Joint Reliability Importance Research Articles

Joint Reliability Importance in Linear $m$-Consecutive-$k$-Out-of-$n$: F Systems

We study the joint reliability importance (JRI) of two components in Lin/m/Con/k/n:F systems. A Lin/m/Con/k/n:F system consists of n linearly ordered binary components, and the system fails iff there are at least m nonoverlapping runs of k consecutive failed components (n ≥ mk). In particular, we obtain expressions for the JRI in Lin/m/Con/k/n:F systems when the components are s-independent & identical, when the components are s-independent & nonidentical, and when the components are exchangeable & s-dependent. We present extensive numerical illustrations.

Joint Integrated Importance Measure for Multi-State Transition Systems

Joint reliability importance (JRI) evaluates the interaction of two components in contributing to the system reliability in a system. Traditional JRI measures mainly concern the change of the system reliability caused by the interactive change of the reliabilities of the two components and seldom consider the probability distributions, transition rates of the object component states, and system performance. This article extends the JRI concept of two components from multi-state systems to multi-state transition systems and mainly focuses on the joint integrated importance measure (JIIM) which considers the transition rates of component states. Firstly, the concept and physical meaning of JIIM in binary systems are described. Secondly, the JIIM for deterioration process (JIIMDP) and the JIIM for maintenance process (JIIMMP) in multi-state systems are studied respectively. The corresponding characteristics of JIIMDP and JIIMMP for series and parallel systems are also analyzed. Finally, an application to an offshore electrical power generation system is given to demonstrate the proposed JIIM.

COMBINATORIAL APPROACH TO COMPUTING COMPONENT IMPORTANCE INDEXES IN COHERENT SYSTEMS

We consider binary coherent systems with independent binary components having equal failure probability q. The system DOWN probability is expressed via its signature's combinatorial analogue, the so-called D-spectrum. Using the definition of the Birnbaum importance measure (BIM), we introduce for each component a new combinatorial parameter, so-called BIM-spectrum, and develop a simple formula expressing component BIM via the component BIM-spectrum. Further extension of this approach allows obtaining a combinatorial representation for the joint reliability importance (JRI) of two components. To estimate component BIMs and JRIs, there is no need to know the analytic formula for system reliability. We demonstrate how our method works using the Monte Carlo approach. We present several examples of estimating component importance measures in a network when the DOWN state is defined as the loss of terminal connectivity.

Joint importance measures for multistate reliability systems

Importance and joint importance measures in reliability engineering are used to identify the weak areas of a system and signify the roles of components in either causing or contributing to proper functioning of the system. Existing joint reliability importance measure of a multistate system with n components provides the joint reliability importance of k (k ≤ n) components. This paper introduces, for two multistate components, joint performance achievement worth, joint performance reduction worth, joint performance Fussell–Vesely measure and joint performance Birnubaum importance measure, using reliability, availability and risk as output performance measures (OPMs) of the multistate system. With reference to a predefined threshold of component performance, the component’s reachable states are restricted to those corresponding to performances either larger or not larger than the threshold level. A steady state performance level distribution with restriction to the component’s states is used to obtain the introduced measures. Use of universal generating function (UGF) for the evaluation of proposed joint importance measures is given. An illustrative example is provided.

ON CONDITIONAL MARGINAL AND CONDITIONAL JOINT RELIABILITY IMPORTANCE

The reliability importance of one or more components when another component is assumed to be working/non-working is measured by Conditional Marginal Reliability Importance (CMRI) and Conditional Joint Reliability Importance (CJRI) respectively. We consider two systems viz the series-in-parallel and series-parallel. The expressions for CMRI and CJRI are derived for both the systems when the components are independent but not identically distributed. It is shown that the sign of the joint importance of three components and Conditional Joint Importance (CJI) can be determined using Schur-convexity (concavity) of the reliability function. The difference in the reliability functions of two coherent systems with n ≥ 3 statistically independent and with dependent components is derived. It is shown to be measured by their covariance, the JRI and the CJRIs. CMRIs and CJRIs of a phased type electronic system and a bridge structure are worked out.

The reliability importance of components and prime implicants in coherent and non-coherent systems including total-order interactions

In the management of complex systems, knowledge of how components contribute to system performance is essential to the correct allocation of resources. Recent works have renewed interest in the properties of the joint ( J) and differential ( D) reliability importance measures. However, a common background for these importance measures has not been developed yet. In this work, we build a unified framework for the utilization of J and D in both coherent and non-coherent systems. We show that the reliability function of any system is multilinear and its Taylor expansion is exact at an order T. We then introduce a total order importance measure ( D T ) that coincides with the exact portion of the change in system reliability associated with any (finite or infinitesimal) change in component reliabilities. We show that D T synthesizes the Birnbaum, joint and differential importance of all orders in one unique indicator. We propose an algorithm that enables the numerical estimation of D T by varying one probability at a time, making it suitable in the analysis of complex systems. Findings demonstrate that the simultaneous utilization of D T and J provides reliability analysts with a complete dissection of system performance.

Analysis for joint importance of components in a coherent system

JRI (Joint Reliability Importance) of two components is a measure of interaction of two components in a system for their contribution to the system reliability. It is defined as the rate at which the system reliability improves as the reliabilities of the two components improve. But, sometimes we may improve system reliability through improving reliabilities of three or more components. This article extends the concepts of JRI & JFI (Joint Failure Importance) of two components to multi-components, and establishes some relationships between JRI & JRI, JFI & JFI, and JFI & JRI. The paper also investigates the concept of Conditional Reliability Importance while the working states of certain components are known. Finally, the JRI of multi-components and Conditional Reliability Importance are analyzed in detail for a k-out-of- n: G system.

Joint importance of multistate systems

Importance measures in reliability engineering are used to identify weak areas of a system and signify the roles of components in either causing or contributing to proper functioning of the system. Traditional importance measures for multistate systems mainly concern reliability importance of an individual component and seldom consider the utility performance of the systems. This paper extends the joint importance concepts of two components from the binary system case to the multistate system case. A joint structural importance and a joint reliability importance are defined on the basis of the performance utility of the system. The joint structural importance measures the relationship of two components when the reliabilities of components are not available. The joint reliability importance is inferred when the reliabilities of the components are given. The properties of the importance measures are also investigated. A case study for an offshore electrical power generation system is given.

Joint reliability importance of k-out-of- n systems

Joint Reliability Importance (JRI) is investigated to provide information on the type and the degree of interactions between two components by identifying the sign and the size of it. In specific, JRI is analyzed for k-out-of- n systems with (i) independently identically distributed (IID) components, (ii) non-identical and independent components and (iii) pair-wise dependent components. The closed form solution of JRI is derived for IID components. By using the solution, the variations of JRI are investigated with respect to the level of redundancy ( n/ k). In non-identical and independent case, the point of sign change of JRI is obtained. It is also shown that the sign of JRI can be determined by the relationships between the Schur-convexity (concavity) and the JRI. For dependent case, only the pair-wise dependence is considered. As a result, the error caused by assuming statistical independence between pair-wise dependent components is shown to be measured by their covariance and JRI.

Efficient algorithms to assess component and gate importance in fault tree analysis

One of the principal activities of risk assessment is either the ranking or the categorization of structures, systems and components with respect to their risk-significance or their safety-significance. Several measures, so-called importance factors, of such a significance have been proposed for the case where the support model is a fault tree. In this article, we show how binary decision diagrams can be use to assess efficiently a number of classical importance factors. This work completes the preliminary results obtained recently by Andrews and Sinnamon, and the authors. It deals also with the concept of joint reliability importance.

Computation of joint reliability importance of two gate events in a fault tree

Joint reliability importance (JRI) of two gate events (GEs) is investigated along with its properties in a fault tree (FT). Computation of JRI of two GEs involves complexity because statistical dependency between GEs exists as a result of replication of basic events (BEs). To avoid complexity in computing the JRI, the topological relationships of two GEs in a FT are identified and classified into three classes. The explicit formula for the JRI of the two GEs is derived. JRI for each class is shown to be computed by using a conventional FT algorithm. By illustrating min. cut set representation of the bridge network, it is also shown that the degree of relationship between two min. cut sets can be measured by the JRI of the corresponding two GEs.

Joint reliability-importance of components

Hong & Lie (1993) defined joint reliability importance (JRI) as a measure of how two components in a system interact in contributing to system reliability. Their definition and theorems regarding JRI were limited to statistically independent component states. This paper removes the statistical independence restriction by showing that similar results hold in the more general case where component failures can be statistically dependent; however, the calculation of actual values becomes more difficult, because covariance terms can appear in the JRI formula. Despite this, the essential determination and interpretation of the signs of the JRI remain unchanged. Thus analysts who wish to use JRI (e.g., as a design heuristic) can do so in working with real systems where statistical independence is not valid. It is further shown that JRI is always nonzero for some classes of systems. >

Joint reliability-importance of two edges in an undirected network

Joint reliability importance (JRI) of two edges in an undirected network is introduced. Concepts of joint failure importance (JFI) and marginal failure importance (MFI), duals of JRI and marginal reliability importance (MRI), are also introduced. The JRI of two edges in an undirected network is represented by the MRI of each edge in subnetworks. Relationships between JRI and MRI, JRI and JFI, and JFI and MFI are presented. From these relationships, it is shown that the JRI is an appropriate quantitative measure of the interactions of two edges in a network, with respect to source-to-terminal reliability. It can also show that the sign of the JRI of two edges can be determined without computing the JRI of these two edges in some special cases.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>