Optimal redundancy allocation for systems considering common-cause failures

Birnbaum importance measures the significance of a component to the system reliability. And it is widely applied in system reliability designs and risk assessments. Some studies have been made on Birnbaum importance for k-out-of-n systems, but most of them assumed that the failures of components are statistically independent of each other. In practice, component failures are usually statistically dependent and common cause failures (CCF) are almost ubiquitous in complex systems. Based on the system-level stress-strength interference (SSI) analysis, Birnbaum importance for k-out-of-n systems with same components and different components are extended. This approach can be applied to dependent systems to find weaknesses of systems in the presence of CCFs. Through two examples, we further illustrate the importance measure and discuss some attractive properties about the new importance measure: i) the extended importance measure is intuitive and simple to use; ii) importance of a component changes regularly with the variation of strength distribution parameters of the component; iii) failure dependence has a great influence on the importance evaluation and further may results in wrong importance ranking of all the components.

In quantitative analysis of common cause failures (CCFs), importance measures for ranking the importance of the CCF events will be significant to limit the CCF analysis framework, find out efficient defence strategies against CCF, and make sensitivity analysis for them. In this paper, three importance measures are defined for different types of common cause failure events: Structure Importance, Probability Importance, and β-Importance. Simplified algorithms for calculating these importance measures are developed.

The first German data base for Common Cause Failures (CCF) had been set up for the German Risk study, Phase B, published in 1989. It was based on three sources: international operating experience from the OECD Incident Reporting System, the national operating experience reflected in the collection of reportable events and plant specific operating experience from the Nuclear Power Plant Biblis unit B. This data base was subsequently substantially extended in terms of additional events and extended observation periods where additional information was collected in the frame of further PSA studies und CCF projects. The reportable events were the key source for this extension. Using this improved data base an updated calculation of CCF probabilities has been performed which was published in the document on PSA data associated to the regulatory PSA guideline.

Common cause events are those specific groups of dependent events that might adversely affect the operation of a redundant system. Common cause failures (CCF) are considered a subset of dependent failures with a major difference that they cannot be explicitly modeled. A CCF is a single point of failure (SPOF) causing a unit and its "perceived" redundant unit to fail simultaneously. During the first few years of commercial nuclear power plant operations, many probability risk assessment (PRA) studies revealed that CCF have significantly contributed to core damages. Consequently, the U.S. Nuclear Regulation Commission (NRC) initiated various CCF analyses in the 1980s. Since then, CCF analyses have been synonymous with nuclear facilities, and a majority of CCF analysis efforts have rightfully been focused on the safety of nuclear plants. Given that many industrial and commercial mission-critical facilities and high-reliability organizations now require a high degree of availability, therefore, CCF cannot be ignored. The objectives of this paper are to present 1) the importance of considering CCF in reliability, availability, and maintainability (RAM) analysis for industrial and commercial mission-critical facilities and high-reliability organizations, 2) simple quantitative analysis methods of CCF for industrial and commercial mission-critical facilities, and 3) the need for including CCF as part of future failure data collection efforts.

Common cause failure analysis of PWR containment spray system by GO-FLOW methodology

Chapter 8 - Methods of Modeling

The reliability is the probability that a device will perform its required function under stated conditions for a specified period of time. The Common Cause Failure (CCFs) is the multiple failures and has long been recognized (U.S. NRC, 1975) as an important issue in the Probabilistic Safety Assessment (PSA) and uncertainty and sensitivity analysis has the important information for the evaluation of system reliability. In this study, two cases has been considered, in the first case, author have made the analysis of reliability of PWR safety system by GO-FLOW methodology alternatively to Fault Tree Analysis and Even Tree because it is success-oriented system analysis technique and comparatively easy to conduct the reliability analysis of the complex system. In the second case, sensitivity analysis has been made in order to prioritize the important parameters which have largest contribution to system reliability and also for common cause failure analysis and uncertainty analysis. For an example of phased mission system, PWR containment spray system has been considered.

A pragmatic approach to modeling common cause failures in multi-unit PSA for nuclear power plant sites with a large number of units

Estimation of the common cause failure probabilities on the component group with mixed testing scheme

Reliability assessment of complex engineered systems is challenging as epistemic uncertainty and common cause failure (CCF) are inevitable. The probabilistic common cause failure (PCCF), which characterizes the simultaneous failures of multiple components with distinguished chances, is a generalized model of traditional CCF model. To accurately assess system reliability, it is of great significance to take both the effects of PCCF and the epistemic uncertainty of components’ state probabilities into account. In this paper, an evidential network model is proposed to assess system reliability with interval-valued PCCFs and epistemic uncertainty associated with components’ state probabilities. The procedures of computing the mass distribution of a component suffering from multiple PCCFs are detailed. The inference algorithm in the evidential network is, then, used to calculate the mass distribution of the entire system. The Birnbaum importance measure is also defined to identify the weak components under PCCFs and epistemic uncertainty. A safety instrumented system is exemplified to demonstrate the effectiveness of the proposed evidential network model in terms of coping with PCCFs and epistemic uncertainty. The importance results show that both the epistemic uncertainty associated with components’ state probabilities and PCCFs have impact on components’ importance.

This paper analyses the problem of epistemic uncertainty in assessing the performance of safety instrumented systems (SIS) using fault trees. The imperfect knowledge concerns the common cause failure (CCF) involved in the SIS in low demand mode. The point-valued CCF factors are replaced by fuzzy numbers, allowing experts to express their uncertainty about the CCF values. This paper shows how these uncertainties propagate through the fault tree and how this induces an uncertainty to the values of the SIS failure probability on demand and to the safety integrity level of the SIS. For the sake of verification and comparison, and to show the exactness of the approach, a Monte Carlo sampling approach is proposed, where by a uniform or triangular second-order probability distribution of CCF factors is considered.

PurposeThis paper aims to deal with the problems of failure dependence and common cause failure (CCF) that arise in reliability analysis of complex systems.Design/methodology/approachFirstly, a dynamic fault tree (DFT) is used to capture the dynamic failure behaviours and converted into an equivalent generalized stochastic petri net (GSPN) for quantitative analysis. Secondly, an efficient decomposition and aggregation (EDA) theory is combined with GSPN to deal with the CCF problem, which exists in redundant systems. Finally, Birnbaum importance measure (BIM) is calculated based on the EDA approach and GSPN model, and it is used to take decisions for system improvement and fault diagnosis.FindingsIn this paper, a new reliability evaluation method for dynamic systems subject to CCF is presented based on the DFT analysis and the GSPN model. The GSPN model is easy to capture dynamic failure behaviours of complex systems, and the movement of tokens in the GSPN model represent the changes in the state of the systems. The proposed method takes advantage of the GSPN model and incorporates the EDA method into the GSPN, which simplifies the reliability analysis process. Meanwhile, simulation results under different conditions show that CCF has made a considerable impact on reliability analysis for complex systems, which indicates that the CCF should not be ignored in reliability analysis.Originality/valueThe proposed method combines the EDA theory with the GSPN model to improve the efficiency of the reliability analysis.

Redundancy allocation problems (RAPs) have attracted much attention for the past thirty years due to its wide applications in improving the reliability of various engineering systems. Because RAP is an NP-hard problem, and exact methods are only applicable to small instances, various heuristic and meta-heuristic methods have been proposed to solve it. In the literature, most studies on RAPs have been conducted for single-level systems. However, real-world engineering systems usually contain multiple levels. In this paper, the RAP on multi-level systems is investigated. A novel memetic algorithm (MA) is proposed to solve this problem. Two genetic operators, namely breadth-first crossover and breadth-first mutation, and a local search method are designed for the MA. Comprehensive experimental studies have shown that the proposed MA outperformed the state-of-the-art approach significantly on two representative examples.

Modeling and quantification of simultaneous failures of multiple components due to common causes is a frequent and often crucial task in safety system reliability and risk assessments. Several models of common cause failures (CCF) are introduced. Their mutual relationships, limitations, and advantages, as well as sources of parametric values, are described. The models are presented in terms of basic multiple‐failure rates and probabilities that are independent of system testing schemes and intervals, and have direct connection to the basic event probabilities needed in system logic models.The early CCF models such as the β factor, binomial failure rate, common load, and distributed failure probability models are all special cases of stochastic reliability analysis. Even if mathematically attractive, these models are inherently constrained by certain mutual couplings between the CCF rates or CCF probabilities.More general α factor and multiple Greek letter models are based on the ratios of multiple‐failure rates or probabilities. In applications, both models need some additional failure rate from outside of the model to yield CCF rates and basic event probabilities.Extensive national and international common cause failure data collection efforts are making it feasible to estimate plant‐specific multiple‐failure rates and probabilities by combining data from many similar systems with empirically oriented Bayesian methods without assuming common generic parametric values. This methodology is briefly described. It takes into account both statistical and assessment uncertainties due to limited observations, interpretations, and documentation of CCF events.

Virtualization has been used in cloud computing to build multiple Virtual Machines (VMs) on a single physical machine, which enables computing resources partition and improving the physical resources utilization efficiency. However, the use of virtualization brings new challenge in reliability modeling for cloud computing. For example, when server failure occurs, all VMs co-located on the server cannot be operated, which is a typical common cause failure (CCFs). Since the task is executed by VMs, the states of VMs decide whether cloud computing can accomplish the given task. This paper proposes a new reliability model for cloud computing considering both server failures and VMs failures. Both fault tree and state-space models are used to solve this problem, and to reduce the computational complexity, a simplified method is provided to reduce the number of states.