A Bayes Reliability Growth Model for A Development Testing Program

The problem of estimating the reliability of a system during development is considered. The development process has several stages at each stage binomial test data are obtained by testing a number of such systems on a success/fail basis. Marginal posterior distributions are derived under the assumption that the development process constrains the reliabilities to be nondecreasing and that the prior distribution for reliability at each stage is uniform. Simulation models are designed to facilitate testing for the validity and computation of the Bayesian model with ordered reliabilities as well as to compare results with other reliability growth models.     

Bayes' Equation, Reliability, and Multiple Hypothesis Testing

The rudiments of applying Bayes' Equation to hypotheses concerning reliability are introduced in a simple manner. The application is a means of obtaining posterior probabilities, for the reliability hypotheses, which are consistent with the prior beliefs and the available test results. The posterior distributions, from which decision theory could formally arrive at optimal estimates, are greatly dependent on the prior distributions. Thus, the discussion centers about the desired properties of a prior and its effects on the posterior for various data situations. Formulations for both continuous-conjugate and discrete representations of the prior beliefs are discussed and contrasted. The use of discrete priors offers many advantages over the use of continuous-conjugate priors.     

A Bayesian Reliability Assessment of Complex Systems for Binomial Sampling

This paper presents a reliability assessment procedure that systematically combines complete system binomial test data with lower level binomial test data obtained from either partial system or component tests. The procedure uses beta prior distributions of all reliabilities, Bayes theorem, and probability moments. The result is a posterior distribution of system reliability that can be used to determine Bayes point and interval estimates. The beta prior distributions evolve from data on predecessor systems similar to the system in question and engineering knowledge about what the various test-alternatives measure.     

融合多源信息的维纳过程性能退化产品的可靠性评估

 针对维纳过程性能退化产品,提出了一种有效融合先验退化信息、寿命数据以及现场退化数据的可靠性评估方法.首先利用Expectation-Maximization(EM)算法基于先验退化信息和寿命数据信息确定参数的先验分布;其次利用贝叶斯方法对参数进行更新,并在此基础上进行可靠性评估.该方法能根据现场退化数据不断地对可靠性进行更新,实现对产品可靠性的实时评估.最后通过金属化膜电容器可靠性评估实例验证了该方法的适用性和有效性.     

A new reliability growth model: its mathematical comparison to the Duane model

The Duane reliability growth model has been traditionally used to model electronic systems undergoing development testing. This paper proposes a new reliability growth model derived from variance stabilisation transformation theory which surpasses the Duane model in typical reliability growth situations. This new model is simpler to plot and fits the data more closely than the Duane model whenever the Duane slope is less than 0.5. This paper explores the mathematical relationships between these two models; and shows that at a Duane slope of 0.5, both models are mathematically equivalent in their capacity to fit the observed data. The instantaneous MTBF of the new model is also developed and compared to that of Duane. As the new model is influenced by the later failures, compared to early failures for the Duane model, it has the further advantage of leading to reduced test times for achieving a specified instantaneous MTBF. As the reliability of electronic systems increases, this has positive implications for testing.     

On Bayesian estimation of system reliability

For a system with n s-independent components, the uncertainty regarding the reliability of components for a fixed point of time is expressed by a Bayesian probability distribution. Using the moments of these distributions, the exact moments of the system reliability distribution are derived, from which a discrete probability density function is obtained on the basis of the principle of maximum entropy. Taking this distribution as a prior distribution for system reliability, a posterior density function for the system reliability is constructed either using the data obtained from life tests conducted at a system level or from field data. For tracking the evolution of the reliability distribution over time, a modified Kalman filter technique, along with use of a Bayesian procedure, is proposed. This method is simple, elegant and easy to compute.     

Modeling bimodal electromigration failure distributions

One of the major tasks in reliability methodology is the correct modeling of electromigration failure distributions. Usually the failures within a sample of test devices are caused by a single physical failure mechanism and the resulting failure distribution can be tight-fitted by a single log-normal distribution. However, it is possible that several failure mechanisms are active within the sample or even one specimen implying multimodal failure distributions. In this paper bimodal log-normal distributions will be discussed, which show two distinct branches as a consequence of two failure mechanisms. In order to describe these failure distributions we use two models – the superposition model and the weak-link model. Both are composed of two log-normal distributions and consider different failure scenarios. We show that they are special cases of one general bimodal model. For each model, coinciding experimental data sets will be presented, which were observed on different via-line structures. The physical failure analysis confirms the model assumptions and supports the bimodal distribution concept.     

Bayes computation for life testing and reliability estimation

Powerful computational techniques for estimating the parameters and the reliability function of complex life distributions, using Bayes methods, from complete and type-II censored samples are given. The Gibbs sampler approach brings considerable conceptual and computational simplicity to the calculation of the posterior marginals and reliability. Considering constrained parameter and truncated data problems in multivariate life distributions, the Gibbs sampler procedure is easy to implement for sets of simulated data     

基于红外热像法的金属裂纹扩展研究北大核心CSCD

疲劳裂纹是金属结构件在工程实际中常见的失效形式之一,裂纹的扩展则会导致大部分塑性功以热量的形式耗散,因此基于红外热像法的金属结构温度监测是实现裂纹扩展评估的有效方法之一。本文分析了金属裂纹扩展过程中材料的热耦合方程,使用ABAQUS软件进行直接热力耦合数值模拟,揭示了塑性功转化系数、拉伸速度对单轴拉伸载荷下含裂纹的Q235试件表面温度变化的影响规律,并基于红外热像仪测量试验得到了同数值模拟吻合度较高的结果,以此验证了此规律的正确性。结果显示,拉伸过程中试件表面温度经过平稳阶段、稳步上升阶段。裂纹扩展过程中,试件表面温度最高点位于裂纹尖端前方。同时拉伸速度越大,试件断裂时间短,裂纹扩展过程中热损失越小,试件表面温升越大。该结果对金属结构的裂纹监测和预警具有重要意义。     

Reliability growth plot - An underutilized tool in reliability analysis

System reliability and performance are improved by continuous improvement effort. The study of the increase in reliability as a function of time is the subject of reliability growth. Although the most well-known reliability growth model, the Duane model, is proposed more than thirty years ago, reliability growth analysis has attracted an increasing interest only recently because of the lack of time for testing and the high reliability of improved products leading to very few failures. In this paper we study a practical approach in reliability growth analysis. Based on the graphical plotting of failure data for some selected models, reliability can easily be estimated and predicted. This approach which is the original idea of the Duane model, overcomes the problem of parameter estimation and model validation that is usually complicated. It is especially useful when the model validation has to be done in order to select a suitable model. The approach, called the First-Model-Validation-Then-Parameter-Estimation approach, is simple and practical for the analysis of reliability growth data. We further develop some models and discuss their applicability in reliability engineering.     

Approaches for reliability modeling of continuous-state devices

Three approaches for reliability modelling of continuous state devices are presented in this paper. One uses the random process to fit model parameters of a statistical distribution as functions of time. This approach allows the data set to be from any general distribution. The second approach uses the general path model to fit parameters of the model as functions of time. The relationship between the random process model and the general path model is illustrated. The third approach uses multiple linear regression to fit the distribution of lifetime directly. This approach has less restriction on the degradation data to be analyzed. All three approaches are illustrated with examples. Finally a mixture model is proposed which can be used to model both catastrophic failures and degradation failures. This mixture model also shows engineers how to design experiments to collect both hard failure data and soft failure data. Topics for further investigation in continuous device reliability modelling include further investigation of the mixture model, application of these models to practical situations, and using complex statistical distributions to fit degradation data     

On the Behavior of Some Quantities Used in Bayesian Reliability Demonstration Tests

Equipment mean time between failures (MTBF) is assumed to be a frequency random variable. The goodness of fit of the uniform prior as a probability model for the MTBF is compared to the goodness of fit of the inverted gamma prior for actual failure data. These distributions can both be adequately fitted to the same failure data when the method of moments is used to fit the distributions. A comparison of posterior producer and consumer risks in a Bayesian reliability demonstration test is made using the fitted inverted gamma and uniform distributions as the priors. There can be rather large differences in the values of the posterior risks even when the two priors fit the data equally well or equally poorly.     

Bayesian Estimation of Parameters of Life Distributions and Reliability from Type II Censored Samples

The Bayesian approach to reliability estimation from Type II censored samples is discussed here with emphasis on obtaining natural conjugate prior distributions. The underlying sampling distribution from which the censored samples are drawn follows a generalized life model (GLM) which includes a model proposed by Epstein and Sobel, Weibull, exponential, and Rayleigh distributions as special cases. Results are given for the Type II asymptotic distribution of largest values, Pareto, and Limited distribution. The natural conjugate prior, Bayes estimate for the generalized scale parameter, posterior risk, Bayes risk and Bayes estimate of the reliability function were derived for the distributions studied. In every case the natural conjugate prior is a 2-parameter family which provides a wide range of possible prior knowledge. Conjugate diffuse priors were derived. A diffuse prior, also called a quasi-pdf, is not a pdf because its integral is not unity. It represents roughly an informationless prior state of knowledge. The proper choice of the parameter for the diffuse prior leads to maximum likelihood, classical uniform minimum-variance unbiased estimator, and an admissible biased estimator with minimum mean square error as the generalized Bayes estimate. A feature of the GLM is the increasing function g(·) with possible applications in accelerated testing. KG(·) is a s-complete s-sufficient statistic for ?, and KG(·)/m is a maximum likelihood estimate for ?. Similar results were obtained for the Pareto, Type II asymptotic distribution of extremes, Pareto (associated with Pearl-Reed growth distribution) and others.     

Void initiation,growth, and coalescence in ductile fracture of metals

Ductile fracture in metals and alloys occurs through the coalescence of voids in the necked region of the specimen. While considerable information exists on the propagation of cracks, the mechanism of their initiation is still unclear. This paper reports onin situ electron microscope investigations aimed at an elucidation of crack initiation and the enlargement of crack nuclei to final rupture. Single crystal ribbons of silver 0.5 − 7.0 μm thick were pulled to fracture inside of a high voltage electron microscope (HVEM). After considerable necking, cracks initiated at the edges; their propagation occurred by the formation of microcracks ahead of the macrocrack, followed by the growth of the microcracks and finally their coalescence. Thesein situ experiments were complemented by stress-strain data obtained from fractured austenitic 304 stainless steel foils; subsequent examination of fracture surfaces in a scanning electron microscope allowed the accurate measurement of intervoid spaclngs. Inter-particle spacings were determined by HVEM. It was found that the average void density is 100 times larger than the average particle density. The combination and analysis of all experimental data led to a detailed model of void initiation and growth, which is based on a dislocation-vacancy mechanism and crystal plasticity.     

Bayesian Analysis of the Weibull Process With Unknown Scale and Shape Parameters

Previously, the Weibull process with an unknown scale parameter was examined as a model for Bayesian decision making. The analysis is extended by treating both the shape and scale parameters as unknown. It is not possible to find a family of continuous joint prior distributions on the two parameters that is closed under sampling, so a family of prior distributions is used that places continuous distributions on the scale parameter and discrete distributions on the shape parameter. Prior and posterior analyses are examined and seen to be no more difficult than for the case in which only the scale parameter is treated as unknown, but preposterior analysis and determination of optimal sampling plans are considerably more complicated in this case. To illustrate the use of the present model, an example is presented in which it is necessary to make probability statements about the mean life and reliability of a long-life component both before and after life testing.     

Using statistics of the extremes for software reliability analysis

This paper investigates the use of StEx (statistics of the extremes) [Castillo, Sarabia 1992; Gumbel 1958; Ang, Tang 1984; Castillo 1988; Castillo, Alvarez, Cobo 1993] for analyzing software failure data for highly reliable systems. StEx classifies most distributions into one of three asymptotic families. The asymptotic family to which a set of data belongs is derived graphically on Gumbel-type probability paper. From the resulting empirical Cdf (cumulative distribution function), the asymptotic family to which the data might belong is hypothesized. Once the asymptotic family for a particular data set is determined, the parameters required for an explicit representation of this asymptotic form are derived using known analytic techniques. Using this approach, actual field data from two software case studies [Musa 1979; Kenney 1993] are analyzed using conventional software reliability growth models and using StEx     

A Two-Stage Failure Model for Bayesian Change Point Analysis

This paper presents a new approach for detecting certain change-points, which may disturb the evaluation of reliability models with covariates, via a two-stage failure model, and stochastic time-lagged regression functions. The proposed model is developed with the Bayesian survival analysis method, and thus the problems for censored (or truncated) data in reliability tests can be resolved. In addition, a Markov chain Monte Carlo method based on Gibbs sampling is used to dynamically simulate the Markov chain of the parameterspsila posterior distribution. Finally, a numeric example is discussed to demonstrate the proposed model.     

Data stability in an application of a software reliability model

The Goel-Okumoto (1979) model of reliability growth is applied to the failure data for a large software development project. This is done by fitting the model parameters to the error counts and test times, which are periodically tabulated. In the early phases of system testing, the problem of inaccurate estimation due to insufficient reliability growth occurs. A simple test is devised to measure the stability of the data with respect to this problem. In practice, such a test on the data can be used to determine when system testing has sufficiently progressed to allow one to expect reasonable estimates from reliability growth models     

Fast and Automated Electromigration Analysis for CMOS RF PA Design

This paper presents fast and automated electromigration (EM) reliability modeling by using automated modeling generation (AMG) algorithm. The AMG converts human based EM modeling into an automated modeling and simulation process with the help of ANSYS parametric design language (APDL) program. For automating the neural model training process, training-driven adaptive sampling is applied to integrate data generation, data distributions determination, model structure adaptation, training and testing into a unified framework. Fully automated reliability model construction and simulation is achieved for the first time. This method effectively shortens the period of EM modeling by using dynamic sampling method. Furthermore, the heat generation from active devices has been considered to describe the heat effect on the interconnect reliability. Through the proposed technique, the allowable sizes, temperature and output power of a CMOS radio frequency power amplifier (RF PA) are derived to give reliability criteria for PA designer.     

圆柱铁氧体微裂纹的激光扫描热成像检测

针对用激光局部加热试样引起的横向热流检测裂纹，对低热导率材料表面的微小裂纹成像信噪比较低的问题，提出基于相邻热信号比较的圆柱铁氧体表面微裂纹检测算法。基于几何模型重构运动的圆周表面各点热信号，以激光扫描方向相邻点热信号的欧氏距离作为特征进行成像。仿真分析确定热信号裁剪区间、参考信号位置等算法参数。对6个具有5~35 m宽度自然裂纹的样品进行实验，结果表明，在线激光2.66 mm/s的扫描速度下，裂纹成像信噪比相比常规方法提高1~2倍，可清晰成像出裂纹的形状。