Fault trees analysis using expert opinion based on fuzzy‐bathtub failure rates

The main objective of fault tree analysis method is to estimate the “Top Event occurrence probability”. This requires determination of failure time distribution functions also known as “Bathtub Curves” for each of the system elements/events. This paper introduces a novel method to determine the failure time distribution functions using possibility theory. For this purpose, fuzzy‐bathtub distributions using expert opinions are generated for basic events and fuzzy formulas are derived for static and dynamic gates fault tree constructions. This process completed by proposed fuzzy Monte Carlo simulation throughout the preferred operational time and uses the actual time‐to‐failure data. Accordingly, the Top Event failure curve and the reliability profile of the system are depicted based on the defuzzificated basic‐events' bathtub‐failure‐rates. The results show that the proposed method not only is feasible and powerful but can also be accurate more than the other probabilistic and possibilistic techniques because of the component failure rates follow the real failure distributions.     

A reliability allocation method of mechanism considering system performance reliability

It is generally believed that the reliability of a mechanical system is determined by its composition. The system operates properly when all of its components do not fail. Based on this assumption, the reliability of the system can be represented by the reliability of its components. A problem arises when applying this hypothesis to a system containing motion mechanisms. There is a phenomenon in motion mechanism that the components do not happen structural failure (we call it “Type I failure”) and joint failure (we call it “Type II failure”), but the function of the mechanism cannot meet the requirements (we call it “Type III failure”). A reliability allocation method, which synthetically considers the composition and Type III failure modes of the motion mechanism, is proposed to solve this problem. A relative dispersion factor is introduced to describe the failure dependence of components and is proposed to calculate the complexity and criticality. A series system reliability allocation model considering three types of failure modes is established. Finally, using an airplane gear door lock mechanism as an example, a comparative analysis of the system reliability allocation results with and without considering Type III failure modes is made. The allocation results show the component reliability value without considering Type III failure modes is less than that when considering them, which will increase the system hazards. The result considering Type III failure modes is more reasonable than that from the traditional method.     

Set theoretic formulation of performance reliability of multiple response time‐variant systems due to degradations in system components

This paper presents a design stage method for assessing performance reliability of systems with multiple time‐variant responses due to component degradation. Herein the system component degradation profiles over time are assumed to be known and the degradation of the system is related to component degradation using mechanistic models. Selected performance measures (e.g. responses) are related to their critical levels by time‐dependent limit‐state functions. System failure is defined as the non‐conformance of any response and unions of the multiple failure regions are required. For discrete time, set theory establishes the minimum union size needed to identify a true incremental failure region. A cumulative failure distribution function is built by summing incremental failure probabilities. A practical implementation of the theory can be manifest by approximating the probability of the unions by second‐order bounds. Further, for numerical efficiency probabilities are evaluated by first‐order reliability methods (FORM). The presented method is quite different from Monte Carlo sampling methods. The proposed method can be used to assess mean and tolerance design through simultaneous evaluation of quality and performance reliability. The work herein sets the foundation for an optimization method to control both quality and performance reliability and thus, for example, estimate warranty costs and product recall. An example from power engineering shows the details of the proposed method and the potential of the approach. Copyright © 2006 John Wiley & Sons, Ltd.     

Reliability Analysis of Zero‐Failure Data with Poor Information

For costly and dangerous experiments, growing attention has been paid to the problem of the reliability analysis of zero‐failure data, with many new findings in world countries, especially in China. The existing reliability theory relies on the known lifetime distribution, such as the Weibull distribution and the gamma distribution. Thus, it is ineffective if the lifetime probability distribution is unknown. For this end, this article proposes the grey bootstrap method in the information poor theory for the reliability analysis of zero‐failure data under the condition of a known or unknown probability distribution of lifetime. The grey bootstrap method is able to generate many simulated zero‐failure data with the help of few zero‐failure data and to estimate the lifetime probability distribution by means of an empirical failure probability function defined in this article. The experimental investigation presents that the grey bootstrap method is effective in the reliability analysis only with the few zero‐failure data and without any prior information of the lifetime probability distribution. Copyright © 2011 John Wiley & Sons, Ltd.     

Fatigue reliability study on T‐welded component considering load shedding

In this paper, a coupled reliability method for structural fatigue evaluation considering load shedding is first proposed based on probabilistic fracture mechanics in which the uncertainties of the structural parameters are taken into account. Then, the method is applied to predict the fatigue reliability of the T‐welded structure to the case of considering load shedding or not. The compared results show that by considering the load shedding, the structural fatigue reliability might be improved with less conservativeness. The influence rules of the load‐shedding coefficient on the fatigue failure probability of the T‐welded component are investigated, and some interesting results are obtained. That is, the influences of load‐shedding coefficient on the fatigue failure probability can be divided into three regions, namely the high, medium and low fatigue failure areas. The last area is the most intriguing when we try to design a T‐welded structure. The thickness of T‐welded structure along the crack propagation direction is found to be one of the important design variables for the design of fatigue reliability, in which the low‐fatigue failure zone is used as one of the reliability constraints. The basic design frame of T‐welded structure is established to constrain the fatigue failure probability within the low‐fatigue failure area.     

Reliability modeling of multi‐state degraded repairable systems and its applications to automotive systems

In this paper, we presented a continuous‐time Markov process‐based model for evaluating time‐dependent reliability indices of multi‐state degraded systems, particularly for some automotive subsystems and components subject to minimal repairs and negative repair effects. The minimal repair policy, which restores the system back to an “as bad as old” functioning state just before failure, is widely used for automotive systems repair because of its low cost of maintenance. The current study distinguishes with others that the negative repair effects, such as unpredictable human error during repair work and negative effects caused by propagated failures, are considered in the model. The negative repair effects may transfer the system to a degraded operational state that is worse than before due to an imperfect repair. Additionally, a special condition that a system under repair may be directly transferred to a complete failure state is also considered. Using the continuous‐time Markov process approach, we obtained the general solutions to the time‐dependent probabilities of each system state. Moreover, we also provided the expressions for several reliability measures include availability, unavailability, reliability, mean life time, and mean time to first failure. An illustrative numerical example of reliability assessment of an electric car battery system is provided. Finally, we use the proposed multi‐state system model to model a vehicle sub‐frame fatigue degradation process. The proposed model can be applied for many practical systems, especially for the systems that are designed with finite service life.     

多失效模式典型结构系统可靠性稳健设计方法研究

应用随机摄动技术与二阶矩方法,结合概率网络估算法（Probability Network Evaluation Technique）,讨论了多失效模式下结构系统的可靠性和可靠性灵敏度问题,并进一步对结构系统的可靠性稳健设计进行了分析。获得了不同失效模式间的相关统计特性,应用概率网络估算法确定了系统的代表失效模式,得出了...     

Sample regeneration algorithm for structural failure probability function estimation

An efficient strategy to approximate the failure probability function in structural reliability problems is proposed. The failure probability function (FPF) is defined as the failure probability of the structure expressed as a function of the design parameters, which in this study are considered to be distribution parameters of random variables representing uncertain model quantities. The task of determining the FPF is commonly numerically demanding since repeated reliability analyses are required. The proposed strategy is based on the concept of augmented reliability analysis, which only requires a single run of a simulation-based reliability method. This paper introduces a new sample regeneration algorithm that allows to generate the required failure samples of design parameters without any additional evaluation of the structural response. In this way, efficiency is further improved while ensuring high accuracy in the estimation of the FPF. To illustrate the efficiency and effectiveness of the method, case studies involving a turbine disk and an aircraft inner flap are included in this study.     

结构可靠性灵敏度因子的一种新指标

通过对可靠性灵敏度的分析和推导,利用灵敏度标准差值构造了一种新的可靠性灵敏度因子。与传统灵敏度因子不同的是,新因子不仅能反映各随机变量对结构失效概率影响的重要性程度,因子的数值大小还能表征将单个变量作为确定性变量处理或将多个变量同时作为确定性量处理时所引起的可靠指标误差大小。据此结论,采用新灵敏度因子进行灵敏度分析时,只需要进行一次分析就能识别出各随机变量对结构失效整体影响的有益信息,可以有效地提高计算效率,降低分析难度。利用数值算例验证说明了所提可靠性灵敏度因子指标的有效性。     

Optimization of a pipe end upsetting process

A method is proposed for the optimization, by finite element analysis, of design variables of sheet metal forming processes. The method is useful when the non-controllable process parameters (e.g. the coefficient of friction or the material properties) can be modelled as random variables, introducing a degree of uncertainty into any process solution. The method is suited for problems with large FEM computational times and small process window. The problem is formulated as the minimization of a cost function, subject to a reliability constraint. The cost function is indirectly optimized through a “metamodel”, built by “Kriging” interpolation. The reliability, i.e. the failure probability, is assessed by a binary logistic regression analysis of the simulation results. The method is applied to the u-channel forming and springback problem presented in Numisheet 1993, modified by handling the blankholder force as a time-dependent variable.     

Experimental characterisation of a CuAg alloy for thermo‐mechanical applications. Part 2: Design strain‐life curves estimated via statistical analysis

Strain‐life fatigue data on copper alloys, especially type CuAg, are seldom available in the literature. This work fills this gap by estimating the strain‐life curves of a CuAg alloy used for thermo‐mechanical applications, from isothermal low‐cycle fatigue tests at 3 temperatures (room temperature, 250°C, 300°C). Regression analysis is used to estimate the median fatigue curves at 50% survival probability. The comparison of median curves with the Universal Slopes Equation model, calibrated on monotonic tensile properties, shows a fairly good agreement. Design strain‐life curves with a lower failure probability and given confidence are estimated by several approximate statistical methods (“Equivalent Prediction Interval,” univariate tolerance interval, Owen's tolerance interval for regression). When higher survival probabilities are considered, the results show a marked decrease in the allowable design strain at a prescribed fatigue life. The suggested procedure thus improves the durability analysis of components loaded thermo‐mechanically.     

On the Reliability Evaluation of Failure Delayed Industrial Systems

This paper presents an analytical approach for the evaluation of multi‐user safety critical systems presenting a failure delayed behavior pattern. As a consequence of a failure event, the performance of these systems worsens progressively due to the internal fault tolerance mechanisms or the complacency of the users regarding the temporary unavailability of the services. A distinctive feature of the approach is the ability to handle stochastic models containing multiple processes with generalized distributions. The approach is based on the determination of analytical expressions to measure reliability, for instance, frequency and probability of failure states, which may be evaluated using general purpose mathematical tools. The paper first reviews other well‐established techniques employed in the assessment of non‐Markovian systems, particularly those based on stochastic Petri nets. The rationale of the new approach and its fundamental algorithms are presented together with a set of illustrative examples which highlight the strengths of the approach, as well as its limitations. Copyright © 2012 John Wiley & Sons, Ltd.     

Transition from partial factors method to Simulation-Based Reliability Assessment in structural design

Advances in computer technology and simulation techniques allow for considering a transition from semiprobabilistic structural reliability assessment concepts, such as partial factor design (PFD), to a fully probabilistic concept applicable in design practice. Referring to the proposed Simulation-Based Reliability Assessment concept (SBRA), reengineering of the reliability assessment process is discussed. The SBRA concept corresponds to the limit states philosophy. The input variables are expressed by bounded histograms, the loads are represented by load duration curves and the Monte Carlo method-based computer programs nad modern PC are used for analyzing the reliability functions containing random variables. The reliability (that is, safety, durability and serviceability) is expressed by probability of failure P_f. Using selected examples and a parametric study, the potential, efficiency and advantages of the proposed method applicable in design practice are illustrated.     

Local estimation of failure probability function by weighted approach

In the reliability-based design of engineering systems, it is often required to evaluate the failure probability for different values of distribution parameters involved in the specification of design configuration. The failure probability as a function of the distribution parameters is referred as the ‘failure probability function (FPF)’ in this work. From first principles, this problem requires repeated reliability analyses to estimate the failure probability for different distribution parameter values, which is a computationally expensive task. A “weighted approach” is proposed in this work to locally evaluate the FPF efficiently by means of a single simulation. The basic idea is to rewrite the failure probability estimate for a given set of random samples in simulation as a function of the distribution parameters. It is shown that the FPF can be written as a weighted sum of sample values. The latter must be evaluated by system analysis (the most time-consuming task) but they do not depend on the distribution. Direct Monte Carlo simulation, importance sampling and Subset Simulation are incorporated under the proposed approach. Examples are given to illustrate their application.     

EURAXLES – A global approach for design,production and maintenance of railway axles: WP1 – Advances in fatigue load analysis and reliability assessment of railway axles

The work presented in this paper was led within the collaborative project “Euraxles” of the FP7 program of the European Commission. It aimed at developing processes and methods that contribute to the minimization of the risk of fatigue failure of railway axles in service. This paper focuses on the development of a method to assess the reliability of axles according to fatigue damage. The proposed approach is mainly based on the stress strength interference analysis (SSIA) and the fatigue‐equivalent‐load (FEL) methods. It aims at calculating the axles’ probability of fatigue failure, by characterizing the variability of real in‐service loads and the scatter of the axles fatigue strength, and at evaluating more accurately the actual design margins. First of all, the main lines of the stress strength interference analysis method are recalled. This method aims at evaluating the in‐service reliability of components for their design or their homologation. It is used in many industries for various applications (mechanical components or systems, electronic elements, etc.). In the second part, the fatigue load analysis method that is proposed for railway axles is described. It starts with a post‐processing of an axle load measurement: from a time signal of forces applied to both wheels fitted on the axle, fatigue cycles of bending moment applied to the axle are identified and transformed into a cyclic equivalent load, the M_eq, which is a measurement of the severity of the initial variable load. Then, virtual but realistic load spectra are generated, thanks to a classification operation followed by a random draw of elementary load data that considers the operation and maintenance conditions of the axle. All the spectra are then analysed thanks to the fatigue‐equivalent‐load method in order to build the distribution of in‐service load severities that gives a picture of the stress to which the axles are submitted. In the third and last part of the paper, the methods are applied to real data of “Société nationale des chemins de fer français” (SNCF), the French national railway operator. Sensitivity analyses are performed in order to quantify the effect on the M_eq of variations of parameters and to verify the convergence and robustness of the process. Finally, results obtained for a passenger coach are given. The comparison between the distribution of load severities and the normative load, defined as according to european standards EN13103, shows that, for the studied axle, the normative load is very conservative. Using the axles fatigue limits identified on full‐scale tests, a stress strength interference analysis is performed to calculate the probability of failure of the axle.     

Reliability analysis of hybrid ceramic/steel gun barrels

ABSTRACT Failure of the ceramic gun‐barrel lining during single‐shot and burst firing events has been studied by combining a finite‐element method based thermo‐mechanical analysis with a structural reliability analysis. An initial distribution of residual stresses in the lined barrel, as introduced during shrink‐fitting of the steel jacket over the ceramic lining, is taken into account. Forced‐convection boundary conditions at the inner surface of the barrel are determined by carrying out an internal‐ballistic analysis, followed by compressible boundary‐layer modeling of the heat transfer coefficient. The results obtained reveal that due to thermal expansion of the steel jacket during single‐shot and burst ballistic events, tensile axial stresses develop in the ceramic lining near the barrel ends. These stresses are sufficiently high, particularly in the case of burst firing, that they can induce formation of circumferential cracks and, in turn, failure of the lining. Using the Weibull structural reliability analysis, the failure probability for the lining has been computed as 0.0025 and 0.0121 for the single‐round and the 10‐round firing modes, respectively. Optimization of the main design, materials and processing parameters in order to minimize the failure probability for the lining is also discussed.     

Analysis of a Factorial Experiment (Partially Confounded 23)

The problem of devising systematic policies for replacement of equipment subject to wear-out involves the detection of increases in failure rates. Detection procedures are defined as stopping times N with respect to the observed sequence of random failures. The concepts of “quickness of detection” and “frequency of false reactions” are made precise and a class of procedures is studied which optimizes the former asymptotically as the latter is reduced to zero. Results of Monte Carlo experiments are given which show that efficient quickness of detection is attainable simultaneously for various levels of increase in failure rates.     

钢框架结构基于变形可靠度的全概率抗震设计

我国抗震设计规范的抗震设计方法并不是真正意义上的概率极限状态设计,结构可靠度的应用也没有体现出结构的体系可靠度设计水平,因此该文提出了基于变形可靠度验算的二阶段抗震设计方法.该方法采用结构可靠度的数值模拟方法,通过验算小震作用下结构构件承载能力极限状态下的抗震可靠度,验算结构小震作用下正常使用极限状态下和大震作用下侧向...     

Coupling finite element and reliability analysis through proper generalized decomposition model reduction

The FEM is the main tool used for structural analysis. When the design of the mechanical system involves uncertain parameters, a coupling of the FEM with reliability analysis algorithms allows to compute the failure probability of the system. However, this coupling leads to successive finite element analysis of parametric models involving high computational effort. Over the past years, model reduction techniques have been developed in order to reduce the computational requirements in the numerical simulation of complex models. The objective of this work is to propose an efficient methodology to compute the failure probability for a multi‐material elastic structure, where the Young moduli are considered as uncertain variables. A proper generalized decomposition algorithm is developed to compute the solution of parametric multi‐material model. This parametrized solution is used in conjunction with a first‐order reliability method to compute the failure probability of the structure. Applications to multilayered structures in two‐dimensional plane elasticity are presented.Copyright © 2013 John Wiley & Sons, Ltd.