Reliability Analysis Of Coherent Systems Research Articles

Preservation of some stochastic orders by distortion functions with application to coherent systems with exchangeable components

AbstractThe preservation of stochastic orders by distortion functions has become a topic of increasing interest in the reliability analysis of coherent systems. The reason of this interest is that the reliability function of a coherent system with identically distributed components can be represented as a distortion function of the common reliability function of the components. In this framework, we study the preservation of the excess wealth order, the total time on test transform order, the decreasing mean residual live order, and the quantile mean inactivity time order by distortion functions. The results are applied to study the preservation of these stochastic orders under the formation of coherent systems with exchangeable 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.

Weighted lattice polynomials of independent random variables

We give the cumulative distribution functions, the expected values, and the moments of weighted lattice polynomials when regarded as real functions of independent random variables. Since weighted lattice polynomial functions include ordinary lattice polynomial functions and, particularly, order statistics, our results encompass the corresponding formulas for these particular functions. We also provide an application to the reliability analysis of coherent systems.

Exploiting symmetry in the reliability analysis of coherent systems

In practice, components in a complex system are not structurally identical. However, we may often find some components that have similar structure positions, and hence one should make use of this piece of information in studying reliability problems. For example, in practical reliability engineering, components are usually in series with each other. There is no need to calculate the structural importance for all these components because all components that are in series with each other will have the same structural importance. In this article we will introduce a definition of symmetry and present a study of this concept for system reliability analysis. It will be shown that the idea, although very simple, can be used to simplify reliability computation, and it can also be used to obtain bounds on system reliability. In Section 2, a general definition of symmetric components is given and some characterizations are indicated. In Section 3, we first develop lower and upper bounds on system reliability and then proceed to give some properties concerning component importance measures that can be of practical importance when deciding which component to improve in such a system. In Section 4, some theoretical results on structural properties of systems having symmetric components are summarized. In particular, we show that the symmetry property is preserved by the dual transformation of the structure function. Throughout the article we assume that the basic components in a system are independent. Our notations and terminologies will follow those given by Barlow and Proschan [I]. The systems considered in this article are assumed to be coherent unless otherwise stated.

Exploiting symmetry in the reliability analysis of coherent systems

Components in a complex system are usually not structurally identical. However, in many cases we may find components that are structurally symmetric, and one should make use of this additional information to simplify reliability analysis. The main purpose of this article is to define and study one such class of systems, namely, those having symmetric components, and to derive some reliability-related properties. © 1996 John Wiley & Sons, Inc.

Heuristic least-cost computation of discrete classification functions with uncertain argument values

We consider the problem of minimizing the expected cost of computing the correct value of a discrete-valued function when it is costly to determine (“inspect”) the values of its arguments. This type of problem arises in distributed computing, in the design of interactive expert systems, in reliability analysis of coherent systems, in classification of pattern vectors, and in many other applications. In this paper, we first show that the general problem is NP-hard and then introduce several efficient heuristic sequential inspection procedures for solving it approximately. We obtain theoretical results showing that the heuristics are optimal in important special cases; moreover, their computational structures make them well suited for parallel implementation. Next, for the special case of linear threshold (or “discrete linear discriminant”) functions, which are widely used in statistical classification procedures, we use Monte Carlo simulation to analyze the performances of the heuristics and to compare the heuristic solutions with the exact (true minimum expected cost) solutions over a wide range of randomly generated test problems. All of the heuristics give average relative errors, compared to the exact optimal solutions, of less than 2%. The best heuristic for this class of functions gives an average relative error of less than 0.05% and runs two to four orders of magnitude faster than the exact solution procedure, for functions with ten arguments.