Common-cause Failure Model Research Articles

Integrated unavailability analysis including test degradation and efficiency, components ageing and common cause failures

The article proposes an integrated model for the unavailability of standby components and systems, considering the impacts of ageing, test degradation and test efficiency on independent and common cause failures (CCF) probabilities. The results showed a considerable impact of test efficiency on systems reliability and risk.The CCF model was expanded to incorporate the additional contribution derived from the repair time of identical and redundant components. Two application cases, of system unavailability and Probabilistic Safety Assessment (PSA), were evaluated for several combinations of test efficiency, degradation and ageing, using the traditional and the expanded CCF models. Ignoring the contribution to CCFs derived from the repair time leads to significant risk underestimations, even when ageing and test degradation are not included.Great uncertainties of the model parameters represent an important restriction for the introduction of adverse test effects in risk analysis, but they are important contributors that must be considered explicitly.

Research on reliability analysis strategy of high-speed train ATP on-board equipment under uncertain information

In view of the incomplete knowledge and lack of data, the system has epistemic uncertainties. This paper uses Bayesian network fusion evidence theory to analyze the reliability of high-speed railway ATP on-board equipment. According to the requirements of safety-critical system reliability analysis, this paper starts with the analysis of system structure and unit module status, comprehensively considering the influence of uncertain information, common cause failure, recovery mechanism, and degraded operation on system reliability. In this paper, with the advantage of the Bayesian network in the description of events in multiple states, evidence theory is used to reason about the system under incomplete information conditions, obtain the availability interval of on-board subsystems and discuss the impact of the degraded operation on system availability. The [Formula: see text] factor model is used to analyze common cause failures, and then the Bayesian network modeling of common cause failures is realized by adding common cause failure nodes. The results show that the method enhances the Bayesian network’s ability to process uncertain information, and the common cause failure data of the train control on-board subsystem is continuously accumulated. The factor model can be used to obtain a more practical common cause failure rate.

Copula-based common cause failure models with Bayesian inferences

In general, common cause failures (CCFs) have been modeled with the assumption that components within the same group are symmetric. This assumption reduces the number of parameters required for the CCF probability estimation and allows us to use a parametric model, such as the alpha factor model. Although there are various asymmetric conditions in nuclear power plants (NPPs) to be addressed, the traditional CCF models are limited to symmetric conditions. Therefore, this paper proposes the copula-based CCF model to deal with asymmetric as well as symmetric CCFs. Once a joint distribution between the components is constructed using copulas, the proposed model is able to provide the probability of common cause basic events (CCBEs) by formulating a system of equations without symmetry assumptions. In addition, Bayesian inferences for the parameters of the marginal and copula distributions are introduced and Markov Chain Monte Carlo (MCMC) algorithms are employed to sample from the posterior distribution. Three example cases using simulated data, including asymmetry conditions in total failure probabilities and/or dependencies, are illustrated. Consequently, the copula-based CCF model provides appropriate estimates of CCFs for asymmetric conditions. This paper also discusses the limitations and notes on the proposed method.

A rapid modeling method and accuracy criteria for common-cause failures in Risk Monitor PSA model

In the development of a Risk Monitor probabilistic safety assessment (PSA) model from the basic PSA model of a nuclear power plant, the modeling of common-cause failure (CCF) is very important. At present, some approximate modeling methods are widely used, but there lacks criterion of modeling accuracy and error analysis. In this paper, aiming at ensuring the accuracy of risk assessment and minimizing the Risk Monitor PSA models size, we present three basic issues of CCF model resulted from the changes of a nuclear power plant configuration, put forward corresponding modeling methods, and derive accuracy criteria of CCF modeling based on minimum cut sets and risk indicators according to the requirements of risk monitoring. Finally, a nuclear power plant Risk Monitor PSA model is taken as an example to demonstrate the effectiveness of the proposed modeling method and accuracy criteria, and the application scope of the idea of this paper is also discussed.

A common cause failure model for components under age-related degradation

This paper discusses component age-related degradation and failure initiated from a shared cause and coupling factor (or mechanism) and the likelihood of the resulting common cause failure (CCF). For these components a CCF model that includes the impacts of any maintenance-related renewal is proposed. Limitations and gaps in the state-of-the-art parametric CCF models for properly handling impacts of shared causes leading to accelerated degradation and aging have been discussed. The proposed approach characterizes the likelihood of CCF based on the conventional parametric CCF model, but unlike the parametric CCF models, time-dependent CCF parameters are estimated from the degradation states including any component rejuvenation achieved through preventive maintenance. Accelerated degradation tests of three identical centrifugal pumps under shared but harsh operating conditions generated several types of sensor monitoring data until failure. Correlation between the sensor monitoring data and observed aging and pump failure times were used to infer the degradation states of the pumps tested. The results concluded that undetected shared causes that could accelerate degradation and aging, for example due to poor maintenance, could significantly affect the CCF parametric model and CCF probability. This could potentially underestimate risk estimates as the undetected components degradation accumulates. The proposed parametric CCF model would be able to determine component-specific dynamic CCF probability, for condition monitored comments using sensor information relatable to degradation and aging.

Fault tree analysis in the R programming environment. Treatmentof common cause failures

Aim. This paper is the continuation of [1] that proposes using the R programming language for fault tree analysis (FTA). In [1], three examples are examined: fault tree (FT) calculation per known probabilities, dynamic FT calculation per known distributions of times to failure for a system’selements. In the latter example, FTA is performed for systems with elements that are described by different functional and service models. Fault tree analysis (FTA) is one of the primary methods of dependability analysis of complex technical systems. This process often utilizes commercial software tools like Saphire, Risk Spectrum, PTC Windchill Quality, Arbitr, etc. Practically each software tool allows calculating the dependability of complex systems subject to possible common cause failures (CCF). CCF are the associated failures of a group of several elements that occur simultaneously or within a short time interval (i.e. almost simultaneously) due to one common cause (e.g. a sudden change in the climatic service conditions, flooding of the premises, etc.). An associated failure is a multiple failure of several system elements, of which the probability cannot be expressed simply as the product of the probabilities of unconditional failures of individual elements. There are several generally accepted models used in CCF probability calculation: the Greek letters model, the alpha, beta factor models, as well as their variations. The beta factor model is the most simple in terms of associated failures simulation and further dependability calculation. The other models involve combinatorial search associated events in a group of n events, that becomes labor-consuming if the number n is large. Therefore, in the above software tools there are some restrictions on the n, beyond which the probability of CCF is calculated approximately. In the current R FaultTree package version there are no above CCF models, therefore all associated failures have to be simulated manually, which is not complicated if the number of associated events is small, as well as useful in terms of understanding the various CCF models. In this paper, for the selected diagram a detailed analysis of the procedure of associated failures simulation is performed for alpha and beta factor models. The Purposeof this paper consists in the detailed analysis of the alpha and beta factor methods for a certain diagram, in the demonstration of fault tree creation procedure taking account of ССF using R’s FaultTree package. Methods. R’s FaultTree scripts were used for the calculations and FTA capabilities demonstration.Conclusions. Two examples are examined in detail. In the first example, for the selected block diagram that contains two groups of elements subject to associated failures, the alpha factor model is applied. In the second example, the beta factor model is applied. The deficiencies of the current version of FaultTree package are identified. Among the main drawbacks we should indicate the absence of some basic logical gates.

A stochastic hybrid systems model of common-cause failures of degrading components

Common-Cause Failures (CCFs) are an important threat to safety critical systems. Most existing CCF models assume that the component failure behavior does not vary over time. Such an assumption is often challenged in practice due to the influence of various degradation mechanisms, e.g., wear, corrosion, fatigue, etc. In this paper, we develop a new model for CCFs considering components degradation. The model is developed in the mathematical framework of Stochastic Hybrid Systems (SHS). The CCFs are modeled as random shock processes that affect a group of components simultaneously and the components degradation processes are modeled by stochastic differential equations derived from physics-of-failures. The benefit of using the SHS model for CCFs is that the developed model is analytically solvable. The system reliability can, then, also be solved analytically in closed form. The proposed CCF modelling framework is demonstrated by a numerical example of a three-unit redundant system and, then, applied to an Auxiliary Feedwater Pump (AFP) system of a Nuclear Power Plant (NPP). A comparison to the Binomial Failure Rate (BFR) model of literature shows that by considering the components degradation processes, the proposed model can accurately describe the CCF effect on the reliability of a system with degrading components.

A practical methodology for modeling and estimation of common cause failure parameters in multi-unit nuclear PSA model

When assessing the risk related to Nuclear Power Plants in terms of impacts on the population health and on the environment, multi-unit issues should be taken into account. The specific aim of a Probabilistic Safety Assessment at site level is to deal with the dependencies existing between the units on that site. One of important dependency factors is the potential existence of the inter-unit common cause failures (CCF) that could affect identical systems (with or without interconnections) present in each unit. As they are identical this makes them potentially sensitive to "inter-unit" CCF, in addition to "intra-unit" CCF that are usually modeled for redundant systems.In this paper, we propose a practical methodology for modelling and estimation of CCF in a multi-unit PSA context. Two methods of modelling multi-unit CCF are firstly presented. A methodology for collecting and analyzing multi-unit CCF data is then proposed. This method is developed by extending the original impact vectors approach to the multi-unit context. Finally, in order to estimate the multi-unit CCF parameters in the case of incomplete data, we propose a CCF simulation method. The application of this method is considered in three different cases and compared with Bayesian and mapping up methods.

Asymmetrical Common-Cause Failures Analysis Method Applied in Fusion Reactors

Fusion reactors like the International Thermonuclear Experimental Reactor (ITER) are generally complex systems, which demand reliability analysis. Common-Cause Failures (CCF) are increasingly important in the reliability analysis of these systems because of the widespread redundancy or similar components in them. However, despite the wide research in CCF, there has been little research on the handling of asymmetries of CCF that is inevitable in ITER. A concept of Multi-Common-Cause Failures (MCCF) and its key assumptions are discussed in this paper. On the basis of MCCF and the assumptions, a transition method named Common-Cause Breakdown Structure (CCBS) was designed to manage the asymmetrical CCF. The CCBS method can be easily applied to most fault tree analysis codes because the CCF treated by CCBS can be handled by traditional CCF models. A redundant system example was modeled and calculated in the reliability and probabilistic safety analysis program RiskA developed by FDS Team. The analysis results for water pumps redundant system applied in Tokamak cooling water system show that CCBS method is adequate and effective.

A general cause based methodology for analysis of common cause and dependent failures in system risk and reliability assessments

Traditional Probabilistic Risk Assessments (PRAs) model dependencies through deterministic relationships in fault trees and event trees and parametric models of common cause failure (CCF) events. Popular CCF models do not recognize system specific defenses against dependencies and are restricted to identical components in redundant configurations. While this has allowed prediction of system reliability with little or no data, it is a limiting factor in many applications such as modeling the characteristics of a specific system design or incorporating the characteristics of failure when assessing a failure event׳s risk significance (known as an Event Assessment, or Significance Determination). This paper proposes the General Dependency Model (GDM), which uses Bayesian Network to model the probabilistic dependencies between components. This is done through the introduction of three parameters for each failure cause, which relate to physical attributes of the system being modeled, i.e., cause condition probability, component fragility, and coupling factor strength. Finally this paper demonstrates the development and use of the GDM in traditional applications of PRA, and for Event Assessments and Significance Determination. Examples of the quantification of the GDM model parameters for these applications are provided.

Topological optimization of reliable networks under dependent failures

We address the design problem of a reliable network. Previous work assumes that link failures are independent. We discuss the impact of dropping this assumption. We show that under a common-cause failure model, dependencies between failures can affect the optimal design. We also provide an integer-programming formulation to solve this problem. Furthermore, we discuss how the dependence between the links that participate in the solution and those that do not can be handled. Other dependency models are discussed as well.

A robust Bayesian approach to modeling epistemic uncertainty in common-cause failure models

In a standard Bayesian approach to the alpha-factor model for common-cause failure, a precise Dirichlet prior distribution models epistemic uncertainty in the alpha-factors. This Dirichlet prior is then updated with observed data to obtain a posterior distribution, which forms the basis for further inferences.In this paper, we adapt the imprecise Dirichlet model of Walley to represent epistemic uncertainty in the alpha-factors. In this approach, epistemic uncertainty is expressed more cautiously via lower and upper expectations for each alpha-factor, along with a learning parameter which determines how quickly the model learns from observed data. For this application, we focus on elicitation of the learning parameter, and find that values in the range of 1 to 10 seem reasonable. The approach is compared with Kelly and Atwood's minimally informative Dirichlet prior for the alpha-factor model, which incorporated precise mean values for the alpha-factors, but which was otherwise quite diffuse.Next, we explore the use of a set of Gamma priors to model epistemic uncertainty in the marginal failure rate, expressed via a lower and upper expectation for this rate, again along with a learning parameter. As zero counts are generally less of an issue here, we find that the choice of this learning parameter is less crucial.Finally, we demonstrate how both epistemic uncertainty models can be combined to arrive at lower and upper expectations for all common-cause failure rates. Thereby, we effectively provide a full sensitivity analysis of common-cause failure rates, properly reflecting epistemic uncertainty of the analyst on all levels of the common-cause failure model.

A new method for explicit modelling of single failure event within different common cause failure groups

Redundancy and diversity are the main principles of the safety systems in the nuclear industry. Implementation of safety components redundancy has been acknowledged as an effective approach for assuring high levels of system reliability. The existence of redundant components, identical in most of the cases, implicates a probability of their simultaneous failure due to a shared cause—a common cause failure.This paper presents a new method for explicit modelling of single component failure event within multiple common cause failure groups simultaneously. The method is based on a modification of the frequently utilised Beta Factor parametric model. The motivation for development of this method lays in the fact that one of the most widespread softwares for fault tree and event tree modelling as part of the probabilistic safety assessment does not comprise the option for simultaneous assignment of single failure event to multiple common cause failure groups. In that sense, the proposed method can be seen as an advantage of the explicit modelling of common cause failures. A standard standby safety system is selected as a case study for application and study of the proposed methodology. The results and insights implicate improved, more transparent and more comprehensive models within probabilistic safety assessment.

Reliability evaluation of wireless sensor networks using an enhanced OBDD algorithm

An enhanced ordered binary decision diagram (EOBDD) algorithm is proposed to evaluate the reliability of wireless sensor networks (WSNs), based on the considerations of the common cause failure (CCF) and a large number of nodes in WSNs. The EOBDD algorithm analyzes the common cause event (CCE) and the network structure when CCE takes place according to the stochastic graph and the CCF model of WSNs. After constructing the ordered binary decision diagram (OBDD) of the original network with node expansion, it uses a set of OBDD variables (SOV) to guide reliability computations along this OBDD. The two steps about OBDD can decrease the cost of OBDD constructions and storage. Furthermore, the efficient OBDD structure and Hash tables can greatly decrease redundant computations of isomorphs. The experiment results show that the EOBDD can be used to evaluate the reliability of WSN efficiently.

Bayes geometric scaling model for common cause failure rates

This paper proposes a mathematical model to associate key operational, managerial and design characteristics of a system with the system's susceptibility towards common cause failure (CCF) events. The model, referred to as the geometric scaling (GS) model, is a mathematical form that allows us to investigate the effect of possible system modifications on risk. As such, the presented methodology results in a CCF model with a strong decision-making character. Based on a Bayesian framework, the GS model allows for the representation of epistemic uncertainty, the update of prior uncertainty in the light of operational data and the coherent use of observations coming from different systems. From a CCF perspective these are particularly useful model features, because CCF events are rare; hence, the operational data available is sparse and is characterised by considerable uncertainty, with databases typically containing events from nominally identical systems from different plants. The GS model also possesses an attractive modelling feature because it significantly decreases the amount of information elicited from experts required for quantification.

An Influence Diagram Extension of the Unified Partial Method for Common Cause Failures

Modelling Common Cause Failures (CCFs) is an essential part of risk analyses, especially for systems such as nuclear power plants, which are required to have high reliability. The Unified Partial Method (UPM) is the main approach of the UK for modelling CCFs. This paper presents an Influence Diagram model for CCFs which extends UPM and represents uncertainty on system performance. This allows more detailed modelling of CCFs in terms of root causes and coupling factors, creates a context for using information in the industry database, and captures the non-linearity in the way system defences influence reliability. A structured expert elicitation process is used to construct the Influence Diagram model and to identify the non-linear structure of the domain, using an example of Emergency Diesel Generators (EDGs) from nuclear power plants. Insights and experiences from the elicitation process are described.

Consistent mapping of common cause failure rates and alpha factors

The problem addressed is how to combine event experience data from multiple source plants to estimate common cause failure (CCF) rates for a target plant. Alternative models are considered for transforming CCF parameters from systems with different numbers of similar components to obtain CCF-rates for a specific group of components. Two sets of rules are reviewed and compared for transforming rates and assessment uncertainties from larger to smaller systems, i.e. mapping down. Mapping down equations are presented also for the alpha-factors and for the variances of CCF rates. Consistent rules are developed for mapping up CCF-rates and uncertainties from smaller to larger systems. These mapping up rules are not limited to a binomial CCF model. It is shown how consistency requirements set certain limits to possible parametric values. Empirical alpha factors are used to estimate robust mapping parameters, and mapping up equations are derived for alpha factors as well. An assessment uncertainty procedure is presented for treating incomplete or vague information when estimating CCF-rates. Numerical studies illustrate mapping rules and procedures. Recommendations are made for practical applications.

Further development of the coupling model

Abstract Uncertainties arising from different sources have to be considered for the quantification of common cause failures (CCFs). At GRS a CCF model (coupling model) has been developed for the estimation of CCF probabilities. An essential feature of the coupling model is the consideration of these uncertainties by using Bayesian estimation methods. Experiences from applying the coupling model to CCF event data over several years and analyzing the results in detail has led to improvements in the application of the model. In this paper the improved methodology of the coupling model is presented. Special emphasis is given to the description of the sources of uncertainties which are considered in the coupling model and the mathematical methodology, how these uncertainties are represented and propagated through the model. In closing topics of future improvements of the coupling models are discussed.

Is mapping a part of common cause failure quantification?

Abstract Important issues in any procedure used for estimating basic event probabilities of common cause failures (CCF) for probabilistic safety assessments (PSA) are: which plants and systems to use, how to combine them, and how to transform data from systems with different numbers of similar components to obtain CCF-rates for a specific group of components. These issues are addressed with focus on the last part called “mapping”. Certain parametric models are considered for transforming CCF event experience from data-source plants to the target plant, the plant of interest. Two sets of rules are reviewed and compared for transforming rates and assessment uncertainties from larger to smaller systems i.e. mapping down. Epistemic uncertainties are taken into account in the estimation. Mapping down equations are presented also for the alpha-factors and for the variances of CCF-rates. Consistent rules are developed for mapping up CCF-rates, uncertainties and alpha factors from smaller to larger systems. These rules are not limited to a binomial CCF model. Consistency requirements are severe and dictate certain limits to possible parametric values. Empirical alpha factors are used to quantify robust mapping ratios of complete CCF-rates. Mapping is critically analyzed and practical recommendations are made.

Loss of safety assessment and the IEC 61508 standard

The standard IEC 61508 contains a lot of useful information and guidance for safety improvement regarding the use of safety systems. However, some of the basic concepts and methods for loss of safety quantification are somewhat confusing. This paper discusses the failure classification, the various contributions to the safety unavailability, and in particular the common cause failure (CCF) model presented in this standard. Suggestions for clarifications and improvements are provided. In particular, a new CCF model is suggested, denoted the Multiple Beta Factor model.