Reliability assessment for systems suffering common cause failure based on Bayesian networks and proportional hazards model

The Bayesian network (BN) is an efficient tool for probabilistic modeling and causal inference, and it has gained considerable attentions in the field of reliability assessment. The common cause failure (CCF) is simultaneous failure of multiple elements in a system under a common cause, and it is a common phenomenon in engineering systems with dependent elements. Several models and methods have been proposed for modeling and assessment of complex systems with CCF. In this paper, a new reliability assessment method is proposed for the systems suffering from CCF in a dynamic environment. The CCF among components is characterized by a BN, which allows for bidirectional reasoning. A proportional hazards model is applied to capture the dynamic working environment of components and then the reliability function of the system is obtained. The proposed method is validated through an illustrative example, and some comparative studies are also presented.     

Reliability sensitivity analysis with random and interval variables

In reliability analysis and reliability‐based design, sensitivity analysis identifies the relationship between the change in reliability and the change in the characteristics of uncertain variables. Sensitivity analysis is also used to identify the most significant uncertain variables that have the highest contributions to reliability. Most of the current sensitivity analysis methods are applicable for only random variables. In many engineering applications, however, some of uncertain variables are intervals. In this work, a sensitivity analysis method is proposed for the mixture of random and interval variables. Six sensitivity indices are defined for the sensitivity of the average reliability and reliability bounds with respect to the averages and widths of intervals, as well as with respect to the distribution parameters of random variables. The equations of these sensitivity indices are derived based on the first‐order reliability method (FORM). The proposed reliability sensitivity analysis is a byproduct of FORM without any extra function calls after reliability is found. Once FORM is performed, the sensitivity information is obtained automatically. Two examples are used for demonstration. Copyright © 2009 John Wiley & Sons, Ltd.     

Reliability study of fracture mechanics based non‐probabilistic interval analysis model

In this paper, we advanced a new interval reliability analysis model for fracture reliability analysis. Based on the non‐probabilistic stress intensity factor interference model and the ratio of the volume of the safe region to the total volume of the region associated with the variation of the standardized interval variables is suggested as the measure of structural non‐probabilistic reliability. We use this theory to calculate the reliability of structure based on fracture criterion. This model needs less uncertain information, so it has less limitation for analysing an uncertain structure or system. Examples of practical application are given to explain the simplicity and practicability of this model by comparing the interval reliability analysis model with probabilistic reliability analysis model.     

引入不确定参数的汽车盘式制动器振动稳定性分析

针对汽车制动器的噪声抑制问题,基于可靠性分析理论,将蒙特卡洛法与响应面法相结合,提出了一种汽车盘式制动器系统振动稳定性的可靠性分析方法。该方法针对制动噪声产生具有不确定性的特点,引入随机和区间不确定性参数对制动器系统进行描述,建立包含随机参数和区间参数的制动器不稳定特征值的响应面近似模型,进而采用Sobol′全局灵敏度分析法和蒙特卡洛法分别对不确定参数的全局灵敏度和系统稳定性的可靠度进行分析。用该方法对某车的浮钳盘式制动器系统进行研究,分析了系统稳定性的可靠度和不确定参数的全局灵敏度,甄别了不确定性参数对系统稳定性的影响,并从可靠性角度提出了改善制动器系统振动稳定性的工程措施。     

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 hierarchical computer-based systems subject to common-cause failures

The results from reliability modeling and analysis are key contributors to design and tuning activities for computer-based systems. Each architecture style, however, poses different challenges for which analytical approaches must be developed or modified. The challenge we address in this paper is the reliability analysis of hierarchical computer-based systems (HS) with common-cause failures (CCF). The dependencies among components introduced by CCF complicate the reliability analysis of HS, especially when components affected by a common cause exist on different hierarchical levels. We propose an efficient decomposition and aggregation (EDA) approach for incorporating CCF into the reliability evaluation of HS. Our approach is to decompose an original HS reliability analysis problem with CCF into a number of reduced reliability problems freed from the CCF concerns. The approach is represented in a dynamic fault tree by a proposed CCF gate modeled after the functional dependency gate. We present the basics of the EDA approach by working through a hypothetical analysis of a HS subject to CCF and show how it can be extended to an analysis of a hierarchical phased-mission system subject to different CCF depending on mission phases.     

Load sharing in series configuration

In reliability engineering, load sharing is typically associated with a system in parallel configuration. Examples include bridge support structures, electric power supply systems, and multiprocessor computing systems. We consider a reliability maximization problem for a high‐voltage commutation device, wherein the total voltage across the device is shared by the components in series configuration. Here, the increase of the number of load‐sharing components increases component–level reliability (as the voltage load per component reduces) but may decrease system–level reliability (because of the increased number of components in series). We provide the solution for the 2 popular life‐load models: the proportional hazard and the accelerated failure time models with the underlying exponential and Weibull distributions for both a single and dual failure modes.     

A hybrid reliability model for structures with truncated probability distributions

In traditional reliability analysis, the uncertain parameters are generally treated by some ideal probability distributions with infinite tails, which, however, seems inconsistent with the practical situations as nearly all the uncertain parameters in engineering structures will get their values within a limited interval. To eliminate such an inconsistence and thereby improve the precision of the reliability analysis, the truncated probability distributions are then employed to quantify the uncertainty in this paper, and a corresponding reliability analysis method is developed. Two cases of positional relations are summarized for the uncertainty domain and the failure surface according to whether their intersection set is non-empty or empty. The probability and non-probability convex model methods are employed to deal with these two cases, respectively, and based on it, a hybrid reliability model is then constructed for truncated distribution problems. An efficient approach is also provided to distinguish these two positional relations and thereby determine which one of the probability and non-probability methods should be used when computing a real hybrid reliability. Five numerical examples are investigated to demonstrate the effectiveness of the present method.     

System-level load–strength interference based reliability modeling of k-out-of-n system

The issue of information loss in the process of system reliability modeling through conventional load–strength interference analysis is discussed first, and the reason why it is impossible to construct dependent system reliability model simply by means of component reliability index is demonstrated. Then, an approach to modeling the reliability of dependent system with common cause failure (CCF) is presented. The approach is based on system-level load–strength interference analysis and a concept of ‘conditional failure probability of component’ as well. With the opinion that load randomness is the direct cause of failure dependence, a discrete type system reliability model is developed via the conditional component failure probability concept. At last, the model's capabilities to estimate system reliability with CCF effect and to predict high multiplicity failure probability based on low multiplicity failure event data are proved.     

Reliability of redundant ductile structures with uncertain system failure criteria

Current reliability based approaches to structural design are typically element based: they commonly include uncertainties in the structural resistance, applied loads and geometric parameters, and in some cases in the idealized structural model. Nevertheless, the true measure of safety is the structural systems reliability which must consider multiple failure paths, load sharing and load redistribution after member failures, and is beyond the domain of element reliability analysis. Identification of system failure is often subjective, and a crisp definition of system failure arises naturally only in a few idealized instances equally important. We analyse the multi-girder steel highway bridge as a k out of n active parallel system. System failure is defined as gross inelastic deformation of the bridge deck; the subjectivity in the failure criterion is accounted for by generalizing k as a random variable. Randomness in k arises from a non-unique relation between number of failed girders and maximum deflection and from randomness in the definition of the failure deflection. We show how uncertain failure criteria and structural systems analyses can be decoupled. Randomness in the transverse location of trucks is considered and elastic perfectly plastic material response is assumed. The role of the system factor modifying the element-reliability based design equation to achieve a target system reliability is also demonstrated.     

Reliability analysis of multi‐state series systems with performance sharing mechanism under epistemic uncertainty

For real engineering systems, it is sometimes difficult to obtain sufficient data to estimate the precise values of some parameters in reliability analysis. This kind of uncertainty is called epistemic uncertainty. Because of the epistemic uncertainty, traditional universal generating function (UGF) technique is not appropriate to analyze the reliability of systems with performance sharing mechanism under epistemic uncertainty. This paper proposes a belief UGF (BUGF)‐based method to evaluate the reliability of multi‐state series systems with performance sharing mechanism under epistemic uncertainty. The proposed BUGF‐based reliability analysis method is validated by an illustrative example and compared with the interval UGF (IUGF)‐based methods with interval arithmetic or affine arithmetic. The illustrative example shows that the proposed BUGF‐based method is more efficient than the IUGF‐based methods in the reliability analysis of multi‐state systems (MSSs) with performance sharing mechanism under epistemic uncertainty.     

The set-theory method for systems reliability of structures with degrading components

The times and frequencies of inspection, maintenance and replacement in structural systems are complicated by uncertain degradation rates of structural characteristics. Although degradation work at the component, or single failure mode level, is ongoing, this paper presents a method for assessing systems reliability where failure events may be described by time-variant parallel and/or series systems. Herein the models for the degradation rates contain random variables and time. For multiple failure modes and a sequence of discrete times, set theory establishes the true incremental failure region that emerges from a safe region. Probabilities via Monte-Carlo simulation require only time-invariant calculations. The cumulative failure distribution is the summation of the incremental failure probabilities. A practical implementation of the theory requires only two contiguous times. Error analysis suggests ways to predict and minimize errors so the method appears sufficiently accurate for engineering applications. Two structures with elastic-brittle material and time-invariant loads show the details of the method and the potential of the approach. It is shown that the proposed method provides a more realistic and efficient way to predict systems reliability than path-tracing methods that are available in the open literature.     

A unified methodology for reliability assessment of systems with active redundancy

The reliability of engineering systems is usually improved by the inclusion of redundant components in the design. Often, the redundant components must all contribute actively to the operation of the system. Examples include structures, water and power distribution systems, and communication networks. For these systems, the failure of each successive component defines a different topological configuration for the system. A reliable system should perform adequately in as many of these configurations as possible. Consequently, the reliability of a system with active redundancy depends on two factors: the probability, considering component failures, that a functional system topology is maintained; and the probability of adequate system performance in each functional configuration. To date, no single reliability measure exists which combines both of these factors, but such a measure would be useful for comparison of alternative redundant designs. Current methods for reliability assessment have been tailored to the purposes of individual engineering disciplines and reflect the inherent physical properties of specific types of systems. However, an increasing need for reliability analysis of large, complex, multidisciplinary systems requires a more general and unified approach. In this paper, we propose a unified, model-based methodology for reliability-based design which provides a single, second moment reliability index for systems with active redundancy. The reliability index of a redundant pipe network is calculated as an illustrative example.     

A fatigue damage accumulation model for reliability analysis of engine components under combined cycle loadings

Rotor components of an aircraft engine in service are usually subjected to combined high and low cycle fatigue (CCF) loadings. In this work, combining with the load spectrum of CCF, a modified damage accumulation model for CCF life prediction of turbine blades is first put forward to take into account the effects of load consequence and load interaction caused by high‐cycle fatigue (HCF) loads and low‐cycle fatigue (LCF) loads under CCF loading conditions. The predicted results demonstrate that the proposed model presents a higher prediction accuracy than Miner, Manson‐Halford model does. Moreover, to evaluate the fatigue reliability of rotor components, reliability model with the failure mode of CCF is proposed on the basis of the stress‐strength interference method when considering the strength degeneration, and its results show that the reliability model with CCF is more suitable for aero‐engine components than that with the failure mode of single fatigue.     

A linguistic risk prioritization approach for failure mode and effects analysis: A case study of medical product development

Failure mode and effects analysis (FMEA) is a widely used risk management technique for identifying the potential failures from a system, design, or process and determining the most serious ones for risk reduction. Nonetheless, the traditional FMEA method has been criticized for having many deficiencies. Further, in the real world, FMEA team members are usually bounded rationality, and thus, their psychological behaviors should be considered. In response, this study presents a novel risk priority model for FMEA by using interval two‐tuple linguistic variables and an integrated multicriteria decision‐making (MCDM) method. The interval two‐tuple linguistic variables are used to capture FMEA team members' diverse assessments on the risk of failure modes and the weights of risk factors. An integrated MCDM method based on regret theory and TODIM (an acronym in Portuguese for interactive MCDM) is developed to prioritize failure modes taking experts' psychological behaviors into account. Finally, an illustrative example regarding medical product development is included to verify the feasibility and effectiveness of the proposed FMEA. By comparing with other existing methods, the proposed linguistic FMEA approach is shown to be more advantageous in ranking failure modes under the uncertain and complex environment.     

多源不确定性条件下气动弹性系统颤振可靠性分析方法

传统的气动弹性系统颤振分析模型大多是在确定性参数条件下建立的,当系统中存在不确定因素时,按确定性方法设计的气动弹性系统存在颤振失效风险。以概率和非概率区间模型为基础,建立了单源不确定性条件下颤振可靠性分析模型;在此基础上,针对含随机和区间多源不确定参数的气动弹性系统颤振可靠性分析问题,提出一种基于分步求解策略的新型混合可靠性分析与度量法,获取多源不确定性条件下气动弹性系统的颤振可靠度,实现了对多源不确定性条件下颤振可靠性的有效评估。数值算例表明,该方法与蒙特卡洛模拟法相吻合,且具有显著的计算效率优势。     

Approximate Reliability and Availability Models for High Availability and Fault‐tolerant Systems with Repair

Systems designed for high availability and fault tolerance are often configured as a series combination of redundant subsystems. When a unit of a subsystem fails, the system remains operational while the failed unit is repaired; however, if too many units in a subsystem fail concurrently, the system fails. Under conditions usually met in practical situations, we show that the reliability and availability of such systems can be accurately modeled by representing each redundant subsystem with a constant, ‘effective’ failure rate equal to the inverse of the subsystem mean‐time‐to‐failure (MTTF). The approximation model is surprisingly accurate, with an error on the order of the square of the ratio mean‐time‐to‐repair to mean‐time‐to‐failure (MTTR/MTTF), and it has wide applicability for commercial, high‐availability and fault‐tolerant computer systems. The effective subsystem failure rates can be used to: (1) evaluate the system and subsystem reliability and availability; (2) estimate the system MTTF; and (3) provide a basis for the iterative analysis of large complex systems. Some observations from renewal theory suggest that the approximate models can be used even when the unit failure rates are not constant and when the redundant units are not homogeneous. Copyright © 2004 John Wiley & Sons, Ltd.     

Reliability analysis of standby systems with multi‐state elements subject to constant transition rates

Standby redundancy has been extensively applied to critical engineering systems to enhance system reliability. Researches on reliability evaluation for standby systems focus more on systems with binary‐state elements. However, multi‐state elements with different performances have played a significant role in engineering systems. This paper presents an approach for reliability analysis of standby systems composed of multi‐state elements with constant state transition rates and absorbing failure states. The approach allows modelling different standby systems beyond cold, warm and hot ones by taking into account differences in possible maintenance of elements in standby and operation modes and dependence of elements' operational behavior on their initial state at the time of activation. An iterative algorithm for reliability evaluation based on element state probabilities is suggested. Illustrating examples of evaluating reliability of different types of homogeneous and heterogeneous standby systems are demonstrated.     

Reliability Analysis Method on Repairable System with Standby Structure Based on Goal Oriented Methodology

This paper presents a reliability analysis method on repairable system with standby structure based on goal oriented (GO) methodology. Firstly, a new combination of GO operator, which is composed of a new logical GO operator named Type 18A operator and a new auxiliary GO operator named Type 20 operator, is created to represent standby mode. The availability formula of standby equipment with translation exception is deduced based on Markov process theory. Then, the application method of combination of GO operator for standby mode and the analysis process of repairable system with standby structure based on GO method are proposed. Thirdly, this new combination of GO operator is applied in availability analysis of the hydraulic oil supply system of power‐shift steering transmission. Finally, the results obtained by the new GO method are compared with the results of fault tree analysis, Monte Carlo simulation, GO methods using Type 2 operator and Type 18 operator to represent the standby mode, respectively. And the comparison results show that this new GO method is applicable and reasonable for reliability analysis of repairable system with standby structure. All in all, this paper provides guidance for reliability analysis of repairable systems with standby structure. Copyright © 2015 John Wiley & Sons, Ltd.     

Reliability Analysis of Multiple Causes of Failure in Presence of Independent Competing Risks

The failures of complex systems always arise from different causes in reliability test. However, it is difficult to evaluate the failure effect caused by a specific cause in presence of other causes. Therefore, a generalize reliability analysis model, which takes into account of the multiple competing causes, is highly needed. This paper develops a statistical reliability analysis procedure to investigate the reliability characteristics of multiple failure causes under independent competing risks. We mainly consider the case when the lifetime data follow log‐location‐scale distributions and may also be right‐censored. Maximum likelihood (ML) estimators of unknown parameters are derived by applying the Newton–Raphson method. With the large‐sample assumption, the normal approximation of the ML estimators is used to construct the asymptotic confidence intervals in which the standard error of the variance‐covariance matrix is calculated by using the delta method. In particular, the Akaike information criterion is utilized to determine the appropriate fitted distribution for each cause of failure. An illustrative numerical experiment about the fuel cell engine (FCE) is presented to demonstrate the feasibility and effectiveness of the proposed model. The results can facilitate continued advancement in reliability prediction and reliability allocation for FCE, and also provide theoretical basis for the application of reliability concepts to many other complex systems. Copyright © 2014 John Wiley & Sons, Ltd.