Uncertainty Importance Measure of Individual Components in Multi-State Systems

Importance and sensitivity analysis of multi-state systems using the universal generating function method

Reliability and covariance estimation of weighted k-out-of-n multi-state systems

Importance analysis of noncoherent systems is limited, and is generally inaccurate because all measures of importance that have been developed are strictly for coherent analysis. This paper considers the probabilistic measure of component importance developed by Birnbaum (1969). An extension of this measure is proposed which enables noncoherent importance analysis. As a result of the proposed extension the average number of system failures in a given interval for noncoherent systems can be calculated more efficiently. Furthermore, because Birnbaum's measure of component importance is central to many other measures of importance; its extension should make the derivation of other measures possible.

Importance measure can be used to identify the most vulnerable components with respect to system functionality or failure. Traditional importance measures may not be effective to evaluate the contribution of an individual component if its reliability value does not fall in the full range between 0 and 1. Based on the cost-reliability relation, this paper proposes a generalized Birnbaum importance measure (GBIM) to quantify the contribution of individual components to system reliability improvement by considering reliability range, manufacturing complexity, and technology feasibility. Since GBIM possesses several unique features in terms of guiding system reliability optimization, in this paper, we further develop a GBIM-based genetic algorithm to solve a type of optimal reliability allocation problem. The numerical studies show that both the computational efficiency and the near global optimality based on GBIM outperforms the methods using the traditional importance measures.

This article presents an original method for evaluating reliability indices for Multi-State Systems (MSSs) in the presence of aleatory and epistemic uncertainties. In many real- world MSSs, an insufficiency of data makes it difficult to estimate precise values for component state probabilities. The proposed approach applies the transferable belief model interpretation of the Dempster–Shafer theory to represent component state beliefs and to evaluate the MSS reliability indices. The example of an oil transmission system is used to demonstrate the proposed approach and it is compared with the universal generating function method. The value of the Dempster–Shafer theory lies in its ability to use several combination rules in order to evaluate reliability indices for MSSs that depend on the reliability of the experts’ opinions as well as their independence.

Many practical methods and different approaches have been proposed to assess Multi-State Systems (MSS) reliability measures. The universal generating function (UGF) method, introduced in 1986, is known to be a very efficient way of evaluating the availability of different types of MSSs. In this paper, we propose an extension of the UGF method considering epistemic uncertainties. This extended method allows one to model ill-known probabilities and transition rates, or to model both aleatory and epistemic uncertainty in a single model. It is based on the use of belief functions which are general models of uncertainty. We also compare this extension with UGF methods based on interval arithmetic operations performed on probabilistic bounds.

In the non-probabilistic uncertainty structural analysis, the input uncertain variables of it, such as loads and material properties, will be propagated to the output responses, which include the displacement, stress and compliance, etc. To measure the effect of these non-probabilistic input variables on the output response, two new uncertainty importance measures on the non-probabilistic reliability index are discussed. For the linear limit state function, the analytical solutions of the importance measures are derived. To reduce computational effort, the discretization method and the surrogate model method are presented to calculate the two importance measures in case of the non-linear limit state. Finally, four examples demonstrate that the proposed importance measures can effectively describe the effect of the input variables on the reliability of the structure system, and the established methods can effectively obtain the two importance measures.

We introduce in this paper a new measure of component importance, called redundancy importance, in coherent systems. It is a measure of importance for the situation in which an active redundancy is to be made in a coherent system. This measure of component importance is compared with both the (Birnbaum) reliability importance and the structural importance of a component in a coherent system. Various models of component redundancy are studied, with particular reference to k/out / of / n systems, parallel-series systems, and series-parallel systems.

The network theory is widely applied to improve the reliability of a complex electromechanical system. In this application, system reliability assessment with network theory has been paid a great deal of attention. Because of instrument malfunctions, staff omissions, imperfect inspection strategies, and complex structures, field failure data are often subject to interval censoring, making the holistic reliability assessment becomes a difficult task. Most traditional methods assume reliability of critical components or partial reliability as system reliability, which may cause a large bias in system reliability estimation. This paper proposes a novel method to evaluate and predict the system reliability of a complex electromechanical system subject to the insufficient fault data problem from a network perspective. First, the system modeling based on network theory is developed to describe the topology of a holistic system. Second, interval‐valued intuitionistic hesitant fuzzy number is proposed in order to solve insufficient data for single component. Then, a new measure—comprehensive reliability—that can reflect the reliability of nodes in combination with functional properties and topological properties, which are formulated by failure data and network model, respectively, is constructed for system reliability assessment. Subsequently, an improved system reliability model based on percolation theory is given in terms of comprehensive reliability of nodes. Finally, to verify the effectiveness of the proposed method, a simulation and a real case study for traction system are implemented.

Multi-state component criticality analysis for reliability improvement in multi-state systems

Smart grid can work effectively only when a reliable, fast communication network is available. The communication network is a prerequisite to connect different protection, control, and monitoring equipment within the substation. Ethernet fulfills all the requisites such as reliable, fast, secure, interoperable, LAN-based communication system for smart substations. Therefore, the main aspect is to improve the reliability of the network by prioritizing the critical components by using the knowledge of component importance measures (CIM). In this chapter, analysis of IEC 61850 ethernet-based substation communication network (SCN) architectures has been examined using various reliability importance measures (RIM). The importance measures namely Birnbaum, improvement potential, criticality importance, and reliability achievement worth have given their justified rankings of the various components of SCN architectures. The practice of these CIMs works towards the identification of the components that can be allocation of resources for the improvement of system reliability.

Component uncertainty importance measure in complex multi-state system considering epistemic uncertainties

A hybrid algorithm of particle swarm optimization (PSO) and local search (LS) is proposed to solve the redundancy allocation problem for series-parallel multi-state systems. The proposed hybrid algorithm is able to design the system structure with a minimum cost to provide a desired level of availability. Unlike most of the previous studies that only consider homogeneous redundancy, the proposed algorithm allows for the heterogeneous redundancy technique. The universal generating function method is applied to evaluate system availability. The standard PSO is modified and novel LS strategies are integrated to adapt to the redundancy allocation problem. Case studies that facilitate comparisons between the proposed hybrid algorithm and other non-hybrid heuristics as well as meta-heuristics reported in the literature (such as genetic algorithms, tabu search, and ant colony optimization) are provided. The results illustrate the advantages of the proposed hybrid algorithm in terms of the solution quality or algorithm efficiency.

Importance measures in reliability systems are used to identify weak components in contributing to proper functioning of the system. Traditional importance measures mainly concern the change of the system reliability as the change of the reliability of one component and seldom consider the expected number of repairs of the objective component in unit time. This paper proposes an improvement potential rate importance (IPR) to verify the effectiveness of the improvement in system reliability for multi-state repairable k-out-of-n: G systems. Then the comparisons between IPR and Birnbaum importance are discussed. Finally, a case study is given to demonstrate the proposed IPR.

Means of measuring and ranking a system's components relative to their importance to the system reliability have been developed by a number of authors. This paper investigates a new ranking that is based upon minimal cuts and compares it with existing definitions. The new ranking is shown to be easily calculated from readily obtainable information and to be most useful for systems composed of highly reliable components. The paper also discusses extensions of importance measures and rankings to systems in which both the system and its components may be in any of a finite number of states. Many of the results about importance measures and rankings for binary systems are shown to extend to the more sophisticated multi‐state systems. Also, the multi‐state importance measures and rankings are shown to be decomposable into a number of sub‐measures and rankings.