The estimation of failure rates for low probability events

In many cases the individual components in an engineering system may have suffered no or perhaps only a single failure during their operating history. Such a history may be that of continuous operation over a period of time or it may be over a number of discrete demands. In spite of the apparent lack, or paucity of failure rate data, it is still important to be able to estimate a failure rate or failure probability. In order to do this, it is necessary for the engineer to decide whether there is available some source of information which, while not precisely related to the problem of interest, has some material bearing on it. If this is the case, it may be possible to construct a probability distribution for the failure rate defined by a most probable value and some measure of the variance. If no such information is available then it will be necessary to use a so-called non-informative prior within a Bayesian inference scheme. We describe here the essential results of such a scheme.

In some cases, experience with similar systems or elicitation by expert judgement may lead to the construction of a prior which gives some guidance as to the most likely value of a failure rate, even though no failures have actually been observed in the system of interest. The choice of prior is not a ‘mechanical’ process and requires some experience as to the type of data of interest and the amount and form of the information available. Ideally, a complete probability distribution would be desirable, obtained by eliciting information from a large number of experts. This situation is rarely practical for logistical and financial reasons. More commonly, one has a most probable value and a standard deviation, or possibly upper and lower confidence limits. Thus, two pieces of information are available and this restricts the algebraic form of the prior to one which contains two arbitrary parameters. The following functions are therefore suitable candidates and have been used in the past to represent the variability of failure rates in various situations. 1.Gamma distribution, 2.Log-normal distribution, 3.Hat function, 4.Log-uniform distribution. The log-normal distribution is useful to represent data which varies in inverse powers of 10 and is symmetrical about the most probable value on a logarithmic scale. The Gamma distribution, on the other hand, will describe data that is skewed about the most probable value on a logarithmic scale with particular emphasis on the suppression of large values of the failure rate. For cases in which little is known about the data except mean values, standard deviations and confidence limits, then the hat function or log-uniform are appropriate. The log-uniform distribution is particularly useful since it represents probabilities that are of equal likelihood on a logarithmic scale between an upper and lower bound. A new form of prior, based on the Cauchy distribution, is found to be useful to represent situations where information about the system is particularly sparse.

This paper explores these issues by first reviewing some of the seminal work in the area and then applying Bayesian methods to obtain quantitative results of direct use for practicing engineers. In particular, the paper gives results for the zero failure case for continuous and discrete systems. An important conclusion of the work is that the most appropriate failure rate to use in prospective studies, for components that have been operating continuously for a time T with no failures, is 0.55/T.     

Cost-effectiveness analysis of seismically isolated pool structures for the storage of nuclear spent-fuel assemblies

This study introduces a method for evaluating cost-effectiveness of seismically isolated pool structures, taking account of fluid–structure interaction effects. As a measure of cost-effectiveness, the procedure estimates minimum life-cycle cost, sum of initial construction cost and excepted damage cist over life-cycle of the structure. The expected damage cost is the function of failure probabilities, which are computed by frequency domain analysis for convenience. Input ground motions are represented by a power spectral density function compatible with site-dependent response spectrums. The interaction effects between flexible walls and contained fluid are considered in the form of the added mass matrix. The thickness of wall and the stiffness of isolator are considered two key design variables in achieving a design with minimum life-cycle cost. The numerical examples show that seismically isolated pool tanks are highly cost-effective in low-to-moderate seismic regions.     

Model of cladding failure estimation for a cycling nuclear unit

Nuclear reactor operating modes under multiple cyclic power changes have been promoted recently, and fuel element cladding behavior under the multiple cyclic power changes has been widely known as a key issue in terms of rod design and reliability. A model of nuclear reactor fuel rod cladding failure estimation under multiple cyclic power changes is proposed. The model is built on the basis of the following admissions of the energy version of creep theory: processes of cladding creep and destruction proceed together and affect each other, intensity of creep process is estimated by specific dispersion power W(τ), while intensity of destruction—by specific dispersion energy A(τ) accumulated during time τ. Having calculated the equivalent stress and the rate of equivalent creep strain, the condition of fuel rod cladding failure used on the basis of the energy version of the theory of creep gives us a criterion to decide if a multiple cyclic power change operating mode is permissible for a given variant of power history and coolant conditions.     

Analysis of the failure probability of pipelines and equipment with service life extension of nuclear power plants

A method is proposed for calculating the failure probability of pipelines and equipment that takes account of experience in operating the structures in different regimes and aging. The random quantities used in the method are parameters characterizing the applied loads and defects as well as the strength, mechanical, and thermophysical properties of metal. An example of a calculation of the failure probability for a RBMK emergency recirculation pipeline of emergency feed pumps with service life extension is presented. __________ Translated from Atomnaya énergiya, Vol. 104, No. 5, pp. 284–290, May, 2008.     

Criteria for seismic analysis of nuclear plant structures and substructures

This paper encompasses criteria used for seismic analysis of nuclear power plant structures such as supporting structures founded on ground, as well as substructures. Nuclear power plant equipment and systems can be treated as substructures. Modeling of structures and substructures is described. Since instructure response spectra play an important role in the design and analysis of nuclear power plant equipment, systems and components, methods for development of instructure response spectra as well as variations of input parameters considered in determining these spectra are described.When the principal contribution to the equipment response is due to flexibility of the supporting substructures, an analytical approach to the problem for obtaining reduced stiffness and associated mass matrices of supporting substructures with finite element representation for use in the dynamic analysis of equipment and supporting structures is presented. When supporting structures and equipment, that have inherently different damping properties, are included as intergral parts of the dynamic models, the approximate evaluation of the modal damping based on the weighted damping according to the modal energy stored in each component is outlined. Use of time history and response spectrum analyses is presented. The effects of relative displacements due to different motion of the support points of substructures in each significant mode of the supporting structures as well as procedures of combining modal responses are detailed.     

Quantification of the probability of containment failure caused by an in-vessel steam explosion for the Sizewell B PWR

AEA Technology has provided an assessment of the probability of α-mode containment failure for the Sizewell B PWR. After a preliminary review of the methodologies available it was decided to use the probabilistic approach described in the paper, based on an extension of the methodology developed by Theofanous et al. (Nucl. Sci. Eng. 97 (1987) 259–325). The input to the assessment is 12 probability distributions; the bases for the quantification of these distributions are discussed. The α-mode assessment performed for the Sizewell B PWR has demonstrated the practicality of the event-tree method with input data represented by probability distributions. The assessment itself has drawn attention to a number of topics, which may be plant and sequence dependent, and has indicated the importance of melt relocation scenarios. The α-mode failure probability following an accident that leads to core melt relocation to the lower head for the Sizewell B PWR has been assessed as a few parts in 10 000, on the basis of current information. This assessment has been the first to consider elevated pressures (6 MPa and 15 MPa) besides atmospheric pressure, but the results suggest only a modest sensitivity to system pressure.     

核电厂厂址选择中飞机坠毁事件的评价程序及概率确定方法

介绍了核电厂厂址选择中对飞机坠毁事件的评价程序,以及在初步筛选评价和详细评价两个不同阶段的飞机坠毁概率确定方法,除了考虑一般空运飞行、机场起落和空中走廊的飞机坠毁概率之外,还考虑了军用空域的军事训练导致的飞机坠毁概率。     

Estimation on probability of radiological hazards for nuclear facilities decommissioning based on fuzzy and event tree method

This paper proposes the estimation method on probability of decommissioning hazards for nuclear facilities. Evaluation method of decommissioning hazardous accidents is based on fuzzy and event tree method. Expert’s knowledge was considered as state of the basic variable with a normal distribution, which was considered to represent the membership function. The proposed method has been successfully applied to the removal of rotary specimen rack in KRR-2.     

Dynamic model for control system design and simulation of a low temperature nuclear reactor

A lumped parameter dynamic model for the primary-loop and the U-tube steam generator of a low temperature power reactor is developed based on the fundamental conservation laws of fluid mass, energy and momentum. The dynamic model is formulated by coupling the point kinetics with reactivity feedback and the thermal-hydraulics of the reactor. The developed dynamic model is implemented on a personal computer using MATLAB/SIMULINK. Numerical simulation results for steady-state and transient responses are then presented, which show that the steady-state precision of the newly developed dynamic model is acceptable and the trend of the transient responses is correct. In addition, the “swell and shrink” behavior of the U-tube steam generator is also verified by numerical simulation. This newly established model can be utilized to control system design and simulation for the low temperature power reactor.     

Seismic damage hazard analysis for requalification of nuclear power plant structures: methodology and application

A methodology for the evaluation of the annual probability of occurrence of post-elastic seismic damage in realistic structures is presented. The seismic damage hazard analysis (SDHA) is carried out here by coupling conventional seismic hazard analysis (SHA) for the site and the structural response to earthquakes of different intensities. The structural performance is statistically investigated by conducting appropriate non-linear dynamic analyses for a limited set of real ground-motion records that might potentially pose a threat to the structure at the site. The merging of these two approaches permits calculation of the seismic hazard faced by the structure in direct damage terms. The methodology is presented in this paper with the aid of a simple illustrative case study where the annual probability of damage and, eventually, failure of a power house steel structure is computed. This methodology can find practical applications in seismic retrofit of nuclear power plant structures and in the evaluation of seismic damage hazards in new structure designs.     

Low-cycle deformation of the structures in a nuclear power plant and methods for calculating them

It is proposed that the fatigue strength of structures in nuclear power plants with a quite long service life be analyzed in two stages: first, the type and location of the process and the effect of basic factors are determined by method of direct analysis of stable cycles and then a more accurate stepped analysis of the deformation kinetics is performed. The real properties of a material are systematized, taking account of creep, in ways that depend on the different types of processes. The methods for calculating the conditions and mechanisms of the progressing shape change and alternating-sign flow are refined. An example of the instability of the processes of cyclic deformation, which limits the possibility of operating structures beyond the limits of elastic adaptability, is examined. The possibilities and conditions for algorithmitization of the choice of material models and ensuring computational accuracy in calculations of deformation kinetics are discussed.     

5×1024×10高速核辐射能谱获取系统研制

在磁约束聚变实验装置的物理实验中，为了测量高温等离子体箱射的某特定能量区域的X射线或其他核箱射能谱的时、空分布，需要在托卡马克的板向和环向方向布置多台X射线探测器，每次放电可同时获得数十个能谱，为了不牺牲能谱中的重要信息(如线辐射)．以及能量分辨的需要，要求每个能谱有1024道，每个谱采集的时间分为：40、80、160、240ms，可自由设定，每道容量16位，每次放电可同时获得50个能谱，可扩展到80个能谱。     

基于概率因果模型与遗传算法的船舶核动力装置故障诊断的新方法

介绍一种将概率因果模型和遗传算法相结合的核动力装置二回路凝给水系统的故障诊断方法,它将概率因果模型的似然函数作为遗传算法的适应函数,从而将复杂系统的故障诊断转化为最优问题。仿真结果表明,该方法能够适应诊断过程中出现的不确定性,并实现多故障诊断,具有较高的诊断可靠性和实用性。     

用PIXE技术分析山东省胃癌高,低发区饮水中的微量元素

介绍了用ＰＩＸＥ技术分析饮水中微量元素的方法，给出了山东省胃癌高发区栖霞县与低发区苍山县饮水中的微量元素谱。两地饮水中微量元素含量的检验显示，Ｔｉ，Ｖ，Ｃｕ，Ｆｅ和Ｆｒ等５种元素栖霞均显著高于苍山县。     

核电站风险指引设备分级的试点研究

风险指引设备分级通过定量化的概率风险分析、纵深防御的确定性分析和敏感性分析3个步骤来综合评估设备的安全重要性.重点研究了风险指引设备分级中的确定性分析评估方法,研究建立了一套改进的风险指引设备分级流程,并以大亚湾核电站的辅助给水系统、安全壳喷淋系统和设备冷却水系统为对象进行试点研究,验证了改进的设备分级流程是合理、有效的.     

Vessels for sodium-cooled fast nuclear reactors: General considerations and critical examination of some vessel structures

In the first part of this paper some general characteristics of vessels for sodium-cooled fast nuclear reactors are discussed, emphasizing their differences with the vessels of thermal nuclear reactors.     

A comparison of the praise code and the paris code for the evaluation of the failure probability of crack-containing components

Two computer codes developed for the calculation of failure probabilities of crack-containing structures are compared with each other. The basic fracture mechanical, statistical, and numerical models used in the codes are described with special emphasis on probabilistic leak-before-break analysis. Sample problems taken from nuclear applications show that very small failure probabilities can be calculated with sufficient numerical accuracy.     

设备失效根本原因分析技术和方法及其在广东核电的应用

系统地介绍了设备失效根本原因分析(RCA)的技术和方法,其中较详细地介绍了设备失效根本原因分析的9个步骤,并以具体的实例说明了设备失效分析的过程,指出了RCA工作中应注意的6个问题。具体地介绍了大亚湾核电站RCA工作在组织目标、分析人、分析技术、外部技术支持体系、纠正措施制定和纠正措施跟踪体系等7个方面的做法和尝试。