Common-cause Failures Research Articles

A novel discrete bat algorithm for heterogeneous redundancy allocation of multi-state systems subject to probabilistic common-cause failure

This paper focuses on a heterogeneous redundancy allocation problem (RAP) for multi-state series-parallel systems subject to probabilistic common-cause failure and proposes a novel discrete bat algorithm to solve it. Although abundant research studies have been published for solving multi-state RAPs, few of them have studied probabilistic common cause failure, which motivates this paper. Due to the insufficient data of components, an interval-valued universal generating function is utilized to evaluate the availability of components and the whole system. The challenge of solving this kind of RAPs lies in not only the reliability estimation, but also the solution method. This paper presents a novel discrete bat algorithm (BA) for effectively dealing with the proposed RAP and alleviating the premature convergence of BA. Two main features of the adaptation are Hamming distance-based bat movement (HDBM) and Q learning-based local search (QLLS). HDBM transfers the Hamming distance between the current bat and the best bat in the swarm to the movement rate. Then, QLLS utilizes Q-learning to adjust the local search strategies dynamically during the iterations. The computational results from extensive experiments demonstrate that the proposed algorithm is powerful, which is more efficient than other state-of-the-arts on this sort of problems.

Formal Analysis of Repairable Phased-Mission Systems With Common Cause Failures

Although several studies have been devoted to the reliability analysis of phased-mission systems (PMSs) considering the influence of common cause failures (CCFs), statistical correlation and repairable behavior still pose challenges to the analysis. In this article, a hierarchical formal model is proposed for the reliability analysis of repairable PMSs with CCFs. The low-level model is based on continuous time Markov chains and multiple beta factor theory used to construct the failure and repair behaviors of different missions under the effect of CCFs. The upper-level model realizes phase transition based on the Erlang distribution. The model can be implemented in PRISM, a tool that supports probabilistic model checking technology, and can be automatically verified by the properties (termed as reliability and availability in this article) defined by continuous stochastic logic. The proposed model introduces the benefits of probabilistic model checking into the analysis of PMSs for the first time. The formal hierarchical model is demonstrated by an example of a field programmable gate array system based on different design modes. Then, the influence of CCFs on the reliability of three different mission phase combinations are discussed. Our model can help researchers verify system properties for dynamic, complex, and continuous tasks in the initial design phase, thereby optimizing the design pattern or task arrangement.

Limitations of traditional tools for beyond design basis external hazard PRA

Probabilistic risk assessment (PRA) is being used increasingly by the nuclear industry for safety during normal operations as well as for the protection against external hazards. Computation of total risk in an external hazard PRA is dependent on hazard assessment, fragility assessment, and systems analysis. A systems analysis for propagation of component fragilities is conducted using event and fault trees. The event and fault trees for an actual power plant can be fairly large in size, which imposes computational challenges. Hence, certain assumptions are employed for computational efficiency. These assumptions typically represent the conditions imposed during the design basis (DB) scenario. The traditional PRA tools based on these assumptions are also widely applied to perform risk assessment in the context of beyond design basis (BDB) scenarios. However, some of these assumptions may not be valid for certain BDB scenarios. In addition, the probability of dependent failures also increases in BDB scenarios due to common cause failures (CCF) which usually results from design modifications, human errors, etc. In this manuscript, a simple and a relatively more complex illustrative examples are used to show the limitation of these assumptions in the numerical quantification of risk for the case of BDB conditions. Case studies with CCF events across multiple fault trees are also presented to illustrate the effect of these assumptions when traditional approach is used in BDB risk assessment. It is shown that the assumptions are valid for the case of DB conditions but may lead to excessively conservative risk estimates in the case of BDB conditions. A Bayesian network based top-down algorithm is proposed as an alternative tool for accurate numerical quantification of total risk in systems analysis.

Explicit and implicit Bayesian Network-based methods for the risk assessment of systems subject to probabilistic common-cause failures

In an engineering system, multiple components may fail simultaneously due to a shared cause or common cause (CC). This kind of failure is referred to as a common-cause failure (CCF), and it contributes greatly to system risk. However, the propagation of a cause condition to the affected components is not always certain (deterministic). The propagation may be probabilistic due to many reasons, such as system specific defences against cause condition propagation. This kind of CCF is also called the probabilistic CCF (PCCF) which is defined as any condition or event that causes multiple components to fail or malfunction simultaneously with different occurrence probabilities. A system subject to PCCFs is sometimes affected by multiple CCs. This paper proposes explicit and implicit Bayesian Network (BN)-based methods to model systems subject to PCCFs considering different relationships among multiple CCs within a single model. The originality of this work lies in the use of BN to model the probabilistic dependencies among multiple CCs under different relationships and their affected components. Both methods are suitable for systems in which multiple CCs affect different components with different dependencies. Finally, the proposed methods are applied to model the risk of gas explosion in coal mines to evaluate the occurrence probability of accidents.

Dynamic Modeling of Reactor Protection System in Nuclear Power Plant for Reliability Evaluation Based on State Transition Diagram

Reliability assessment of a digital dynamic system using traditional Fault Tree Analysis (FTA) is difficult. This paper addresses the dynamic modeling of safety-critical complex systems such as the digital Reactor Protection System (RPS) in Nuclear Power Plants (NPPs). The digital RPS is a safety system utilized in the NPPs for safe operation and shut-down of the reactor in emergency events. A quantitative evaluation reliability analysis for the digital RPS with 2-out-of-4 architecture using the state transition diagram is presented in this paper. The study assesses the effects of independent hardware failures, Common Cause Failures (CCFs), and software failures on the failure of the RPS through calculating Probability of Failure on Demand (PFD). The results prove the validity of the proposed method in analyzing and evaluating reliability of the digital RPS and also show that the CCFs and longer detection time are the main contributions to the PFD of digital RPS.

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.

Component-Level Reliability Evaluation Model for Cyber Power Devices

Reliability evaluation of power components in the presence of automation devices and cyber links is critical for the improved performance of a smart grid. This work presents a model representing a cyber power component for reliability studies, incorporating interdependency and common-cause failure while reducing computational complexity. Power-component failure, automation-component failure, communication failure, communication delay, and cyberattack are incorporated to develop a comprehensive component-level reliability-evaluation model. A multistate model is proposed with 36 states for a cyber-enabled power component by integrating cyber links as a part of the smart component. Based on the power system reliability analysis, this model is reduced to a 12-state model. Finally, a two-state model is presented for its practical adaptation to specific applications. Due to the nature of the smart component, the following basic applications are considered in this work: (i) health monitoring, (ii) real-time monitoring, and (iii) actuation. A sensitivity analysis is carried out to evaluate the impact of cyber failure and cyberattacks on the reliability of the smart component. Model-reduction techniques, reliability-evaluation procedures, and example case study are provided in order to validate the proposed method.

Stability and Numerical Analysis of a Standby System

A model for repairable standby parallel system consisting of two identical components with common cause failure (CCF) and human error is introduced in this article by a semigroup approach. The stability of the system is verified by the pure analysis technique, the co-final related theory and functional analysis method. It is discussed that four different reliability indices of the studied model are consistent with each other both analytically and numerically. The simulations and comparisons demonstrate the validity of the proposed technique.

Hazard analysis for identifying common cause failures of digital safety systems using a redundancy-guided systems-theoretic approach

Replacing the existing aging analog instrumentation and control (I&C) systems with modern safety control and protection, digital technology offers one of the foremost means of performance improvements and cost reductions for the existing nuclear power plants (NPPs). However, the qualification of digital I&C systems remains a challenge, especially considering the issue of software common-cause failures (CCFs), which are difficult to address. With the application and upgrades of advanced digital I&C systems, software CCFs have become a potential threat to plant safety because most redundant designs use similar digital platforms or software in the operating and application systems. With complex designs of multilayer redundancy to meet the single-failure criterion, digital I&C safety systems (e.g., engineered safety-features actuation system [ESFAS]) are of a particular concern in the U.S. Nuclear Regulatory Commission (NRC) licensing procedures. This paper applies a modularized approach to conduct redundancy-guided systems-theoretic hazard analysis for an advanced digital ESFAS with multilevel redundancy designs. Systematic methods and risk-informed tools are incorporated to address both hardware and software CCFs, which provide guidance to eliminate the causal factors of potential single points of failure in the design of digital safety systems in advanced plant designs.

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

AbstractThe 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.

Investigating an assessment model of system oil leakage considering failure dependence.

Corrosion has made petrochemical infrastructure becomes a significant hazard of the surrounding environment. It is an excellent approach to reduce the risk of environmental pollution by improving the accuracy of determining the leakage probability of the equipment system. In this work, a reliability-based methodology was proposed to assess the system leakage probability with multiple pipe segments under the common cause failure (CCF). Specifically, the existence of FD between the pipe segments was examined under the CCF so that a system leakage assessment model was developed considering the FD. Thereby a novelty corrosion-induced leakage risk management framework was developed. After leakage evaluation for an oil pipeline, it was found that the results obtained were too conservative if ignoring FD, which will develop a wasteful maintenance plan. Overall, the findings in this work may be an opportunity for managers to improve maintenance efficiency.

Availability analysis of safety-critical and control systems of NPP using stochastic modeling

Non-functional requirements are essentially important and play vital role for applications ranging from safety-critical systems (SCS) to simple gaming applications to ensure their quality. SCS demands not only for safe and reliable systems but systems those remain safe and available while under attacks. Availability analysis approaches include, but are not limited to cluster technique, Markov based chain models, Reliability Block Diagrams (RBD), Fault Tree Analysis (FTA) and Flow Network. The classical approaches fail to account for the comprehensive and accurate analysis of the diverse characteristics such as temporal behavior of systems, uncertainty in system behavior and failure data, functional dependencies among components and multiple failure modes for components or systems. This paper presents a novel approach for the availability analysis of a Digital Feed Water Control System (DFWCS) of nuclear power plant, which considers the maintenance and repair of the main-steam safety valves. The approach will be useful when no operational profile data is available for that. The system has been modeled using Stochastic Petri Net capturing all the system requirements along with the partial failures of its subsystems and common-cause failures and analyzed using TimeNet tool. The proposed methodology proves to be efficient and overcomes the limitations of the traditional approaches and the Markov model approach as it computes the state-transition probabilities, rather than assuming or qualitatively assessing it.

Analysis of Design Parameters in Safety-Critical Computers

Nowadays, safety-critical computers are extensively used in many civil domains like transportation including railways, avionics, and automotive. In evaluating these safety critical systems, previous studies considered different metrics, but some of safety design parameters like failure diagnostic coverage (C) or common cause failure (CCF) ratio have not been seriously taken into account. Moreover, in some cases safety has not been compared with standard safety integrity levels (IEC-61508: SIL1-SIL4) or even have not met them. Most often, it is not very clear that which part of the system is the Achilles heel and how design can be improved to reach standard safety levels. Motivated by such design ambiguities, we aim to study the effect of various design parameters on safety in some prevalent safety configurations, namely, 1oo2 and 2oo3, where 1oo1 is also used as a reference. By employing Markov modeling, we analyzed the sensitivity of safety to important parameters including: failure rate of processor, failure diagnostic coverage, CCF ratio, test and repair rates. This study aims to provide a deeper understanding on the influence of variation in design parameters over safety. Consequently, to meet appropriate safety integrity level, instead of improving some parts of a system blindly, it will be possible to make an informed decision on more relevant parameters.

Distributionally Robust Design for Redundancy Allocation

In this paper, we consider a redundancy allocation problem for a series parallel system with uncertain component lifetimes that minimizes system costs while safeguarding system reliability over a given threshold level. We consider mixed redundancy strategies of cold standby and active redundancy with multiple types of components. We address lifetime uncertainty in the framework of distributionally robust optimization. In particular, we assume the probability distributions of the component lifetimes are not exactly known with only limited distributional information (e.g., mean, dispersion, and support) being available. We protect the worst-case system reliability constraint over all the possible component lifetime distributions that are consistent with the given distributional characteristics. The proposed modeling framework enjoys computationally attractive structures. The evaluation of the worst-case system reliability in our redundancy allocation problem can be transformed into a linear program, and the resulting overall redundancy allocation optimization problem can be cast as a mixed integer linear program that does not induce any additional integer variables (other than original allocation variables). In addition, the extreme joint distribution of component lifetimes can be efficiently recovered by solving a linear program. Our modeling framework can also be extended to incorporate the startup failures and common-cause failures for cold standbys and active parallels, respectively, to cater to more computationally complex settings. Finally, the computational experiments positively demonstrate the performance of the proposed approach in protecting system reliability.

Multivalued decision diagram-based common cause failure analysis in phased-mission systems

Due to a shock or shared root cause, multiple system components may fail at the same time contributing significantly to the entire system failure. Such dependent component failures are referred to as common cause failures (CCFs). A rich body of research has been conducted for addressing effects of CCFs in reliability analysis of diverse types of systems. This paper first adapts multiple-valued decision diagrams (MDDs) for analyzing reliability of a non-repairable phased-mission system (PMS) subject to CCFs caused by external shocks. An explicit method and two implicit methods based on MDDs are proposed and compared. While the three MDD-based methods differ in terms of space and computation complexities, examples show that all these methods offer low computational complexity while addressing dynamics and dependencies caused by CCFs and phased operations.

Assessment of the Common Cause Failure(CCFs) effect on Safety Instrumented System(SIS) by usign the Fault Tree Analysis (FTA) method

The reliability of the safety-instrumented system (SIS) has received a lot of attention during the past decade, with the emergence of the new standards such as International Electrotechnical Commission IEC61508, and IEC61511, that provides a general framework for the design and implementation of these safety barriers. Among the problems influencing on the global SIS reliability: Common Cause Failure (CCF), which contributes too many accidents, that has a negative impacts, so it must be considered in the risk and reliability assessment for these systems. The aim of this work is to focus on the effects of common cause failures (CCFs) on the reliability of a SIS, by implementing a comparative SIS dependability study with and without consideration the CCFs, using the beta factor model, and the fault tree analysis (FTA) 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 development of methodology for assessing the inter-unit common cause failure in multi-unit PSA model

The inter-unit common cause failure (CCF) is an event that multiple components are failed simultaneously by common factors may existent in nuclear power plants on a site. The inter-unit CCF can be identified as one of the inter-unit dependencies that has an impact on the multi-unit probabilistic safety assessment (MUPSA). For instance, it may adversely affect the accident mitigation in accident scenarios of multiple units. Therefore, the MUPSA model should be developed considering the inter-unit CCF.In this study, we proposed two methods with the Swain's dependency model and the CCF data in the single-unit PSA (SUPSA) to calculate the inter-unit CCF. The Swain's dependency model is used to calculate the conditional probability considering the dependency level between each CCF event in two different units. To perform the case study, the inter-unit CCF events of emergency diesel generators (EDGs) and alternate AC diesel generators (AAC DGs) in 4 units of different pressurized water reactor (PWR) types were analysed in the case of the multi-unit loss of off-site power (MULOOP). It is expected that methodologies in this study will contribute to the multi-unit level 1 PSA model development as well as evaluating the site risk in the future.

Reliability and importance analysis of uncertain system with common cause failures based on survival signature

Redundant design has become the commonly used technique for ensuring the reliability of complex systems, which calls for great concern to common cause failure problems in such systems. Incomplete data in combination with vague judgments from experts introduce imprecision and epistemic uncertainties in the performance characterization of components. These issues need to be taken into account for assessing the system reliability. In this paper, a comprehensive reliability assessment method is presented by adopting the concept of survival signature to estimate the reliability of complex systems with multiple types of components. Particular attention is devoted to common cause failures (CCFs), which are modeled and quantified by decomposed partial α-decomposition method. Uncertainties caused by incomplete data for CCF events are reduced by hierarchical Bayesian inference. The component importance measure is enhanced to assess the importance of various possible CCF scenarios and to identify their potential impact on system reliability. The presented method is used to analyze the reliability of a dual-axis pointing mechanism for communication satellite, which is a commonly used satellite antenna control mechanism. The engineering application demonstrates the effectiveness of the method.

Research on level 1 PSA and risk-informed design for ACP100

Advanced China Power 100 (ACP100) is a kind of multi-purpose small modular reactor (SMR) based on the present pressurized water reactor (PWR) technology. It adopts the integrated reactor technology routes, satisfies the current nuclear safety codes and guides issued by National Nuclear Safety Administration (NNSA), and also refers to the safety standards of International Atomic Energy Agency (IAEA). In the design phase, Probabilistic Safety Assessment (PSA) technology plays an important role to demonstrate the total safety level, identify the design vulnerabilities, and provide suggestions for the improvement of ACP100. After the brief summary of the level 1 PSA and its risk-informed design method, the level 1 PSA analysis was carried out for ACP100. The identification of initiating events (IEs), the event tree analysis, fault tree analysis and accident sequence quantification were performed. The main PSA results are shown in the paper, such as core damage frequency (CDF), dominating accident sequences, significant common cause failures (CCF). Finally, different design options and their impacts on risk which can be reflected by risk return were evaluated to avoid using the risk-increased design based on the quantitative risk calculation for the sake of increasing the ACP100’s safety. Consequently, the results show that the point estimated value of the total CDF of level 1 IEs PSA for operations at power of ACP100 is 1.42E-07/ry. After the design improvement proposed in this paper, the CDF (point estimate) of ACP100 can be reduced to 6.78E−08/ry. The risk were obviously reduced and the safety of the ACP100 is significant improved. This research provides a technical reference for future new nuclear reactor design.