Evaluation Of Failure Probability Research Articles

Failure Probability Evaluation Due to Tin Whiskers Caused Leads Bridging on Compressive Contact Connectors

This paper presents a failure probability assessment of compressive contact connectors due to tin whiskers caused leads bridging. Based on scanning electron microscope measurements, we establish probability distributions of four involved variables: whisker length, orientation, origin location, and counts. A failure probability model is developed and used to calculate the failure probability in terms of two types of failure definition: 1) national electronics manufacturing initiative (NEMI) acceptance criteria, and 2) leads bridging caused by tin whiskers. Results indicate that, in terms of the NEMI criteria, there is more than a 50% chance that the connectors would fail to meet the maximum allowable whisker length for class 2 products at six-month ambient storage, while the probability goes up to 74% for class 2, or 62% for class 3 at one year. However, the failure probability for tin whisker caused leads bridging is fairly low, only 0.0002% for six-month storage, 0.0074% for one-year storage, and even 0.0515 % for five-year storage. Therefore, although the connectors may fail to meet NEMI acceptance criteria for maximum allowable whisker length, the whiskers do not pose significant field risk to cause leads bridging at ambient storage.

Reliability-based optimization in engineering using decomposition techniques and FORMS

In this paper a review of some decomposition techniques previously given by the authors to solve bi-level problems is presented within a unified formulation, and a new variant is investigated. Different reliability-based optimization problems in engineering works are formulated and solved: (a) the failure-probability safety-factor problem that makes the compatibility of the classical approach, based on safety-factors; and the modern probability-based approach possible; (b) a modern reliability-based approach where the design is based on minimizing initial/construction costs subject to failure-probability and safety-factor bounds for all failure modes; (c) minimizing the expected total cost of a structure, including maintenance and construction, which depend on the failure probabilities; and (d) a mixed model minimizing the expected total cost adding failure-probability and safety-factor bounds for all failure modes. In these four problems, the objective consists of selecting the values of the design variables that minimize the corresponding cost functions subject to some reliability conditions together with geometric and code constraints. The solution becomes complex because the evaluation of failure probabilities using first-order reliability methods (FORM) involves one optimization problem per failure mode, so that decomposition methods are used to solve the problem. The proposed methods use standard optimization frameworks to obtain the reliability indices and to solve the global problem within a decomposition scheme. An advantage of these approaches is that the optimization procedure and the reliability calculations are decoupled. In addition, a sensitivity analysis is performed using a method that consists of transforming the data parameters into artificial variables, and using the dual associated variables. To illustrate the methods, a breakwater design example is used.

Evaluation of Failure Probability of Ships on the Baltic Sea by Means of Simulation Model and Statistical Data

Evaluation of Failure Probability of Ships on the Baltic Sea by Means of Simulation Model and Statistical DataThe ship technical failures contribution in overall number of navigational accidents are significantly smaller than those caused by human factor but in safety analysis they cannot be neglected. The paper presents stochastic modeling the technical failures of ships with respect of most important ship systems such as main engine, power generators and steering gear. The data for simulation was obtained from analysis of ships statistical data of polish owners. Obtained results could be useful for estimation of transport loses or potential environmental threats and planning the response action against them.

A Study on the Improvement of the Accuracy of Failure Probability of Breakwaters in view of Sliding Displacement by Monte Carlo Simulation

The Monte Carlo Simulation method is widely used for the evaluation of failure probability of breakwaters in view of sliding displacement. The method might be used more frequently in the future as the new technical standards for port and harbor facilities employ the performance-based design methodology. The accuracy of the result of the simulation depends on the pseudorandom number generating method and iteration number. This study aims at presenting the appropriate pseudorandom number generating method and iteration number for the evaluation of failure probability of breakwaters in view of sliding displacement.

Reliability sensitivity method by line sampling

Reliability sensitivity refers to the derivative of the failure probability with respect to the distribution parameter of basic random variable. Conventionally, this requires repetitive evaluations of the failure probability for different distribution parameters, which is a direct but computationally expensive task. An efficient simulation algorithm is presented to perform reliability sensitivity analysis using the line sampling technique, which gives a good failure probability evaluation for high-dimensional problems and still presents a comparative one for low-dimensional problems. On the basis of the line sampling procedure for failure probability analysis, the concept and implementation are presented for reliability sensitivity. It is shown that the desired information about reliability sensitivity can be obtained by a very limited increase of computation effort based on the failure probability analysis by the line sampling technique. The presented reliability sensitivity algorithm is more efficient than the one based on the direct Monte Carlo technique, especially for cases where the failure probability is low and the number of random variables is large, which is illustrated by several examples. Additionally, limitations of the line sampling based reliability sensitivity method are demonstrated by a numerical example as well.

Single bolt in plane tension joint tests on E-glass/epoxy composite plate

The evaluation and prediction of failure probability and safe levels of composite materials is of extreme importance in terms of manufacturing and structural design. The experimental investigations described in the present paper were conducted to study the strength and failure behaviour of composite plate under pin loaded conditions. Pin bearing tests were carried out on E-glass/epoxy composite plate fabricated by hand lay-up. The experiments investigated the effect of important parameters, including specimen geometry and stacking sequence, on the failure characteristics. Tests were performed with two different stacking sequences: [0/90/+30/−30]s and [0/90/+60/−60]s. Geometrical configurations of specimens such as ratio of edge distance to pin diameter (E/D) and ratio of specimen width to pin diameter (W/D) were suitably varied to observe all possible failure modes. A total of 150 different pin loaded composite plate specimens, two laminate configurations, five edge: pin/diameter ratios, five width: pin/diameter ratios and three samples for each condition were tested under static loading conditions. Failure strength and failure modes were observed in specimens. The specimen tested exhibited different failure modes, consisting of bearing, net tension and shear out, depending on the geometry adopted. Based on the experiments, effects of stacking sequence and geometric parameters on bearing strength, shearing and net tension stress at failure were systematically investigated. Net tension and shear out failure modes were catastrophic, therefore they were undesirable. These modes were also not as safe as bearing failure mode. Bearing failure was desirable for pin loaded composites, due to non-catastrophic damage progression with increasing load. From the experiments, it was shown that the failure mode was a strong function of W/D. The experimental measurements indicated that the load carrying capacity of a pin loaded hole could be changed by altering the specimen geometry and stacking sequence. Therefore, the geometry of the pin connected joints was designed to undertake bearing failure only. In addition, it was found that glass/epoxy with [0/90/±30]s yielded the highest bearing strengths. High bearing strengths were reached when E/D and W/D ratios were ≥4 for both [0/90/+30/−30]s and [0/90/+60/−60]s stacking sequences.

Evaluation of Containment Failure Probability by Ex-Vessel Steam Explosion in Japanese LWR Plants

The containment failure probability due to ex-vessel steam explosions was evaluated for Japanese BWR and PWR model plants. A stratified Monte Carlo technique (Latin Hypercube Sampling (LHS)) was applied for the evaluation of steam explosion loads, in which a steam explosion simulation code JASMINE was used as a physics model. The evaluation was made for three scenarios: a steam explosion in the pedestal area or in the suppression pool of a BWR model plant with a Mark-II containment, and in the reactor cavity of a PWR model plant. The scenario connecting the generation of steam explosion loads and the containment failure was assumed to be displacement of the reactor vessel and pipings, and failure at the penetration in the containment boundary. We evaluated the conditional containment failure probability (CCFP) based on the preconditions of failure of molten core retention within the reactor vessel, relocation of the core melt into the water pool without significant interference, and a strong triggering at the time of maximum premixed mass. The obtained mean and median values of the CCPF were 6.4x 10−2 (mean) and 3.9x 10−2 (median) for the BWR suppression pool case, 2.2x10−3 (mean) and 2.8x10−10 (median) for the BWR pedestal case, and 6.8X10−2 (mean) and 1.4x10−2 (median) for the PWR cavity case. The evaluation of CCFPs on the basis of core damage needs consideration of probabilities for the above-mentioned preconditions. Thus, the CCFPs per core damage should be lower than the values given above. The specific values of the probability were most dependent on the assumed range of melt flow rate and fragility curve that involved conservatism and uncertainty due to simplified scenarios and limited information.

Evaluation of Containment Failure Probability by Ex-Vessel Steam Explosion in Japanese LWR Plants

Evaluation of Containment Failure Probability by Ex-Vessel Steam Explosion in Japanese LWR Plants

Failure probability assessment of wall-thinned nuclear pipes using probabilistic fracture mechanics

The integrity of nuclear piping system has to be maintained during operation. In order to maintain the integrity, reliable assessment procedures including fracture mechanics analysis, etc., are required. Up to now, this has been performed using conventional deterministic approaches even though there are many uncertainties to hinder a rational evaluation. In this respect, probabilistic approaches are considered as an appropriate method for piping system evaluation. The objectives of this paper are to estimate the failure probabilities of wall-thinned pipes in nuclear secondary systems and to propose limited operating conditions under different types of loadings. To do this, a probabilistic assessment program using reliability index and simulation techniques was developed and applied to evaluate failure probabilities of wall-thinned pipes subjected to internal pressure, bending moment and combined loading of them. The sensitivity analysis results as well as prototypal integrity assessment results showed a promising applicability of the probabilistic assessment program, necessity of practical evaluation reflecting combined loading condition and operation considering limited condition.

921 平均応力・応力振幅の不確定性を考慮した破壊確率評価手法に関する研究

921 平均応力・応力振幅の不確定性を考慮した破壊確率評価手法に関する研究

Probabilistic fracture mechanics analysis of nuclear structural components: a review of recent Japanese activities

This paper describes a review of recent Japanese activities on probabilistic fracture mechanics (PFM) analyses. Japan Atomic Energy Research Institute (JAERI) has sponsored research committees on PFM organized by Japan Society of Mechanical Engineers (JSME) and Japan Welding Engineering Society (JWES) for more than 10 years. The purpose of the continuous activity is to establish standard procedures for evaluating failure probabilities of Japanese nuclear structural components such as PV&P and steam generator tube, combining the state-of-the-art knowledge on structural integrity of nuclear structural components and modern computer technology such as parallel processing. This paper shows two topics of the newest results of JWES committee, PFM analysis of aged reactor pressure vessel considering embedded cracks and PFM analysis of piping considering seismic loading, and one topic by JAERI itself, development of PTS analysis code for transient loading (PASCAL).

Buckling failure analysis of random composite laminates subjected to random loads

The buckling failure probability evaluation of laminated composite plates subjected to different in-plane random loads is investigated. The material properties, fiber angles and layer thickness of the laminates are treated as base-line random variables (BLRV). The statistics of buckling strengths of the laminates are determined by the buckling analysis of the stochastic finite element method. The buckling failure probabilities of the laminates subjected to random loads are obtained using the statistics of buckling strengths, the probability theories and the probability integration in the load space. The feasibility and accuracy of the present approach are validated using the results obtained by the Monte-Carlo method (MCM). Numerical examples are presented to demonstrate the feasibility and application of the developed procedure and to investigate effects of stochastic dependence between buckling strengths corresponding to different failure modes and between random loads on the reliability of the composite laminates.

Evaluation of buckling and first-ply failure probabilities of composite laminates

A procedure for failure probability evaluation of composite laminates subjected to inplane loads is proposed. The material properties, fiber angles and layer thicknesses of the laminates are treated as random variables in the reliability analysis. The statistics of first-ply failure loads and buckling strengths of the laminates are determined via the stochastic finite element method. The failure probabilities of the laminates which are susceptible to buckling and first-ply failure are computed using the statistics obtained in the stochastic finite element analysis. The feasibility and accuracy of the present approach are validated using the results obtained via the Monte-Carlo method. A number of examples of reliability analysis of composite laminates subject to in-plane loads are given to illustrate the applications of the procedure.

Seismic failure probability evaluation of redundant fast breeder reactor piping system by probabilistic structural response analysis

The seismic failure probability and the correlation coefficient of the multiple failure mode of the heat transport system of a three-loop fast breeder reactor have been evaluated based on a probabilistic structural response analysis. It has been found that the most probable failure mode of the heat transport system has less impact on the core cooling capability than other modes. The correlation coefficient of the heat transport system loops is approximately 0.9. It is found that the correlation comes from the common structural properties rather than the common seismic input. The present approach is useful for quantifying the correlation coefficient and the seismic fragility of the redundant component failure that is used in the systems analysis.

Probabilistic fracture mechanics analyses of nuclear pressure vessels under PTS events

This paper describes some recent research activities on probabilistic fracture mechanics (PFM) for nuclear reactor pressure vessels (RPVs) performed by the RC111 research committee of the Japan Society of Mechanical Engineers (JSME) under a subcontract of the Japan Atomic Energy Research Institute (JAERI). To establish standard procedures for evaluating failure probabilities of nuclear RPVs, we have performed PFM analyses for aged RPV under pressurized thermal shock (PTS) events. The basic problems are chosen from some of US benchmark problems such as EPRI (Electric Power Research Institute) and US NRC (Nuclear Regulatory Commission) joint PTS benchmark problems and H.B. Robinson problems. Employed in this study are four PFM computer codes developed in Japan and in USA. Various sensitivity analyses are performed to quantitatively evaluate the influences of the input data, i.e. (a) initial crack shape, (b) the probabilistic distribution of initial crack depth, (c) cladding, (d) RT NDT shift, (e) impurity content, (f) the through-wall distributions of material properties, (g) pre-service inspection (PSI) and (h) warm prestressing. It is clearly shown that in most cases, these data affect failure probabilities significantly. Therefore, we should use in the PFM analyses as reliable input data as possible. If any reliable data are not available, the data resulting in most conservative results could be chosen, referring the analysis results presented in this paper.

A study on probabilistic fracture mechanics for nuclear pressure vessels and piping

This paper describes some recent research activities on probabilistic fracture mechanics (PFM) for nuclear pressure vessels and piping (PV&P) performed by the RC111 research committee of the Japan Society of Mechanical Engineers (JSME) under a subcontract of the Japan Atomic Energy Research Institute (JAERI). To establish standard procedures for evaluating failure probabilities of nuclear PV&P, we have set up the following three kinds of PFM round-robin problems on: (a) primary piping under normal operating conditions, (b) aged reactor pressure vessel (RPV) under normal and upset operating conditions, and (c) aged RPV under pressurised thermal shock (PTS) events. The basic problems of the last one are chosen from some US benchmark problems such as EPRI (Electric Power Research Institute) and US NRC (Nuclear Regulatory Commission) joint PTS benchmark problems. For the above round-robin problems, various sensitivity analyses are performed to quantify effects of uncertainty of data on failure probabilities. This paper summarizes some sensitivity studies on the above three kinds of problems mainly varying material properties such as flow stress, fracture toughness, fatigue crack growth rate, Cu content. Employed in this study are the PFM computer codes developed in Japan and USA. Failure probabilities of nuclear PV&P are quantitatively discussed in detail.

Reliability-based shape optimization of two-dimensional elastic problems using BEM

A reliability-based shape optimization is formulated using the advanced first order second moment (AFOSM) method for the evaluation of failure probability, and the boundary element method (BEM) for the calculation of stress and evaluation of shape design sensitivity. A fully analytical approach is adopted for the design sensitivity analysis where the boundary intergral equation (BIE) is implicitly differentiated. In order to illustrate the application of the present methodology two examples are taken. One is a plate with a central hole. Loads and yield stress are taken as random parameters with normal distribution. The other is a fillet problem where load, yield stress and Poisson's ratio are taken randomly. The results are compared with deterministic cases and their practicability is shown.

Failure probability evaluation for normally distributed load-strength model with unknown parameters

The failure probability evaluation methods for load-strength interference model are established when both load, L, and strength, S, follow normal distributions, assuming none of the normal distribution parameters are known. Based on Fisher's fiducial analysis, a failure probability evaluation method is obtained for single load application. A numerical integration method is developed to evaluate the failure probability for multiple load applications.

Approximated Evaluation of Failure Probability for Structural System Using Conditional Safety Indices.

This paper deals with the approximated evaluation method for failure probability of structural systems using conditional safety indices. In general, it is difficult to compute an exact solution of the structural reliability problem with correlations of design variables and limit state functions. It is expected that the conditional safety index proposed will be a useful measure for the safety of complicated structural systems. The merit of this new measure is that the characteristics of statistics and geometry are identical on standardized space. Therefore the conditional safety index yields a practical effective interval of system reliability. When the high-order product sets of a failure event is obtained, the new assessment of the bounds for the estimation of failure probability is also significant. However, the evaluation process of conditional safety indices requires a sequential conditional correlation matrix so that it is the complicated process to calculate high-order simultaneous probability. This paper also proposes the method for transforming the vector of original safety indices into the vector of conditional safety indices using cholesky decomposition of the correlation matrix. In addition, it is suggested that the multi-integral can be approximated by the product of simple integrals using conditional safety indices.

Structural failure probabilities of the HDR-containment

A method to calculate failure probabilities of critical cross sections of containment structures is developed. Uncertainties of structural as well as of material parameters are taken into account. The HDR-containment under shaker loading conditions is utilized as sample structure. This provides the possibility to verify the mechanical i.e. structural model. The failure probabilities are calculated by utilizing the response surface method (RSM) along with advanced simulation procedures. Based on these developments a computational procedure for the evaluation of structural failure probabilities due to earthquake loading is suggested. Failure is defined in terms of exceedance probabilities (first passage problem). For this purpose, a new numerical approach is introduced, which is based on suitable transformations and simulation techniques such as adaptive sampling.