conditional residual lifetimes of coherent systems

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.