Estimation of threshold stress in accelerated life-testing

The author presents a method that uses accelerated life-test data to estimate the mean life at the service stress and the threshold stress below which a failure is unlikely to occur. The relation between stress and mean-life at that stress is assumed to follow an inverse power law that includes a threshold stress. The failure times at a given stress are assumed to follow a Weibull distribution in which the shape parameter varies with the stress. This model extends the well-known Weibull inverse power law model. If only the mean life but not a specific percentile point at a service stress is sought, the maximum likelihood method is useful for parameter estimation. This is a tradeoff in the parametric approach. For adoption of an appropriate probability model, the likelihood ratio test as well as the Akaike Information Criterion are used. Type I right censored data are considered. Extensions of the method are discussed     

基于MAM的白光OLED恒定应力加速寿命试验研究

为了短时间内获得白光有机发光显示器(OLED)的可靠性寿命信息,通过对其开展三组恒定电流应力加速寿命试验采集样品失效试验数据,应用对数正态分布函数描述白光OLED的寿命分布。在图分析法(MAM)的基础上,基于自行开发的寿命预测软件,绘制了对数正态概率双坐标纸,计算出白光OLED的平均寿命和中位寿命。数值结果表明,白光OLED寿命服从对数正态分布,加速寿命方程符合逆幂定律,精确计算的加速参数使得对其寿命的快速估算成为可能。结果可为生产厂商和用户提供参考和指导。     

Weibull分布下基于MAM的白光OLED寿命预测

为了得到白光有机发光二极管(OLED)寿命信息,降低试验成本,开展了三组恒定电流应力加速寿命试验。采用Weibull函数描述其寿命分布,基于图分析法(MAM)和MATLAB绘制的Weibull概率双坐标纸,描点作图并估计形状参数和尺度参数,实现了白光OLED的寿命预测。数值结果表明,白光OLED样品在各加速应力下失效机理保持不变,加速模型满足逆幂定律,精确计算的加速参数使得OLED寿命快速估算成为可能。     

Graphical Analysis of Accelerated Life Test Data with the Inverse Power Law Model

In this paper, graphical methods are presented for analyzing accelerated life test data with the inverse power law model, when all test units are run to failure. The inverse power law model is described, and graphical methods for estimating its parameters from such complete data are given. These methods are illustrated with accelerated test data on time to breakdown of an insulating fluid. While the methods are presented with the inverse power law model, they can be used for analyzing many other accelerated life test situations. These methods are presented so that they can be used by individuals with a limited statistical background.     

Graphical analysis for Birnbaum-Saunders distribution

The Birnbaum-Saunders distribution has been shown to be the failure time distribution for fatigue failure in particular and for stochastic wear-out failure in general. In this paper, we present a simple graphical technique, analogous to probability plotting, to estimate the parameters and check for goodness-of-fit of failure times following the Birnbaum-Saunders distribution. Using known results from regression analysis, confidence intervals for the parameters can easily be established. A salient feature of our method is that it can be used for censored data where no analytical method is available for estimation. Finally a numerical example is given to illustrate the procedure and to compare our results with that of the maximum likelihood estimation.     

A nonparametric approach to progressive stress accelerated lifetesting

Progressive-stress accelerated life testing in which the stress on an unfailed item increases linearly with test time when the time transformation function is a version of the inverse power law is considered. The approach is nonparametric in that not many assumptions are made about life distribution. A testing pattern is introduced, and it is explained how to draw inferences from progressive stress tests. An estimator of life distribution at the usual stress level is proposed     

Analysis of Accelerated Life Test Data?Least Squares Methods for the Inverse Power Law Model

This expository paper presents simple least squares methods for analyzing accelerated life test data with the inverse power law model, when all test units are run to failure. These methods are illustrated with accelerated test data on time to break-down of an insulating fluid.     

Accelerated Life Testing?Step-Stress Models and Data Analyses

This paper presents statistical models and methods for analyzing accelerated life-test data from step-stress tests. Maximum likelihood methods provide estimates of the parameters of such models, the life distribution under constant stress, and other information. While the methods are applied to the Weibull distribution and inverse power law, they apply to many other accelerated life test models. These methods are illustrated with step-stress data on time to breakdown of an electrical insulation.     

Reliability bounds and critical time for the Birnbaum-Saundersdistribution

The Birnbaum-Saunders distribution, under certain conditions, can be used to model the fatigue failure-time caused by the catastrophic crack size. Reliability bounds for the Birnbaum-Saunders distribution and point and interval estimates for the critical time of the failure (hazard)-rate are discussed. The confidence intervals are constructed under the assumption that both parameters are unknown. This method is not affected by censoring, as long as confidence intervals for the parameters can be established. Numerical examples illustrate the procedure     

Some properties of confidence bounds on reliability estimation for parts under varying stresses

Reliability estimation is usually performed on a part under a constant stress level. However, a part could experience several different stress levels, or profiled stress, during its lifetime. One such example is when the part is subject to step-stress accelerated life testing. Studying the reliability estimation & its confidence bounds for a part under varying stresses will generalize the existing estimation methods for accelerated life testing. In this paper, we derive the reliability function of a part under varying stresses based on a Weibull failure time distribution, and cumulative damage model. The reliability confidence bounds, based on a s-normal approximation, are given explicitly, and their limiting properties are discussed. A step-stress accelerated life testing example is used to illustrate these interesting properties, which provides the insights of the limitation of the current test plan, and how to design a better one.     

Bayes estimation of hazard and acceleration in accelerated testing

In accelerated life testing, the time transformation function &thetas;(t) is often unknown, even if that function is assumed to be linear. If &thetas;(t) is known, data in the accelerated condition can be adjusted to provide information about the failure time distribution in the use condition. If &thetas;(t) is unknown, the usual estimation procedures require data from the use condition as well as data from the acceleration condition. In this work it is assumed that the uncertainty about &thetas; can be modeled by a prior distribution, chosen from the truncated Pareto family of distributions, and that the uncertainty in λ, the failure rate, can be modeled by a prior distribution from the gamma family. Under these assumptions, the posterior distributions and their first two moments are provided for both λ and &thetas;. Thus, this complete Bayes approach to accelerated life testing with the assumed model allows the adjustment of data taken in the accelerated condition to provide the user with the important estimates in the use condition. The results are illustrated by examples     

A fast mechanical test technique for life time estimation of micro-joints

A novel accelerated mechanical testing method for reliability assessment of micro-joints in the electronic devices is presented as an alternative to time consuming thermal and power cycling test procedures. A special experimental set-up in combination with an ultrasonic resonance fatigue testing system and a laser Doppler vibrometer is used to obtain fatigue life curves of micro-joints under shear loading. Using this method fatigue life curves of Al wire bonded micro-joints were obtained up to 10⁹ number of loading cycles and discussed with regard to micro-mechanisms of the bond failure. Failure analysis of the fatigued micro-joints showed that the predominant failure mechanism of power cycling tests, bond wire lift-off, was reproduced by the mechanical testing procedure. Life time of the micro-joints was modelled using a Coffin–Manson type relationship and showed a good correlation to life time curves obtained by power cycling tests. The major advantage of the proposed fast mechanical testing method is the significant reduction of the testing time in comparison with conventional thermal and power cycling tests. Furthermore subsequent examination of the failure surface provides a reliable tool for improvement of the bonding process. The proposed high frequency fatigue testing system can be applied as a rapid qualification and screening tool for various kinds of interconnects in electronic packaging.     

Fatigue life prediction model for accelerated testing of electronic components under non-Gaussian random vibration excitations

In this paper, a novel fatigue life prediction model for electronic components under non-Gaussian random vibration excitations is proposed based on random vibration and fatigue theory. This mathematical model comprehensively associates the vibration fatigue life of electronic components, the characteristics of vibration excitations (such as the root mean square, power spectral density, spectral bandwidth and kurtosis value) and the dynamic transfer characteristics of an electronic assembly (such as the natural frequency and damping ratio) together. Meanwhile a detailed solving method was also presented for determining the unknown parameters in the model. To verify the model, a series of random vibration fatigue accelerated tests were conducted. The results obtained show that the predicted fatigue life based on the model agreed with actual testing. This fatigue life prediction model can be used for the quantitative design of vibration fatigue accelerated testing, which can be applied to assess the long-term fatigue reliability of electronic components under Gaussian and non-Gaussian random vibration environments.     

On the Relationship between Two Fatigue-Life Models

The relationship between two fatigue life distributions, namely the Birnbaum-Saunders and the Inverse Gaussian, is further investigated. An intimate connection exists between the two models, viz, the Birnbaum-Saunders is a mixture of two probability distributions: 1) an Inverse Gaussian random variable, and 2) the reciprocal of an Inverse Gaussian random variable. Advantages and disadvantages of the two distributions are discussed. The arguments favour the Birnbaum-Saunders distribution from a stochastic modeling point of view, whereas the Inverse Gaussian distribution seems to be the more attractive of the two with respect to statistical analysis and analysis of censored data.     

Determination of Acceleration Factor in Predicting the Field Life of Plated Through Holes From Thermal Stress Data

Accelerated thermal stress tests nowadays have widely been used in qualification and reliability assessment of printed wiring boards (PWBs). Predicting the field life of plated through holes (PTHs) from test data has been a primary goal of this type of testing. Understanding the PTH cycles to failure (CTF) versus temperature relationship and having a good estimate of acceleration factor (AF) not only expedites the data processing process but also helps in optimizing test conditions and minimizing the number of tests, and hence, reducing the test cost. In this paper, three different PTH CTF-temperature models, including an inverse power law (IPL) model, an IPC model, and an enhanced PTH fatigue-life prediction model, are discussed and evaluated in their effectiveness of determining acceleration factors for the purpose of PTH field life prediction under different test conditions. In addition, using the third model, AF influencing factors, including PTH geometric dimensions, PWB glass transition temperatures (Tg), and the temperature dependency of PWB material properties, are also discussed to provide information for accelerated test design in PWB qualification and reliability assessment.      

Robust estimation of the Birnbaum-Saunders distribution

The Birnbaum-Saunders distribution is prevalent in the engineering sciences as an effective means of modeling fatigue life. In practice however, there is no guarantee that the collected data follow such a model. Consequently, this paper considers the robust estimation of the parameters and quantiles of this distribution. Our robust estimation technique is based on OBRE (optimal bias-robust estimator) and assigns a weight to each observation and gives estimates of the parameters and quantiles based on data which are well modeled by the distribution. Thus, observations which are not consistent with the proposed distribution can be identified and the validity of the model assessed. An `application to aluminum fatigue data' and `simulation results' provide strong evidence in support of OBRE. OBRE performs more than adequately for practical purposes. Furthermore, efficiency in many ways becomes a nonissue as we move away from the model. We must give up some degree of efficiency to gain robustness, and OBRE provides a powerful method of doing so. The simulation study shows that compromises can be made which are effective in both regards. Since statistical-confidence intervals can be calculated for OBRE, robust statistical-confidence interval estimates for the critical time of the hazard rate can also be obtained. These techniques are fundamental in describing, analyzing, and comparing fatigue data so that engineers can achieve the desired reliability on a rational basis and at the same time avoid serious consequences stemming from incorrect inference     

基于加速退化数据的BS分布的统计推断

BS分布是可靠性分析中的一个重要的失效分布模型，它可以用于很多产品的退化失效分析中。对基于加速退化试验数据的BS分布的统计推断方法进行了研究，给出了BS模型的加速退化方程及其适用性。     

基于指数分布的加速寿命试验简论

讨论了4种用于描述加速寿命试验中失效分布参数和环境条件之间关系的失效物理模型。针对阿伦尼斯模型,探讨了加速寿命试验中的参数估计方法,构建了参数的极大似然估计(MLE)方程组,解得加速寿命试验中失效分布参数的MLE值,进而通过转化,借助于标准正态分布表获得其寿命指标的近似值,并通过一个实例介绍了其具体应用。     

A multiplicative damage model for strength of fibrous compositematerials

Knowledge of the tensile strength properties of a fibrous composite material is essential in the design of reliable structures from that material. Determination of statistical models for the tensile strength of a composite material which provide good fits to experimental data from tensile tests on material specimens is therefore important for engineering design. Perhaps the most commonly used statistical model is the Weibull distribution, based on `weakest link of a chain' arguments. However, in many cases the usual Weibull distribution does not adequately fit experimental data on tensile strength for composite materials made from brittle fibers such as carbon. Here, an alternative model is developed for tensile strength of carbon composites, which is based on a multiplicative cumulative-damage approach. This approach results in a 3-parameter extension of the Birnbaum-Saunders fatigue model and incorporates the material specimen size (size effect) as a known variable. This new distribution can also be written as an inverse Gaussian-type distribution, which can be interpreted as the first passage of the accumulated damage past a damage threshold, resulting in material failure. The new model fits experimental tensile-strength data, for carbon micro-composites better than existing models, providing more accurate estimates of material strength