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Let (Xi,Yi), i = 1, . . ., n be a pair where the first coordinate Xi represents the lifetime of a component, and the second coordinate Yi denotes the utility of the component during its lifetime. Then the random variable Y[r:n] which is known to be the concomitant of the rth order statistic defines the utility of the component which has the rth smallest lifetime. In this paper, we present a dynamic analysis for an n component system under the above-mentioned concomitant setup. [ABSTRACT FROM AUTHOR]

In this paper, a general formula for computing the joint reliability importance of two components is obtained for a binary coherent system that consists of exchangeable dependent components. Using the new formula, the joint reliability importance can be easily calculated if the path sets of the system are known. As a special case, an expression for the joint reliability importance of two components is also obtained for a system consisting of independent and identical components. Illustrative numerical results are presented to compare the joint reliability importance of two components in the bridge system for the two cases when the components are exchangeable dependent and when the components are independent and identical. [ABSTRACT FROM AUTHOR]

The purpose of this article is to develop a Monte-Carlo simulation algorithm for computing mean time to failure (MTTF) of weighted-k-out-of-n:G and linear consecutive-weighted-k-out-of-n:G systems. Our algorithm is based on the use of appropriately defined stochastic process which represents the total weight of the system at timet. These stochastic processes are explicitly defined and used along with the ordered component lifetimes to simulate MTTF of the systems with weighted components. [ABSTRACT FROM PUBLISHER]

We consider two different sets of exchangeable samples which are assumed to be dependent. A single set of observations is obtained from these two dependent samples. The distribution of single order statistic, and the joint distribution of the minimum and an arbitrary order statistic are derived. The results are illustrated in the context of reliability problem. [ABSTRACT FROM AUTHOR]

This paper is concerned with the Birnbaum importance measure of a component in a binary coherent system. A representation for the Birnbaum importance of a component is obtained when the system consists of exchangeable dependent components. The results are closely related to the concept of the signature of a coherent system. Some examples are presented to illustrate the results. [ABSTRACT FROM AUTHOR]

A coherent system of order n that consists two different types of dependent components is considered. The lifetimes of the components in each group are assumed to follow an exchangeable joint distribution, and the two random vectors, which represent the lifetimes of the components in each group are also assumed to be dependent. Under this particular form of dependence, all components are assumed to be dependent but they are categorized with respect to their reliability functions. Mixture representation is obtained for the survival function of the system's lifetime. Mixture representations are also obtained for the series and parallel systems consisting of disjoint modules such that all components of Type I are involved in one module (subsystem) and all components of Type II are placed in the other module. The theoretical results are illustrated with examples. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 388-394, 2015 [ABSTRACT FROM AUTHOR]

This paper is concerned with dynamic reliability modeling of three-state systems consisting of three-state s-independent components. The components and the systems are assumed to be in three states: perfect functioning, partial performance, and complete failure. Survival functions of such systems are studied in different state subsets. It is shown that the survival function of a three-state system with a general structure can be represented as a mixture of the survival functions of the three-state \bf k-out-of-n:G systems. The results are illustrated for the three-state consecutive- \bf k-out-of-n:G systems whose components degrade according to a Markov process. [ABSTRACT FROM AUTHOR]

This paper is concerned with dynamic reliability analysis of three-state k-out-of-n:G systems. It is assumed that the components and the systems can be in three states: perfect functioning, partial performance and complete failure. Using the concept of permanent, we study marginal and joint survival functions for the lifetime of two different three-state k-out-of-n:G systems that consist of independent and nonidentical components. Illustrative examples are also provided for the components which follow the Markov degradation process. [ABSTRACT FROM AUTHOR]

A multistate k-out-of- n system model is an extension of binary k-out-of- n system model by allowing multiple performance levels for the system and its components. Various definitions of multistate k-out-of- n system model have been proposed in the literature. Previous studies on these systems mostly focus on reliability evaluation algorithms. The present paper investigates the lifetimes of multistate systems. In particular, the lifetimes of two different multistate k-out-of- n system models are represented in terms of order statistics, and bounds and approximations are presented using these representations. The results are illustrated for a multistate system whose components' degradation occurs according to a Markov process. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we obtain an expression between the sums of the marginal distributions of the order statistics and the common marginal distribution of an exchangeable random sequence. We also derive an expression between the sums of the joint distribution of two order statistics and the two dimensional joint distribution of an exchangeable random sequence. [Copyright &y& Elsevier]

A k-out-of-n:G system consists of n components, and operates if at least k of its components operate. Its reliability properties have been widely studied in the literature from different perspectives. This paper is concerned with the reliability analysis of a k-out-of-n:G system equipped with a single warm standby unit. We obtain an explicit expression for the reliability function of the system for arbitrary lifetime distributions. Two different mean residual life functions are also studied for the system. [ABSTRACT FROM AUTHOR]

Abstract: Consider a system consisting of n components each with its own positive integer-valued random weight (capacity). The system is assumed to have a performance level above c if there are at least working components, and the total weight of all working components is above c. We study the reliability properties of such a system. A recursive formula is obtained for computing the system state probabilities. We present a Monte-Carlo simulation algorithm to observe the time spent by the system in state c or above. The algorithm is based on the use of ordered lifetimes of components. We illustrate the results with numerical computations. [Copyright &y& Elsevier]

In this article, we study reliability properties of m-consecutive- k-out-of- n: F systems with exchangeable components. We deduce exact formulae and recurrence relations for the signature of the system. Closed form expressions for the survival function and the lifetime distribution as a mixture of the distribution of order statistics are established as well. These representations facilitate the computation of several reliability characteristics of the system for a given exchangeable joint distribution or survival function. Finally, we provide signature-based stochastic ordering results for the system's lifetime and investigate the IFR preservation property under the formulation of m-consecutive- k-out-of- n: F systems. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011 [ABSTRACT FROM AUTHOR]

In this article we study the distribution and expected value of the number of working components at time t in a consecutive k-out-of-n system under the condition that it is working at time t. We provide the exact distribution of the corresponding conditional random variable and compute its expected value for the system consisting of exchangeable dependent components. The results are also extended to any coherent system by the aid of system signature. Finally, we present illustrative and computational results for some systems having Lomax components. [ABSTRACT FROM AUTHOR]

We study the conditional lifetimes of consecutive -out-of- systems. We provide explicit representations for the conditional survival functions of these systems when 2κ≥>n. The mean residual life functions are obtained, and ordering results are provided. A signature-based evaluation of residual lifetimes is also presented, and some stochastic comparison results are obtained for particular consecutive systems. [ABSTRACT FROM AUTHOR]

Abstract: Consider a system which has independent components (or subsystems) each consisting of dependent elements. Let , denote the random strength vector of the th component, where denotes the random strength of the th element of the th component. The elements of the components are subjected to a common random stress over time. In this paper, we setup a multivariate stress–strength model based on the conditional ordering between s and and evaluate the reliability of coherent structures in this setup. [Copyright &y& Elsevier]

This paper concerns the joint behaviour of precedence and exceedance statistics in random threshold models. Joint distributions of precedence and exceedance statistics, both exact and asymptotic, are obtained, and the results are illustrated for random thresholds based on order statistics and record values. [ABSTRACT FROM AUTHOR]

Let (X1, Y1), (X2, Y2),... be a sequence of independent and identically distributed (i.i.d.) pairs of random variables with two possible outcomes at each coordinate. Runs in the second coordinate are considered until the appearance of the first success in the first coordinate. [ABSTRACT FROM AUTHOR]

Concomitants of order statistics are considered for the situation in which the random vectors ( X 1 , Y 1 ), ( X 2 , Y 2 ),..., ( X n , Y n ) are independent but otherwise arbitrarily distributed. The joint and marginal distributions of the concomitants of order statistics and stochastic comparisons among the concomitants of order statistics are studied in this situation. [ABSTRACT FROM AUTHOR]