Reliability Of Coherent Systems Research Articles

WNBUE Class and its Applications to Signature-Based Bounds for Reliability of Coherent Systems

WNBUE Class and its Applications to Signature-Based Bounds for Reliability of Coherent Systems

Comparing the reliability of coherent systems with heterogeneous, dependent and distribution-free components

ABSTRACT In recent years, there has been a growing interest in comparing the reliability of systems with dependent components. Most of the recent works consider Archimedean copulas to define the dependency structure of systems and examine specific familiy of distributions. In this work, we provide distribution-free results to compare, in the usual stochastic order under some majorization conditions, coherent systems with heterogeneous and dependent components where the dependency structure can be defined by any copula. Applications of our main results for specific copulas and different families of marginal distributions are also given.

A study on multi-level redundancy allocation in coherent systems formed by modules

The present work studies the effect of redundancies on the reliability of coherent systems formed by modules. Different redundancies at components’ level versus redundancies at modules’ level are investigated, including active and standby redundancies. For that, a new model is presented. This model takes into account the dependence among the components, as well as, the dependence among the modules of the system. In both cases, the dependence structure is modeled by copula functions. Several results are provided to compare systems consisting of heterogeneous components. The comparisons are distribution-free with respect to the components. In particular, we consider the cases when the components in the modules are independent and connected (or not) in series, and when the components are dependent within the modules. In both cases, it is assumed that the modules can be dependent. Furthermore, the case in which the components in each module are identically distributed (dependent or independent) is also considered. We illustrate the theoretical results with several examples.

Allocations of cold standbys to series and parallel systems with dependent components

AbstractIn the context of industrial engineering, cold‐standby redundancies allocation strategy is usually adopted to improve the reliability of coherent systems. This paper investigates optimal allocation strategies of cold standbys for series and parallel systems comprised of dependent components with left/right tail weakly stochastic arrangement increasing lifetimes. For the case of heterogeneous and independent matched cold standbys, it is proved that better redundancies should be put in the nodes having weaker [better] components for series [parallel] systems. For the case of homogeneous and independent cold standbys, it is shown that more redundancies should be put in standby with weaker [better] components to enhance the reliability of series [parallel] systems. The results developed here generalize and extend those corresponding ones in the literature to the case of series and parallel systems with dependent components. Numerical examples are also presented to provide guidance for the practical use of our theoretical findings.

Reliability sensitivity analysis of coherent systems based on survival signature

The reliability sensitivity can be used to rank distribution parameters of system components concerning their impacts on the system’s reliability. Such information is essential to purposes such as component prioritization, reliability improvement, and risk reduction of a system. In this article, we present an efficient method for reliability sensitivity analysis of coherent systems using survival signature. The survival signature is applied to calculate the reliability of coherent systems. The reliability importance of components is derived analytically to evaluate the relative importance of the component with respect to the overall reliability of the system. The closed-form formula for the reliability sensitivity of the system with respect to component’s distribution parameters is derived from the derivative of lifetime distribution of a component to further investigate the impacts of the distribution parameters on the system’s reliability. The effectiveness and feasibility of the proposed approaches are demonstrated with two numerical examples.

Uncertainty theory as a basis for belief reliability

Belief reliability is a newly developed, model-based reliability metric which considers both what we know (expressed as reliability models) and what we don’t know (expressed as epistemic uncertainty in the reliability models) about the reliability. In this paper, we show that due to the explicit representation of epistemic uncertainty, belief reliability should not be regarded as a probability measure; rather, it should be treated as an uncertain measure in uncertainty theory. A minimal cut set-based method is developed to calculate the belief reliability of coherent systems. A numerical algorithm is, then, presented for belief reliability analysis based on fault tree models. The results of application show that the developed methods require less computations than the structure function-based method of classical reliability theory.

The Reliability of Coherent Systems Subjected to Marshall–Olkin Type Shocks

In the classical Marshall–Olkin model, the system is subjected to two types of shocks coming at random times, and destroying components of the system. In statistics and reliability engineering literature, there are numerous papers dealing with various extensions of this model. However, none of these works takes into account the system structure, i.e., in existing shock models usually the system structure is not considered. In this work, we consider a new shock model involving the system structure. More precisely, we consider a coherent system which is subjected to Marshall–Olkin type shocks. We investigate the reliability, and mean time to failure (MTTF) of such systems subjected to shocks coming at random times. Numerical examples and graphs are provided, and an extension to a general model is discussed.

Reliability of coherent systems with a single cold standby component

In this paper, the influence of a cold standby component on a coherent system is studied. A method for computing the system reliability of coherent systems with a cold standby component based on signature is presented. Numerical examples are presented. Reliability and mean time to failure of different systems are computed.

A study on reliability of coherent systems equipped with a cold standby component

In this paper, we investigate the effect of a single cold standby component on the performance of a coherent system. In particular, we focus on coherent systems which may fail at the time of the first component failure in the system. We obtain signature based expressions for the survival function and mean time to failure of the coherent systems satisfying the abovementioned property.

On profust reliability of coherent systems: signature-based expressions

In this article we study profust reliability of non-repairable coherent systems through the concept of system signature. We obtain explicit expressions for the profust reliability and mean time to fuzzy failure of coherent systems. We compute and present mean time to failure and mean time to fuzzy failure of all coherent systems with three and four components. Finally, we illustrate the results for a well known class of coherent systems called m-consecutive- k-out-of- n:F.

Reliability of a Coherent System in a Multicomponent Stress-Strength Model

SYNOPTIC ABSTRACT The problem of finding system reliability is difficult in a multicomponent stress-strength model because the strengths of different components may be different, and they may experience the same or different stress levels. In a single-component stress-strength model, reliability of a component is the probability of its strength being greater than the stress imposed on it. In a multicomponent stress-strength model, we must take into account the structure function of the system and respective stress and strength levels of the components while determining the system reliability. In this article we show how the stress-strength reliability of a multicomponent system, at least its lower bound, can be derived. The stress-strength reliability of a system is expressed here as a function of the stress-strength reliabilities of its individual components. This generalized expression helps evaluate the stress-strength reliability of different coherent systems, regardless of the dependent or independent nature of the stress and strength variables.

About the Authors

About the Authors

Improving system reliability using conditional reliability importance

This paper presents a way to improve the system reliability of coherent systems consisting of components with independently distributed lives. Performing better maintenance, using better quality components, replacing older components by newer ones, or reducing operational load on the critical components are some of the ways in which the system reliability can be improved. The issue arises when we wish to select an optimal arrangement of components, keeping in view the cost effectiveness of the method adopted. Here an attempt has been made to improve system reliability by reallocating the components considering their reliability importance. To achieve this, the knowledge of the order of the component reliabilities is sufficient. Their individual values are not required for deciding if the positions of the components need to be changed. The method is illustrated with examples of different systems. A numerical example is given to explain how the procedure can be used to arrive at an optimal arrangement of components. An application of the result derived in this paper has been discussed in the context of the main power supply system of a nuclear power plant.

Computational algebraic algorithms for the reliability of generalized k-out-of- n and related systems

Identities and bounds for the reliability of coherent systems are analysed and computed using the techniques of commutative algebra. The techniques are applied to the analysis of some of the most relevant k-out-of- n class systems. The efficiency of the algebraic approach in obtaining exact identities, bounds and asymptotic formulas shows good performance when compared with results from the literature. The papers points to some new applications of these techniques that emphasize the connection of algebra and probability in this context.

Constrained (k, d)-out-of-n systems

Two new coherent system reliability models, which generalise k-out-of-n:F and consecutive k-out-of-n:G systems, are proposed and explicit formulae for the reliabilities of these systems are derived when the components are independent and identical and when they are Markov dependent. Our method of deriving reliability functions is based on the use of classical combinatorial arguments. These extensions consider an additional constraint on the number of working components between successive failures. More explicitly, in addition to the working conditions of k-out-of-n:F and consecutive k-out-of-n:G systems there must be at least d consecutive working components between any of two successive failures. This type of consideration might be useful in some situations including the analysis of constrained binary sequences arising in communications systems, and particular infrared detecting systems.

Rearrangement of Components in a System Using Component Importance Measures

In this paper we consider the system reliability of coherent systems consisting of components with independently distributed lives. In reliability engineering, increasing the system reliability is an important issue, which can be achieved in various ways, such as, by using high quality components, by reducing the operational load on the components, by implementing better maintenance etc., but selecting the optimal way is a difficult job. Here an attempt has been made to increase the system reliability of coherent systems by rearranging the components pairwise using various component importance measures.

A unified way of comparing the reliability of coherent systems

Consider a coherent system S hat has n and a structure function /spl phi/. The state of S is determined by the states of the components allocated at the n nodes and /spl phi/. If the reliabilities of these it components are expressed by an n-dimensional vector p, then the reliability of S is a function of p. Using the concepts of node-criticality introduced by Boland et al. (1989), the main theorem in this paper proposes a unified approach by which the reliabilities of S corresponding to 2 different values of p can be compared. The conditions in the main theorem are both necessary and sufficient for k-out-of-n systems. Application of this theorem to various situations yields a unified approach for obtaining previous results in the literature. Also, the application of this theorem immediately extends the results established for k-out-of-n systems to coherent systems.

Reliability of systems by mixture forms of uncertainty

In this paper we focus on reliability analysis of systems whose components can be described in both a probability context and a possibility context. We introduce a uniform representation of reliability characteristics by different forms of uncertainty. The time-dependent reliability analysis of one-unit systems is presented. The various properties and methods for computing the reliability of coherent systems are studied. For illustrating the results obtained, series and parallel systems are considered and a numerical example is proposed.

Reliability bounds for coherent structures with independent components

In this article a minimal path upper bound and a minimal cut lower bound on the reliability of a coherent system are derived for the case of independent (but not necessarily identical) components. Coupling these bounds with the classical Esary and Proschan's (1963) bounds, some limit theorems are established for the reliability of large coherent systems under quite general conditions.

Application of the stein-chen method for bounds and limit theorems in the reliability of coherent structures

The Stein-Chen method for establishing Poisson convergence is used to approximate the reliability of coherent systems with exponential-type distribution functions. These bounds lead to quite general limit theorems for the lifetime distribution of large coherent systems. © 1993 John Wiley & Sons, Inc.