Application of Cumulative Degradation Model to Acceleration Life Test

A general degradation model which includes conventional acceleration tests such as fixed, progressive, and step stress experiments is derived from the reaction theory under the assumption of linear degradation accumulation. Its application to the acceleration test is discussed. According to the reaction theory, degradation of the characteristic parameter, ? is connected to reaction rate K and time t by a linear transformation function f(?) = Kt. The total degradation is determined by the linear accumulation of the Kiti product such as f(?n)= # Kiti. This relationship is also expressed as a generalized Miner's equation #(ti/Li) = 1 in which ti and Li are the actual stressing time and expected life under the ith stress condition, respectively, and # ti is the life expectancy of the component under successive stress conditions from i = 1 to n. Validity of this linear accumulation assumption is investigated under various stress application paths. For monotonic step-up, cyclic, and random stress, the rule almost holds as a whole, but monotonic step-down stress sometimes causes erroneous recovering effects of the parameter. The degradation accumulation principle is effectively applicable to integrate degradation and failure pattern information and also to avoid some shortcomings of conventional life test methods. 1) For example, in order to find efficiently the life vs. stress plot, we could combine the degradation (failure fraction) vs. stress diagram, obtained by one step stress experiment, and the knowledge of the degradation pattern obtained by a constant stress test.     

Graphical Analysis of Accelerated Life Test Data with a Mix of Failure Modes

An accelerated test of a product under high stress yields life data that are extrapolated to estimate the life distribution at low stress. When the data contain competing failure modes, the dominant modes under high stress may not dominate under low stress. This has made experimenters doubt the validity of tests yielding such data. This expository paper presents new graphical methods for estimating: 1) a separate relationship between life and stress for each failure mode, 2) the life distribution at low stress when all modes act, and 3) the life distribution that would result if certain modes are eliminated. Data from a temperature-accelerated life test of electrical insulation illustrate the methods.     

运算放大器在高ESD应力作用下的失效模式和失效位置研究

本研究以常用的运算放大器之一LM741为例进行了高ESD应力条件下的运算放大器的失效研究,研究通过物理观察和电学测试的手段考察了LM741失效位置及失效模式与ESD击打模式之间的关系。研究表明,不同的应力击打模式均造成几种相同的失效位置和模式,而且对失效部位的物理观察发现：所造成芯片上的失效并非在芯片上的电路的单元内部,而在于电路的各个单元之间的绝缘层或者是连接电路单元的金属连线,这一发现为下一步ESD的失效建模和仿真提供了重要的试验依据。     

WT55型1.25厘米体效应管加速寿命试验

本文给出了WT55型1.25厘米体效应管加直流工作点,以环境温度为加速变量的寿命试验结果.器件的突然烧毁严重影响其可靠性,使失效率约为10~(-5)/小时.然而,试验表明,器件实际寿命可达数百万小时.高温直流功率负荷筛选能有效地淘汰早期失效器件,尤其是淘汰突然烧毁失效器件.选择适当的筛选条件,将使器件在40℃环境温度下工作时,获得低于1000菲特的失效率.文章讨论了筛选条件的选择.严格封帽前的镜检,对提高器件可靠性有积极意义.     

Optimum Simple Step-Stress Plans for Accelerated Life Testing

This paper presents optimum plans for simple (two stresses) step-stress tests where all units are run to failure. Such plans minimize the asymptotic variance of the maximum likelihood estimator (MLE) of the mean life at a design stress. The life-test model consists of: 1) an exponential life distribution with 2) a mean that is a log-linear function of stress, and 3) a cumulative exposure model for the effect of changing stress. Two types of simple step-stress tests are considered: 1) a time-step test and 2) a failure-step test. A time-step test runs a specified time at the first stress, whereas, a failure-step test runs until a specified proportion of units fail at the first stress. New results include: 1) the optimum time at the first stress for time-step test and 2) the optimum proportion failing at the low stress for a failure-step test, and 3) the asymptotic variance of these optimum tests. Both the optimum time-step and failure-step tests have the same asymptotic variance as the corresponding optimum constant-stress test. Thus step-stress tests yield the same amount of information as constant-stress tests.     

Investigation of Arrhenius acceleration factor for integrated circuit early life failure region with several failure mechanisms

Use of the Arrhenius equation for analysis of burn-in and life test data has been called into question in recent years. Validity of the Arrhenius activation energy is asserted to be restricted to only one failure mechanism. Therefore, if multiple failure mechanisms apply to an integrated circuit type, the temperature acceleration factor must be complex. In this study a model is constructed using the Weibull distribution for the failure rate applicable when there are multiple failure mechanisms. In this model a different Arrhenius activation energy corresponds to each failure mechanism. It is shown that under conditions expected to be valid for most integrated circuits, an empirical effective Arrhenius activation energy can be computed that is valid for life test data taken under typical conditions to better than 10%. This provides some justification for the continued usage of a simple Arrhenius equation as an empirical model to analyze life test data.     

Accelerated life tests at higher usage rates

Accelerated life tests are extensively used to provide quickly the information about the life distributions of products. Test units are subjected to elevated stresses which yield shorter lives. For some products whose life is defined by usage, e.g., mileage and cycles, test units are also run at higher usage rates (UR) to compress the test time. This paper presents a method for testing products at both higher stress levels, and UR. Censoring time is pre-determined and fixed, while censoring usage is a function of UR. A UR effect model is proposed to describe the dependence of usage to failure (UTF) on UR. The relationship between UTF, and stress and UR is established, and used to estimate the UTF distribution at design stresses and usual UR. The model parameters are estimated by maximum likelihood method. The best compromise test plans, which choose the UR, stress levels, and sample sizes, are devised by minimizing the asymptotic variance of the estimator of a life percentile at design stresses and usual UR. The efficiency, and sensitivity of the test plans are evaluated. The results show that the test plans are efficient, and robust.     

Analysis of electrical parameters of InGaN-based LED packages with aging

As the light-emitting diode (LED) becomes a mature technology in the general illumination space, there is a tendency to operate LEDs at high current densities and temperatures in order to gain higher light output at lower cost. Further, there is interest among intelligent-lighting platform developers to offer predictive maintenance capabilities to users. The existing useful life prediction model defines LED lifetime based on parametric failure; however, there is a need for a useful life prediction model based on catastrophic failure, which can occur with the degradation of components in an LED package. Electrical parameters, especially package series resistance, are good indicators of LED package health (i.e., remaining useful life) and could potentially be sensed real-time in an application. In this study, the series resistance variation pattern until catastrophic failure was measured at different current and temperature stress conditions. The degradation mechanisms at each phase of variation were explained and, using available models, activation energies and exponents were extracted. The experimental data suggest electromigration-induced metal migration from the contact metallization layer to the semiconductor is the cause of short circuit catastrophic failure of LED packages. The variation patterns of ideality factor and reverse leakage current support this hypothesis. The information presented can be used to develop a catastrophic life estimation model for LED packages under current and temperature stress.     

Optimum Accelerated Life-Tests for the Weibull and Extreme Value Distributions

This paper presents charts for optimum accelerated life-test plans for estimating a simple linear relationship between an accelerating stress and product life, which has a Weibull or smallest extreme value distribution, when the data are to be analyzed before all tests units fail. The plans show that one need not run all test units to failure and that more units ought to be tested at low test stresses than at high ones. The plans are illustrated with a voltage-accelerated life test of an electrical insulating fluid.     

An advanced area scaling approach for semiconductor burn-in

In semiconductor manufacturing, early life failures are avoided by putting the produced items under accelerated stress conditions before delivery. The products’ early life failure probability p is assessed by means of a burn-in study, in which a sample of the stressed items is investigated for early failures. The aim is to prove a target failure probability of the produced devices and release stress testing of the whole population. Given the failure probability level on a reference product, the failure probabilities of so-called follower products with different chip sizes are then obtained by means of area scaling. Classically, area scaling is done with respect to the whole area of the chips. Nevertheless, semiconductors can be partitioned into different chip subsets, which can have different likelihoods of failures. In this paper, we propose a novel area scaling model for the chip failure probability p, which enables us to scale the chip subsets separately from each other. The main idea is to adapt the classical estimators of the failure probabilities of the chip partitions according to the number of failures on the different chip subsets. This leads to a more appropriate estimation of the failure probabilities of the follower products and helps to improve the efficiency of burn-in testing.     

A reliability model for SAC solder covering isothermal mechanical cycling and thermal cycling conditions

This paper presents an alternative to the use of energy-based methodologies for life cycle predictions of solder interconnects. Isothermal mechanical cycling testing has been conducted using joint-scale solder samples on a novel testing apparatus. The test data shows that work as a single parameter is insufficient in predicting failure; nor does the inclusion of cyclic frequency and mean temperature improve work-based methodologies. Here, a novel semi-empirical approach is presented in which stress, strain, strain rate and temperature are individually treated to create a model capable of predicting material behaviour under arbitrary cyclic loading conditions. The model constants are fitted to the results of the isothermal mechanical cycling tests, using load drop as a measure of damage. The calibrated model is then employed to predict the failure of a BGA device under thermal cycling. The modelling results show state-of-the-art agreement with the test data and superiority over Morrow model constants from literature that have been applied to this data set.     

Stress analysis in silicon die under different types of mechanical loading by finite element method (FEM)

Stress analysis is of crucial importance in the design of components and systems in the electronics industry. In this paper, the authors present a new strength criterion combined with finite element analysis (FEA) to predict the failure stress of silicon die. Several different models of pushers were designed to apply load in the vfBGA reliability test until some units failed the electrical test. Meanwhile, finite element analysis was performed in order to find the location of the highest stress and the expected modes of failure. In the simulation, a parametric study of the effect of different types of pushers on the internal stress of the die is carried out and the failure stress can be determined eventually. The potential for chip damage under certain pushers during electrical tests has been assessed and the relationship between the maximum principal stress and the thickness of the silicon die is also explored.     

Reliability Physics Models

The generalized stress-strength model which is prevalent in current literature is perhaps the closest that analysts have come to a general physical model. To obtain a failure density function and associated hazard function one must assume a certain probability distribution for the part strength and a particular amplitude distribution and frequency of occurrence distribution for the part stress. If one assumes a normal strength distribution and Poisson distributed stress occurrence times with normally distributed amplitudes, then this leads to an exponential failure density function and a constant hazard. Such a model is probably best suited for situations in which the part generally lasts a long time and only seems to fail when on occasion a large stress occurs. In many situations the failure of parts seems to fit a different pattern. The part is operated at nearly a constant stress level; however, the part strength gradually deteriorates with time. As time goes on the rate of deterioration should increase sharply as wear-out is reached and cause an increase in hazard. A probabilistic model which fits this hypothesis is a constantly applied stress and a Rayleigh distributed part strength. The parameter of the Rayleigh distribution is allowed to increase in an exponential fashion with time which produces the strength deterioration effect. Basically the failure rate turns out to depend on the square of the applied stress; however, if the strength deterioration rate is allowed to be a function of the input stress, other behaviors are predicted.     

聚合物整体灌装电路板热应力分析

电路板的聚合物整体灌装是一种提高电子器件在极端工况下可靠性的方法。针对该方法所面临的热应力失效问题,采用有限元数值方法研究了含15个元器件的整体灌装电路板在环境温度改变和器件产热两种热载荷下的热应力分布,并通过参数化模拟分析了不同几何和材料参数对元器件及其接合层中热应力分布的影响。结果表明整体灌装加剧了IC器件及其接合层的热应力,该模拟工作为提高整体灌装方案的热应力可靠性提供参考。     

Analysis of grouped and censored data from step-stress life test

This paper studies statistical analysis of grouped and censored data obtained from a step-stress accelerated life test. We assume that the stress change times in the step-stress life test are fixed and the lifetimes observed are type I censored. Maximum likelihood estimates and asymptotic confidence intervals for model parameters are obtained. We provide an asymptotic statistical test for the cumulative exposure model based on the grouped and type I censored data. We also present the optimum test plan for a simple step-stress test when the lifetime under constant stress is assumed exponential. Finally we give an application of our methods by applying our analysis process to a real life data set. The proposed statistical methodology is especially useful when intermittent inspection is the only feasible way of checking the status of test units during a step-stress test.     

Prognostic Degradation Models for Computing and Updating Residual Life Distributions in a Time-Varying Environment

This paper presents a degradation modeling framework for computing condition-based residual life distributions of partially degraded systems and/or components functioning under time-varying environmental and/or operational conditions. Our approach is to mathematically model degradation-based signals from a population of components using stochastic models that combine three main sources of information: real-time degradation characteristics of component obtained by observing the component's in-situ degradation signal, the degradation characteristics of the component's population, and the real-time status of the environmental conditions under which the component is operating. Prior degradation information is used to estimate the model coefficients. The resulting generalized stochastic degradation model is then used to predict an initial residual life distribution for the component being monitored. In-situ degradation signals, along with real-time information related to the environmental conditions, are then used to update the residual life distributions in real-time. Because these updated distributions capture current health information and the latest environmental conditions, they provide precise lifetime estimates. The performance of the proposed models is evaluated using real world vibration-based degradation signals from a rotating machinery application.      

Application of multi-output Gaussian process regression for remaining useful life prediction of light emitting diodes

Light-emitting diodes (LEDs) are the preferred technology today when it comes to lighting both for indoor and outdoor applications, predominantly due to their high efficiency, environmental resilience and prolonged lifetime. Given their widespread use, there is a need to quickly qualify them and accurately predict the reliability of these devices. Due to their inherently long operational life, most LED reliability studies involve the use of degradation tests and application of filter-based prognostic techniques for dynamic update of degradation model parameters and estimation of the remaining useful life (RUL). Although they are in general very effective, the main drawback is the need for a specific state-space model that describes the degradation. In many cases, LED degradation trends are affected by a multitude of unknown factors such as unidentified failure modes, varying operational conditions, process and measurement variance, and environmental fluctuations. These variable factors that are hard to control tend to complicate the selection of a suitable state-space model and in some cases; there may not be a single model that could be used for the entire lifespan of the device. If the degradation patterns of LEDs under test deviate from the state space models, the resulting predictions will be inaccurate. This paper introduces a prognostics-based qualification method using a multi-output Gaussian process regression (MO-GPR) and applies it to RUL prediction of high-power LED devices. The main idea here is to use MO-GPR to learn the correlation between similar degradation patterns from multiple similar components under test and thereby, bypass the need for a specific state space model using available data of past units tested to failure.     

Derated Capacity States of a Large Thermal Generating Unit

Large thermal generation units operate under derated capacity conditions for considerable part of their up time as a result of the failure of its auxiliary units. The long term behaviour of such a unit is simulated by presenting a multilevel model, using state space methods. Truncation of the state space is adopted to reduce computation without introducing appreciable error.     

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     

Application of coupled electro-thermal and physics-of-failure-based analysis to the design of accelerated life tests for power modules

In the reliability theme a central activity is to investigate, characterize and understand the contributory wear-out and overstress mechanisms to meet through-life reliability targets. For power modules, it is critical to understand the response of typical wear-out mechanisms, for example wire-bond lifting and solder degradation, to in-service environmental and load-induced thermal cycling. This paper presents the use of a reduced-order thermal model coupled with physics-of-failure-based life models to quantify the wear-out rates and life consumption for the dominant failure mechanisms under prospective in-service and qualification test conditions. When applied in the design of accelerated life and qualification tests it can be used to design tests that separate the failure mechanisms (e.g. wire-bond and substrate-solder) and provide predictions of conditions that yield a minimum elapsed test time. The combined approach provides a useful tool for reliability assessment and estimation of remaining useful life which can be used at the design stage or in-service. An example case study shows that it is possible to determine the actual power cycling frequency for which failure occurs in the shortest elapsed time. The results demonstrate that bond-wire degradation is the dominant failure mechanism for all power cycling conditions whereas substrate-solder failure dominates for externally applied (ambient or passive) thermal cycling.