A comprehensive review of the lognormal failure distribution with application to LED reliability

Life-test data for many semiconductor devices obey the lognormal law of failure. In this paper we offer a survey of the key statistical properties of the lognormal distribution which are relevant in device engineering. The statistical developments are illustrated throughout by specific examples drawn from life-test data for GaP red LEDs which show lognormal failure behavior. Additional theoretical justification for accepting the lognormal distribution in the case of these devices is provided by the statistical recasting of the diffusion theory of red LED degradation.The treatment of the fundamental concepts of reliability in terms of cumulative failure function, instantaneous failure rate, mean time for failure (MTTF), etc., although concise, is self-contained. Moreover, the estimation of the two characteristic parameters (median life, standard deviation) of the lognormal distribution from sample data by means of a number of alternative procedures (graphical, least-square, maximum likelihood) is discussed in detail. The efficient determination of the MTTF and failure rate is facilitated by convenient charts developed here which relate these quantities to the parameters median life and standard deviation at 5, 10, 20 and 40 years of device service life. In order to assess the uncertainty associated with the estimates, the confidence limits on the median life and standard deviation of the population as a function of confidence level and sample size are given in novel graphical forms. Finally, error bounds for the MTTF and failure rate of the population are also presented.     

Confidence limits on the failure rate and a rapid projection nomogram for the lognormal distribution

In order to predict the sample failure rate from a limited number of early malfunctions, we have developed the rapid lognormal projection nomogram (RLPN) which we present at 1, 5, and 10 years of service. In the core of each diagram is a family of curves showing the variation of failure rate as a function of sample median life and standard deviation. Superimposed are Arrhenius plots for a series of activation energies, all referenced with respect to a fixed time. We also display the standard deviation as a function of relative median life, using cumulative failure as a parameter. The RLPN provides graphical means to estimate the failure rate at the planned service life and operating temperature in an efficient manner from the time to failure at the aging temperature and sample size for known or assumed values of the standard deviation and activation energy. To obtain the confidence limits for the failure rate of the lognormal distribution at the 90% confidence level, we have derived an approximate formula that relates the bounds to the service life and the sample's size, median life, and standard deviation. Then, by an appropriate selection of the independent variables and parameters, the confidence intervals are displayed as a series of curve families. The applications of the diagrams are discussed by means of illustrative examples taken from the field of GaAs FETs.     

A New Nonparametric Growth Model

This paper proposes a new nonparametric reliability growth model for the analysis of the failure rate of a system that is undergoing development test. The only restrictions on the actual, unknown failure distribution for each stage of testing is that it be continuous, have only one unknown parameter ?, and have an associated unimodal likelihood function. No assumptions regarding the parametric form of the failure rate of the development process are made, only that there is no decay in the reliability of the system during the design changes. The parameters are assumed to be ordered from one test stage to the next such that ?1 ? ?2 ? ... ? ?m. The new model performs very well based on relative error and mean square error. The model is generally superior to the popular AMSAA model, regardless of the actual underlying failure process. In addition, the results indicate a notable bias in the AMSAA model, early in the development process, regardless of the actual underlying failure process.     

Symbolic Macromodeling for Statistical Simulation of Operational Amplifiers

Symbolic circuit simulator is traditionally applied to the small-signal analysis of analog circuits. This paper establishes a symbolic behavioral macro-modeling method applicable to both small-signal and large-signal analysis of general two-stage operational amplifiers (op-amps). The proposed method creates a two-pole parametric macromodel whose parameters are analytical functions of the circuit element parameters generated by a symbolic circuit simulator. A moment matching technique is used in deriving the analytical model parameter. The created parametric behavioral model can be used for op-amps performance simulation in both frequency and time domains. In particular, the parametric models are highly suited for fast statistical simulation of op-amps in the time-domain. Experiment results show that the statistical distributions of the op-amp slew and settling time characterized by the proposed model agree well with the transistor-level results in addition to achieving significant speedup.     

基于HCT-FEM和3D电磁模型的SAW滤波器性能仿真系统

该文基于分层级联有限元(HCT-FEM)和三维电磁模型构建了一套声表面波(SAW)滤波器性能仿真系统。采用Matlab协同COMSOL建立的HCT-FEM模型计算声学元件导纳,用ANSYS建立的三维电磁模型计算含芯片走线、引线/金属球、封装外壳及测试电路的外部电磁S参数,并在ADS软件中对SAW滤波器频率响应进行复原。将该系统应用于一款芯片级封装(CSP)的普通SAW滤波器和一款表贴封装(SMD)的单晶薄膜SAW滤波器电性能仿真,仿真与实测结果吻合较好。     

A simple procedure for Bayesian estimation of the Weibull distribution

Practical use of Bayesian estimation procedures is often associated with difficulties related to elicitation of prior information, and its formalization into the respective prior distribution. The two-parameter Weibull distribution is a particularly difficult case, because it requires a two-dimensional joint prior distribution of the Weibull parameters. The novelty of the procedure suggested here is that the prior information can be presented in the form of the interval assessment of the reliability function (as opposed to that on the Weibull parameters), which is generally easier to obtain. Based on this prior information, the procedure allows constructing the continuous joint prior distribution of Weibull parameters as well as the posterior estimates of the mean and standard deviation of the estimated reliability function (or the CDF) at any given value of the exposure variable. A numeric example is discussed as an illustration. We additionally elaborate on a new parametric form of the prior distribution for the scale parameter of the exponential distribution. This distribution is not a Gamma (as might intuitively be expected); its mode is available in a closed form, and the mean is obtainable through a series approximation.     

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。     

Parametric orchestral sonification of EEG in real time

The authors introduce a device for the parametric sonification of electroencephalographic (EEC) data. The device allows auditory feedback of multiple EEG characteristics in real time. Six frequency bands are assigned as instruments from a MIDI device. The time-dependent parameters modulate the timing, pitch, and volume of the instruments. Using this, we studied subjects' ability to perform a discrimination task with parametric sonification in real time.     

基于威布尔分布的某半导体器件贮存寿命分布规律初探

对有机电致发光二极管（Organic Light-Emitting Diode,OLED）微型显示器件进行90℃、80℃、70℃的高温贮存试验,获得产品的失效数据。基于威布尔分布模型,采用最小二乘法进行参数估计,对失效数据分析,获得OLED微型显示器件失效分布函数。应用经典可靠性理论,计算产品在90℃、80℃、70℃的特征寿命、可靠寿命及平均故障间隔时间（Mean Time Between Failure,MTBF）。采用Arrhenius模型,依据90℃、80℃、70℃的贮存特征寿命,获得常温下产品的贮存特征寿命。分析结果表明,该方法合理、简便、有效,数据结果可以进一步应用到推导产品常温贮存寿命。     

Relation of a Physical Process to the Reliability of Electronic Components

An ensemble of electronic components having a random variation of some parameter, such as surface contamination, is considered. A physical process is postulated which leads to a change in one of the operating characteristics of the device. When this operating characteristic attains a value outside an acceptable range, the device is considered to have failed. The failure rate is calculated directly from the time behavior of the physical process and compared, for illustration, to the Weibull failure law. The parameters of the Weibull law are then related to the parameters of the physical process and the distribution of starting parameters.     

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.     

基于半马尔科夫过程的变压器故障率预测及研究

设备的故障率曲线是制定维修策略的重要指标之一。为了合理估计变压器的故障率,本文提出了基于半马尔科夫过程的预测模型。模型中考虑了变压器的热老化过程和随机故障过程。热老化过程根据绝缘纸平均聚合度的取值范围划分为4个状态,状态间的转移时间假设服从威布尔分布,威布尔分布的尺度参数由经验公式获得;随机故障过程考虑了由雷击和短路冲击引起的2个随机故障状态,老化状态和随机故障状态之间的转移时间假设服从指数分布,转移率由故障统计数据获得。对模型中威布尔分布的形状参数进行适当取值后,可获得符合实际统计结果的变压器故障率曲线。     

Analysis of a 2-phase model for optimization ofcondition-monitoring intervals

Condition monitoring is a maintenance strategy where decisions are made depending on either continuously or regularly measured equipment states. It reduces uncertainty with respect to actual states of equipment, and can thus avoid unnecessary repair or replacement. However, it involves capital expenditure and/or operational costs to perform measurements. This paper presents a basic model for the economic evaluation and optimization of the interval between successive condition measurements (also called inspections), where measurements are expensive and cannot be made continuously. It assumes that the technique can detect an intermediate state to failure for a failure mode of interest. The influence of competing risks is analyzed, leading to the conclusion that once the cost-effectiveness of the condition-monitoring has been established, competing risks need not be considered in determining the optimum condition monitoring interval. Inspection is cost-effective if the intermediate state has a: (1) nondecreasing hazard rate, and (2) shorter mean residence time than the good state (good-as-new condition), while costs of failure are high enough compared with inspection and repair costs in the intermediate state. Assuming that the distribution of the residence time in the second state is unimodal, estimation of the mean (or scale parameter) and standard deviation of this state, in many cases, provides enough information to make a good decision on the inspection interval. The most important model parameters are identified by sensitivity analyses; it is shown that the model can be simplified without seriously affecting optimal decision making     

Reliability Analysis of Systems Comprised of Units with Arbitrary Repair-Time Distributions

This work demonstrates the feasibility of reliability modeling of systems with repair capability using a semi-Markov process. A two-unit system with exponential failure times but general repair times is studied. Formulas for state-transition probabilities, waiting-time distribution functions, and mean time in each state are developed. These quantities are expressed in terms of the Laplace transform of repair time distribution functions. Once these quantities are known, mean time to system failure and system availability, as well as other system parameters, can be found using matrix manipulations. In addition, time-dependent results may be obtained. A numerical example varying the parameter in a repair-time law is presented. The formulas developed can be extended to larger systems with repair capability for only one unit at a time and exponential failure times.     

The failure rate function estimated from parameter drift measurements

A theoretical model for prediction of the component drift failure rate as a function of time from component parameter drift rates is described. The model assumes statistical independence of the initial value and the drift of the parameter. To use the model it is necessary to know the distribution of the initial value of the component parameter, the component parameter drift function and the distribution of the functional parameters. Further the concept of “component working lifetimes” is discussed. Two different definitions are suggested, both based on the assumptions of a Weibull distribution for the wear-out lifetimes and an exponential distribution to give the earlier “constant” failure rate.     

Multiresolution statistical analysis of high-resolution digitalmammograms

A multiresolution statistical method for identifying clinically normal tissue in digitized mammograms is used to construct an algorithm for separating normal regions from potentially abnormal regions; that is, small regions that may contain isolated calcifications. This is the initial phase of the development of a general method for the automatic recognition of normal mammograms. The first step is to decompose the image with a wavelet expansion that yields a sum of independent images, each containing different levels of image detail. When calcifications are present, there is strong empirical evidence that only some of the image components are necessary for the purpose of detecting a deviation from normal. The underlying statistic for each of the selected expansion components can be modeled with a simple parametric probability distribution function. This function serves as an instrument for the development of a statistical test that allows for the recognition of normal tissue regions. The distribution function depends on only one parameter, and this parameter itself has an underlying statistical distribution. The values of this parameter define a summary statistic that can be used to set detection error rates. Once the summary statistic is determined, spatial filters that are matched to resolution are applied independently to each selected expansion image. Regions of the image that correlate with the normal statistical model are discarded and regions in disagreement (suspicious areas) are flagged. These results are combined to produce a detection output image consisting only of suspicious areas. This type of detection output is amenable to further processing that may ultimately lead to a fully automated algorithm for the identification of normal mammograms     

表面波声电光效应耦合波方程

从参量互作用基本方程出发,导出表面波声光效应的耦合波方程,再将电光效应视作微扰,分别考虑晶体压电效应产生的交变电场和外加直流电场的影响,对此方程进行修正,得到表面波声电光效应耦合波方程。通过求解方程,得出衍射效率计算公式。由于表面波声电光器件多了一个信号输入端口,使用起来更加灵活,在实时信号处理中,如相关、卷积、匹配滤波、频谱分析、矩阵光计算等领域具有广阔应用前景。     

A thin-membrane surface-acoustic-wave vapor-sensing device

An integrated silicon-based vapor sensor is realized with a ZnO-on-Si surface-acoustic-wave (SAW) oscillator containing an absorptive polymer located on a thinned, membrane region of the device. If the membrane thickness is comparable with or smaller than a SAW wavelength, wave energy is present at both membrane surfaces. Thus the SAW transducers and associated amplifiers can be protected by an enclosure, leaving only the polymer exposed to the ambient atmosphere. Experiments on a 30 MHz, ZnO-on-silicon thin-membrane temperature-compensated SAW oscillator for vapor sensing are described. The use of the multi-channel device for solubility parameter sensing is discussed.     

声表面波谐振器回波信号的频率估计

声表面波(SAW)谐振器测量技术能在高温、高压、强电磁辐射和强电磁干扰等恶劣环境下,实现无线无源的参数检测。针对声表面波谐振器回波信号的非平稳特点,该文提出一种回波信号的频率测量方法“数字频率有效位数跟进法”(DFSPT)。仿真结果表明,该方法与现有的基于傅里叶变换法(FFT)和奇异值分解法(SVD)的方法相比,其能根据信噪比的不同,自行确定数字频率有效数字的位数,提高了频率估计的精度和稳定性。无线SAW温度传感器实验表明,该方法的频率估计标准差小,鲁棒性高。     

Connecting parametric aging to catastrophic failure throughthermodynamics

There have been numerous studies with Arrhenius theory in reliability. However, very few actually apply to parametric reliability analysis. This paper provides fundamental details in this area of reliability physics. The authors derive a thermally activated time-dependent model for both parametric and catastrophic Arrhenius aging. It is shown how aging dynamics depend upon thermodynamics specific to device reliability physics and how catastrophic phenomena can be correlated to device life dynamics