System Reliability Analysis Method Research Articles

The Gears System Reliability Analysis with Correlation among the Components of Gear Box in Self-Propelled Gun

Against the accurately solving of system reliability was inadequate, the Copula function was applied in system reliability analysis of weapon equipment, the paper established system reliability model which obtained the second shift single driving, and obtained the common relationship between travel and system reliability degree, it tested that Copula function was better to solve correlation problem in the system reliability model .It provided a method for system reliability analysis and reliability susceptive analysis.

Reliability Research of Fiber-Access Devices Monitoring System on Fault Tree

The method of fault tree analysis is an important method for complex system reliability analysis of large scale. Fiber-access devices monitoring system is an important system of electric power communication transmission. Firstly it introduces the method of fault tree analysis, and then use the fault tree modeling technique for the fault tree to model refers to the fault of optical access equipment monitoring system, and carries on the qualitative analysis and quantitative analysis. It provides theoretical basis for system improvement and maintenancs.

The Selection of Power Supply Mode Based on Reliability's Social Costs

Selecting the power supply mode for important power consumers involves two aspects of reliability and economy. Combining with the power system reliability analysis method and taking full account of each component failure mode and their combination patterns, this paper embarks from the reality, accurately calculated the reliability indices of these power supply modes by minimal-cut sets, and then used the reliability indices to estimate the power losses of the users, finally used the theory of reliability cost-benefit and took the minimizing social costs that consist of reliability costs and outage losses as the goal to compare and analyze the reliability cost and the users outage losses under different power supply modes, obtained the suitable power supply mode for different important level of users.

Network Service Reliability Analysis Model

This paper proposes a network system reliability analysis method based on service. The significance of the network services becomes increasingly prominent in many fields like communication and aviation industry. More and more services depend on network transmission. Thus, the dependability and the reliability of network system are paid more and more attention. The reliability of network is related to several factors, such as hardware equipment, software services, human factors and so on. Most previous papers pay more attention on the hardware equipment factors than the others. The reliability of network is measured by if the equipment is normal running. Sometimes the hardware equipment is in normal operation, but some users may think that the network service is unavailable due to the network congestion, software errors or man-made mistakes which have no effect on the calculation of the reliability. There is a gap between the state of service execution in terms of reliability and what the network reliability data suggests. This paper attempts to propose a network service reliability analysis method based on service to bridge the gap. The paper satisfies these needs in the following ways:(1) we analyses various factors affecting reliability of the network system; (2) we establish the reliability block diagram of service operating process and calculate the reliability of the equipment by the diagram (3) we analyze a case utilizing the model in (2). This method will not overestimate the availability of network system. It enhances the previous study by utilizing the analysis based on service. With this method the gap between the service experience of users in term of reliability and the result reliability of the method will be bridged.

Extension of Hassan and Wolff method for system reliability analysis of soil slopes

While a soil slope may have a large number of potential slip surfaces, its system failure probability is usually governed by a few representative slip surfaces due to the high correlation between factors of safety (FOS) of different slip surfaces. This paper shows that, despite its embedded empiricism, the Hassan and Wolff method can identify with reasonable accuracy not only the most critical slip surface, but also representative slip surface for system reliability analysis. In the Hassan and Wolff method, the assumed distribution of FOS has important effect on the calculated failure probability and it is not appropriate to always assume FOS is lognormally distributed. Whether the system effect in a slope reliability analysis is obvious can be judged easily by comparing the values of reliability index of different representative slip surfaces. Combined with the response surface method, the Hassan and Wolff method can be extended into a practical tool for system reliability analysis utilizing existing deterministic slope stability analysis programs. A simple equation is provided to estimate the bounds of system failure probability based on the most critical slip surface.

System Reliability Evaluation Based on Stochastic Limit Analysis

It is quite difficult to estimate system reliability of complex structures which involve lots of potential failure modes. A novel method for system reliability analysis of frame structure was proposed based on stochastic limit analysis. Stochastic limit load was firstly calculated based on the elastic modulus reduction method (EMRM) by taking the uncertainty of structural resistance into account. Once the limit state equation was established by the stochastic limit load, the system reliability index can be calculated by the first-order reliability method (FORM) efficiently. Numerical example illustrates the efficiency and accuracy of the proposed method by comparing with the traditional failure mode analysis approaches.

An efficient method for system reliability analysis of planar mechanisms

This article presents an efficient method for system reliability analysis of planar mechanisms with random dimensions and joint clearances. The reliability of the mechanism is defined as the probability that the output error remains within a specified limit in the entire target trajectory of the mechanism. Since the currently used methods for system reliability analysis are approximate in nature, this article presents a more efficient and innovative method based on the minimum cross-entropy principle for probabilistic analysis used in the information theory. The mechanism reliability problem is formulated as a series system reliability analysis that can be solved using the distribution of maximum output error. To derive this distribution, fractional moments of the output error are estimated from a small simulated sample of trajectories of mechanism motion which serve as constraints in the minimization of cross entropy. The proposed method is illustrated by analyzing the reliability slider–crank and a four-bar function generator. The comparison of the results with those obtained from the Monte Carlo simulations confirms the high accuracy of the proposed method.

An approach to system reliability analysis with fuzzy random variables

Nondeterministic variables of certain distributions are employed to represent uncertainties, which are usually treated as the stochastic factors to reliability models. However, model parameters may not be precisely represented due to some factors in engineering practices, such as lack of sufficient data, data with fuzziness and unknown or non-constant reproduction conditions. To address these issues, fuzzy random variables are implemented and two developments are made in this paper. The first development is that the Saddlepoint Approximation (SAP)-simulation is extended to conduct reliability analysis accounting for the time-dependent degradation process and fuzzy random variables, and we attempt to give a method to select a proper saddlepoint. The second development is that two system reliability analysis methods are proposed for different scenarios of reliability modeling processes. It could be suitable for the system consisting of structural components with gradual failure, whose reliability can be obtained by the method in the improved SPA-simulation, also for system consisting of components with sudden failure, whose reliability can be acquired from site field or experiments. An illustrated example is followed to testify the proposed methods.

Probabilistic Approach to System Reliability of Mechanism with Correlated Failure Models

In this paper, based on the kinematic accuracy theory and matrix‐based system reliability analysis method, a practical method for system reliability analysis of the kinematic performance of planar linkages with correlated failure modes is proposed. The Taylor series expansion is utilized to derive a general expression of the kinematic performance errors caused by random variables. A proper limit state function (performance function) for reliability analysis of the kinematic performance of planar linkages is established. Through the reliability theory and the linear programming method the upper and lower bounds of the system reliability of planar linkages are provided. In the course of system reliability analysis, the correlation of different failure modes is considered. Finally, the practicality, efficiency, and accuracy of the proposed method are shown by a numerical example.

System reliability analysis of spatial variance frames based on random field and stochastic elastic modulus reduction method

This paper presents the stochastic elastic modulus reduction method for system reliability analysis of spatial variance frames based on the perturbation stochastic finite element method (PSFEM) and the local average of a random field. The stochastic responses and reliability index of each element of a structural frame are characterized by the PSFEM and the first-order second-moment method, to properly handle the correlation structures and scale of fluctuation of random fields. A strategy of elastic modulus adjustment for the estimation of system reliability is developed to determine the range and magnitude of elastic modulus reduction, by taking the element reliability index as a governing parameter. The collapse mechanism and system reliability index of a stochastic framed structure are determined through iterative computations of the PSFEM. Compared with the failure mode approaches in traditional system reliability analysis, the proposed method avoids two major difficulties, namely the identification of significant failure modes and estimation of the joint probability of failure modes. The influences of the correlation structure and scale of fluctuation of the random field upon system reliability are investigated to demonstrate the accuracy and computational efficiency of the proposed methodology in system reliability analysis of spatial variance frames.

Reliability block diagram with general gates and its application to system reliability analysis

For those systems that can be modeled with perfect nodes and unreliable arcs such as communication systems, a reliability graph with general gates (RGGG) was developed. Similarly, for more efficient system reliability analysis of those systems that can be modeled with unreliable nodes and perfect arcs, a reliability block diagram with general gates (RBDGG) was developed as an intuitive and easy-to-use method for system reliability analysis. One of the unique characteristics of RBDGG is to allow node connection relations of general gates such as the AND gate and the k-out-of- n gate other than the OR gate connection relation of the conventional reliability block diagram (RBD). Mathematical formulations for RBDGG and a method of mapping a RBDGG model into an equivalent Bayesian network model without losing the one-to-one matching characteristic of the RBDGG for quantitative analysis is also provided. With the application to two example systems, the usefulness of the proposed RBDGG is demonstrated.

Advance first order second moment (AFOSM) method for single reservoir operation reliability analysis: a case study

Reservoir system reliability is the ability of reservoir to perform its required functions under stated conditions for a specified period of time. In classical method of reservoir system reliability analysis, the operation policy is used in a simple simulation model, considering the historical/synthetic inflow series and a number of physical bounds on a reservoir system. This type of reliability analysis assumes a reservoir system as fully failed or functioning, called binary state assumption. A number of researchers from various research backgrounds have shown that the binary state assumption in the traditional reliability theory is not extensively acceptable. Our approach to tackle the present problem space is to implement the algorithm of advance first order second moment (AFOSM) method. In this new method, the inflow and reservoir storage are considered as uncertain variables. The mean, variance and covariance of uncertain variables are determined using moment values of reservoir state variables. For this purpose, a stochastic optimization model developed based on the constraint state formulation is applied. The proposed model of reliability analysis is used to a real case study in Iran. As a result, monthly probabilities of water allocation were computed from AFOSM method, and the outputs were compared with those from Monte Carlo method. The comparison shows that the outputs from AFOSM method are similar to those from the Monte Carlo method. In term of practical use of this study, the proposed method is appropriate to determine the monthly probability of failure in water allocation without the aid of simulation.

New methods for system reliability analysis of soil slopes

A slope may have many possible slip surfaces. As sliding along any slip surface can cause slope failure, the system failure probability of a slope is different from the probability of failure along an individual slip surface. In this paper, we first suggest an efficient method for evaluating the system failure probability of a slope that considers a large number of possible slip surfaces. To obtain more insights into the system failure probability of a slope, we also propose a method to identify a few representative slip surfaces most important for system reliability analysis among a large number of potential slip surfaces and to calculate the system failure probability based on these representative slip surfaces. An equation for estimating the bounds of system failure probability based on the failure probability of the most critical slip surface is also suggested. The system failure probability is governed by only a few representative slip surfaces. For a homogenous slope, the failure probability of the most critical slip surface is a good approximation of the system failure probability. For a slope in layered soils, the system failure probability can be significantly larger than the failure probability of the most critical slip surface.

A Generalized Complementary Intersection Method (GCIM) for System Reliability Analysis

This paper presents a Generalized Complementary Intersection Method (GCIM) that can predict system reliability for series, parallel, and mixed systems. The GCIM is an extension of the original study, referred to as the Complementary Intersection Method (CIM). The CIM was developed to assess system reliability for series systems. The contribution of this paper is to generalize the original CIM so that it can be used for system reliability analysis regardless of system structures (series, parallel, and mixed system). First, we derive a closed-form system reliability formula for a parallel system through its transformation into a series system using De Morgan’s law. Second, a unified system reliability analysis framework is proposed for mixed systems by defining a new System Structure matrix (SS-matrix) and employing the Binary Decision Diagram (BDD) technique. The SS-matrix is used to present any system structure in a comprehensive matrix form. Then the BDD technique together with the SS-matrix automates the process to identify system’s mutually exclusive path sets, of which each path set is a series system. As a result, system reliability with any system structure can be decomposed into the probabilities of the mutually exclusive path sets. Five engineering examples are used to demonstrate that the proposed GCIM can assess system reliability regardless of the system structures.

Efficient system reliability analysis illustrated for a retaining wall and a soil slope

Although first-order reliability method is a common procedure for estimating failure probability, the formulas derived for bimodal bounds of system failure probability have not been widely used as expected in present reliability analyses. The reluctance for applying these formulas in practice may be partly due to the impression that the procedures to implement the system reliability theory are tedious. Among the methods for system reliability analysis, the approach suggested in Ditlevsen 1979 is considered here because it is a natural extension of the first-order reliability method commonly used for failure probability estimation corresponding to a single failure mode, and it can often provide reasonably narrow failure probability bounds. To facilitate wider practical application, this paper provides a short program code in the ubiquitous Excel spreadsheet platform for efficiently calculating the bounds for system failure probability. The procedure is illustrated for a semi-gravity retaining wall with two failure modes, a soil slope with two and eight failure modes, and a loaded beam with three failure modes. In addition, simple equations are provided to relate the correlated but unrotated equivalent standard normals of the Low and Tang 2007 FORM procedure with the uncorrelated but rotated equivalent standard normals of the classical FORM procedure. Also demonstrated are the need for investigating different permutations of failure modes in order to get the narrowest bounds for system failure probability, and the use of SORM reliability index for system reliability bounds in a case where the curvature of the limit state surface cannot be neglected.

System reliability analysis with saddlepoint approximation

System reliability is usually estimated through component reliability, which is commonly computed by the First Order Reliability Method (FORM). The FORM is computationally efficient, but may not be accurate for nonlinear limit-state functions. An alternative system reliability analysis method is proposed based on saddlepoint approximation. Unlike the FORM that linearizes limit-state functions in a transformed random space, the proposed method linearizes the limited-state functions without any transformation. After the linearization, the joint probability density of limit-state functions is estimated by the multivariate saddlepoint approximation. Without the nonnormal-to-normal transformation, the present method is more accurate than the FORM when the transformation increases the nonlinearity of limit-state functions. As demonstrated in the two examples, the new method is also as efficient as the FORM.

Evaluation of multivariate normal integrals for general systems by sequential compounding

System reliability analysis often requires efficient and accurate evaluation of a multivariate normal integral. Despite recent advances in system reliability analysis methods, it is still a challenging task especially when the definition of the system event is complex; the system has a large number of components; and/or the component events have significant statistical dependence. This paper presents a new method developed for evaluating multivariate normal integrals defined for general system events including series, parallel, cut-set and link-set systems. The method compounds two components coupled by union or intersection sequentially until the system becomes a single compound event. Efficient numerical procedures are developed for obtaining the reliability index of the new compound event, and the correlation coefficients between the compound event and the remaining component events, at each step of the sequential compounding. The accuracy and efficiency of the proposed method, and its applicability to various types and sizes of multivariate normal integrals are demonstrated by numerical examples.

Multi‐scale system reliability analysis of lifeline networks under earthquake hazards

AbstractRecent earthquake events evidenced that damage of structural components in a lifeline network may cause prolonged disruption of lifeline services, which eventually results in significant socio‐economic losses in the affected area. Despite recent advances in network reliability analysis, the complexity of the problem and various uncertainties still make it a challenging task to evaluate the post‐hazard performance and connectivity of lifeline networks efficiently and accurately. In order to overcome such challenges and take advantage of merits of multi‐scale analysis, this paper develops a multi‐scale system reliability analysis method by integrating a network decomposition approach with the matrix‐based system reliability (MSR) method. In addition to facilitating system reliability analysis of large‐size networks, the multi‐scale approach enables optimizing the level of computational effort on subsystems; identifying the relative importance of components and subsystems at multiple scales; and providing a collaborative risk management framework. The MSR method is uniformly applied for system reliability analyses at both the lower‐scale (for link failure) and the higher‐scale (for system connectivity) to obtain the probability of general system events, various conditional probabilities, component importance measures, statistical correlation between subsystem failures and parameter sensitivities. The proposed multi‐scale analysis method is demonstrated by its application to a gas distribution network in Shelby County of Tennessee. A parametric study is performed to determine the number of segments during the lower‐scale MSR analysis of each pipeline based on the strength of the spatial correlation of seismic intensity. It is shown that the spatial correlation should be considered at both scales for accurate reliability evaluation. The proposed multi‐scale analysis approach provides an effective framework of risk assessment and decision support for lifeline networks under earthquake hazards. Copyright © 2009 John Wiley & Sons, Ltd.

System reliability analysis by enhanced Monte Carlo simulation

The main focus of this paper is on the development of a Monte Carlo based method for estimating the reliability of structural systems. The use of Monte Carlo methods for system reliability analysis has several attractive features, the most important being that the failure criterion is usually relatively easy to check almost irrespective of the complexity of the system. The flip side of such methods is the amount of computational efforts that may be involved. However, by reformulating the reliability problem to depend on a parameter and exploiting the regularity of the failure probability as a function of this parameter, it is shown that a substantial reduction of the computational efforts involved can be obtained.

Complementary Intersection Method for System Reliability Analysis

Although researchers desire to evaluate system reliability accurately and efficiently over the years, little progress has been made on system reliability analysis. Up to now, bound methods for system reliability prediction have been dominant. However, two primary challenges are as follows: (1) Most numerical methods cannot effectively evaluate the probabilities of the second (or higher)–order joint failure events with high efficiency and accuracy, which are needed for system reliability evaluation and (2) there is no unique system reliability approximation formula, which can be evaluated efficiently with commonly used reliability methods. Thus, this paper proposes the complementary intersection (CI) event, which enables us to develop the complementary intersection method (CIM) for system reliability analysis. The CIM expresses the system reliability in terms of the probabilities of the CI events and allows the use of commonly used reliability methods for evaluating the probabilities of the second–order (or higher) joint failure events efficiently. To facilitate system reliability analysis for large-scale systems, the CI-matrix can be built to store the probabilities of the first- and second-order CI events. In this paper, three different numerical solvers for reliability analysis will be used to construct the CI-matrix numerically: first-order reliability method, second-order reliability method, and eigenvector dimension reduction (EDR) method. Three examples will be employed to demonstrate that the CIM with the EDR method outperforms other methods for system reliability analysis in terms of efficiency and accuracy.