Analysis of step-stress accelerated-life-test data: a new approach

A linear cumulative exposure model (LCEM) is used to analyze data from a step-stress accelerated-life-test, in particular, those with failure-free life (FFL). FFL is characterized by a location parameter in the distribution. For the 2-parameter Weibull distribution, the Nelson cumulative exposure model is a special case of LCEM. Under LCEM a general expression is derived for computing the maximum likelihood estimator (MLE) of stress-dependent distribution parameters under multiple censoring. The estimation procedure is simple and is illustrated by a set of experimental data using the 3-parameter Weibull distribution     

A modified Weibull distribution

A new lifetime distribution capable of modeling a bathtub-shaped hazard-rate function is proposed. The proposed model is derived as a limiting case of the Beta Integrated Model and has both the Weibull distribution and Type 1 extreme value distribution as special cases. The model can be considered as another useful 3-parameter generalization of the Weibull distribution. An advantage of the model is that the model parameters can be estimated easily based on a Weibull probability paper (WPP) plot that serves as a tool for model identification. Model characterization based on the WPP plot is studied. A numerical example is provided and comparison with another Weibull extension, the exponentiated Weibull, is also discussed. The proposed model compares well with other competing models to fit data that exhibits a bathtub-shaped hazard-rate function.     

Uniqueness of maximum likelihood estimators of the 2-parameterWeibull distribution

We present a simple statistic, calculated from either complete failure data or from right-censored data of type-I or -II. It is useful for understanding the behavior of the parameter maximum likelihood estimates (MLE) of a 2-parameter Weibull distribution. The statistic is based on the logarithms of the failure data and can be interpreted as a measure of variation in the data. This statistic provides: (a) simple lower bounds on the parameter MLE, and (b) a quick approximation for parameter estimates that can serve as starting points for iterative MLE routines; it can be used to show that the MLE for the 2-parameter Weibull distribution are unique     

Moment estimators for the 3-parameter Weibull distribution

Weibull moments are defined generally and then calculated for the 3-parameter Weibull distribution with non-negative location parameter. Sample estimates for these moments are given and used to estimate the parameters. The results of a simulation investigation of the properties of the parameter estimates are discussed briefly. A simple method of deciding whether the location parameter can be considered zero is described     

激光诱导击穿光谱的飞灰碳含量定量分析方法

燃煤飞灰碳含量是影响锅炉工作效率的重要特性指标之一,文中开展激光诱导击穿光谱技术（LIBS）实现飞灰未燃碳的定量分析方法研究,为LIBS应用于飞灰含碳量的快速/在线检测奠定基础。根据所探测的LIBS特征光谱,将线性和非线性化学计量学方法,包括多元线性回归（MLR）和偏最小二乘回归（PLSR）线性分析分析方法,以及非线性的极限学习机（ELM）和支持向量机回归（SVR）模型应用于飞灰未燃碳的预测分析中,结合交叉验证法对模型进行验证。对比线性和非线性模型的结果可以看出,非线性模型的预测结果明显优于线性模型,其中采用基于K-CV参数优化的非线性SVR模型具有比较理想的分析结果,有助于提高飞灰碳含量分析的精确度和准确度,采用三折叠交叉验证法对模型进行验证,得到模型的决定系数R2均为0.99,相对偏差的平均值ARD分别为1.54%、3.45%、3.51%,相对标准误差RSD的平均值分别为7.53%、2.89%、7.18%。     

Maximum Likelihood Estimation For The 2-Parameter Weibull Distribution Based On Interval-Data

MLE techniques are presented for estimating time-to-failure distributions from interval-data. Interval-data consist of adjacent inspection times that surround an unknown failure time. Censored interval-data bound the unknown failure time with only a lower time. The 2-parameter Weibull distribution is examined as the failure distribution. Parameter estimates from interval-data and from the midpoints of the intervals are compared for 6 shapes of the Weibull distribution. The results from Monte Carlo simulation runs are used to examine the s-bias and S-variability of the parameter estimates.     

Lorentzian型布里渊频谱特征提取时模型的影响

为了在提取Lorentzian型布里渊频谱特征时选择最佳模型,以线性最小二乘法和非线性最小二乘法构造的目标函数为研究对象,系统地比较目标函数构造对频谱特征提取的影响。数值产生了不同信噪比、扫描频率间隔、g0、vB和vB的布里渊信号,比较了两种模型得到的频谱特征参数的准确性和计算耗时,并用真实布里渊散射信号进行了验证。结果表明:在不含干扰的理想状态下两种模型都能达到非常高的精度,随着噪声含量/扫描频率间隔的增加两种模型的准确性都下降,但线性模型明显大于非线性模型,实际时应采用非线性模型。实验测量的布里渊散射谱信号验证了分析结果的正确性。     

Confidence Limits for Weibull Regression With Censored Data

The response variable in an experiment follows a 2-parameter Weibull distribution having a scale parameter that varies inversely with a power of a deterministic, externally controlled, variable generically termed a stress. The shape parameter is invariant with stress. A numerical scheme is given for solving a pair of nonlinear simultaneous equations for the maximum likelihood (ML) estimates of the common shape parameter and the stress-life exponent. Interval and median unbiased point estimates for the shape parameter, stress-life exponent and a specified percentile at any stress, are expressed in terms of percentage points of the sampling distributions of pivotal functions of the ML estimates. A numerical example is given.     

Identification of constant-posture EMG-torque relationship about the elbow using nonlinear dynamic models

The surface electromyogram (EMG) from biceps and triceps muscles of 33 subjects was related to elbow torque, contrasting EMG amplitude (EMGσ) estimation processors, linear/nonlinear model structures, and system identification techniques. Torque estimation was improved by 1) advanced EMGσ processors (i.e., whitened, multiple-channel signals); 2) longer duration training sets (52 s versus 26 s); and 3) determination of model parameters via pseudoinverse and ridge regression methods. Dynamic, nonlinear parametric models that included second- or third-degree polynomial functions of EMGσ outperformed linear models and Hammerstein/Weiner models. A minimum error of 4.65 ± 3.6% maximum voluntary contraction (MVC) flexion was attained using a third-degree polynomial, 28th-order dynamic model, with model parameters determined using the pseudoinverse method with tolerance 5.6 × 10 (-3) on 52 s of four-channel whitened EMG data. Similar performance (4.67 ± 3.7% MVC flexion error) was realized using a second-degree, 18th-order ridge regression model with ridge parameter 50.1.     

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     

Tables for Exact Lower Confidence Limits for Reliability and Quantiles, Based on Least-Squares Estimators of Weibull Parameters

For the 2-parameter Weibull distribution, this paper gives tables to obtain exact lower s-confidence limits for reliability on the basis of the least-squares method and median plotting positions. The tables use a method based on the ancillary property of these estimators. They apply to samples of size N = 3(1)13, censored after the first m observations, m = 3(1)N. The same tables enable one to obtain lower s-confidence limits for population quantiles. The use of the tables is illustrated with a numerical example.     

GaAs MESFET大信号模型参数的计算机提取

利用GaAs MESFET的小信号S参数及瞬态I—V特性的测量数据,建立了GaAsMESFET的大信号分析模型,编制计算机程序,进行了参数拟合并比较了GaAs MESFET两种非线性模型的适用范围,使用分步优化的方法拟合GaAs MESFET小信号S参数,获取了大信号模型中的线性参数,非线性参数值利用最小二乘法及直接优化法相结合的算法提取。为非线性电路、功率放大器、混频器、振荡器提取了准确的设计参数。     

Sequential tests for integrated-circuit failures

We propose a sequential probability ratio test (SPRT) based on a 2-parameter Weibull distribution for integrated-circuit (IC) failure analysis. The shape parameter of the Weibull distribution characterizes the decreasing, constant, or increasing failure rate regions in the bath tub model for IC. The algorithm (SD) detects the operating region of the IC based on the observed failure times. Unlike the fixed-length tests, the SD, due to its sequential nature, uses the minimum average number of devices for the test for fixed error tolerances in the detection procedure. We find that SD is, on average, 96% more statistically efficient than the fixed-length test. SD is highly robust to the variations in the model parameters, unlike other existing sequential tests. Since the accuracy of the tests and the test length are conflicting requirements, we also propose a truncated SD which allows a better control of this tradeoff. It has both the sequential nature of examining measurements and the fixed-length property of guaranteeing that the tolerances be met approximately with a specified number of available measurements     

Estimation of Weibull Parameters With Competing-Mode Censoring

Existing results are reviewed for the maximum likelihood (ML) estimation of the parameters of a 2-parameter Weibull life distribution for the case where the data are censored by failures due to an arbitrary number of independent 2-parameter Weibull failure modes. For the case where all distributions have a common but unknown shape parameter the joint ML estimators are derived for i) a general percentile of the j-th distribution, ii) the common shape parameter, and iii) the proportion of failures due to failure mode j. Exact interval estimates of the common shape parameter are constructable in terms of the ML estimates obtained by using i) the data without regard to failure mode, and ii) existing tables of the percentage points of a certain pivotal function. Exact interval estimates for a general percentile of failure-mode-j distribution are calculable when the failure proportion due to failure-mode-j is known; otherwise a joint s-confidence region for the percentile and failure proportion is calculable. It is shown that sudden death endurance test results can be analyzed as a special case of competing-mode censoring. Tabular values for the construction of interval estimates for the 10-th percentile of the failure-mode-j distribution are given for 17 combinations of sample size (from 5 to 30) and number of failures.     

Confidence and `A' and `B' Allowable Factors for the Weibull Distribution

s-Confidence and `A' and `B' allowable factors for sample sizes 2-30, obtained by Monte Carlo techniques, for populations whose property measurements can be represented by a 2-parameter Weibull distribution are developed. The factors for the Weibull case are presented here in graphical form which allows practical engineering application and readily shows sample size effects. A numerical example illustrates the use of the factors.     

Multi-output regression using a locally regularised orthogonalleast-squares algorithm

The paper considers data modelling using multi-output regression models. A locally regularised orthogonal least-squares (LROLS) algorithm is proposed for constructing sparse multi-output regression models that generalise well. By associating each regressor in the regression model with an individual regularisation parameter, the ability of the multi-output orthogonal least-squares (OLS) model selection to produce a parsimonious model with a good generalisation performance is greatly enhanced     

Goodness-of-fit tests for type-I extreme-value and 2-parameterWeibull distributions

This study investigates the properties of the Kolmogorov-Smirnov (K-S), Cramer-von Mises (C-M) and Anderson-Darling (A-D) statistics for goodness-of-fit tests for type-I extreme-value and for 2-parameter Weibull distributions, when the population parameters are estimated from a complete sample by graphical plotting techniques (GPT). Three GPT-median ranks, mean ranks, symmetrical sample cumulative distribution (symmetrical ranks)-are combined with the least-squares method (LSM) on extreme-value and Weibull probability paper to estimate the population parameters. The critical values of the K-S, C-M, A-D statistics are calculated by Monte Carlo simulation, in which 10⁶ sets of samples for each sample size of 3(1)20, 25(5)50, and 60(10)100 are generated. The power of the K-S, C-M, A-D statistics are investigated for 3 graphical plotting techniques and for maximum likelihood estimators (MLE). A Monte Carlo simulation provided the power results using 10⁴ repetitions for each sample size of 5, 10, 25, 40. The power comparison showed that: Among 3 GPT, the symmetrical ranks give more powerful results than the median and mean ranks for the K-S, C-M, A-D statistics; Among 3 GPT and the MLE, the symmetrical ranks provide more powerful results than the MLE for the K-S and A-D statistics; for the C-M statistic, the MLE provide more powerful results than 3 GPT; Generally, the A-D statistic coupled with the symmetrical ranks and LSM is most powerful among the competitors in this study and is recommended for practical use     

Maximum-likelihood parameter estimation of discrete homogeneousrandom fields with mixed spectral distributions

This paper presents a maximum-likelihood solution to the general problem of fitting a parametric model to observations from a single realization of a real valued, 2-D, homogeneous random field with mixed spectral distribution. On the basis of a 2-D Wold-like decomposition, the field is represented as a sum of mutually orthogonal components of three types: purely indeterministic, harmonic, and evanescent. The proposed algorithm provides a complete solution to the joint estimation problem of the random field components. By introducing appropriate parameter transformations, the highly nonlinear least-squares problem that results from the maximization of the likelihood function is transformed into a separable least-squares problem. In this new problem, the solution for the unknown spectral supports of the harmonic and evanescent components reduces the problem of solving for the transformed parameters of the field to linear least squares. Solution of the transformation equations provides a complete solution of the field model parameter estimation problem     

Comment on: A general linear-regression analysis applied to the3-parameter Weibull distribution

This paper: (1) examines the results of Yong-Ming Li (see ibid., vol.43, p.255-63, 1994) and points out its errors and shortcomings; and (2) proposes a new graphical method for estimating the parameters of a 3-parameter Weibull distribution     

Determining constant voltage lifetimes for silicon nitride capacitors in a GaAs IC process by a step stress method

The lifetimes of metal–insulator–metal (MIM) capacitors are predicted from voltage step stress data. Capacitor areas of 400, 5625 and 11,250 μm² are investigated. The reliability of capacitors subjected to a single or triple DC pulse prior to a breakdown voltage ramp test is predicted at use conditions (5 V). The method of maximum likelihood is employed in this analysis. With this approach, it is found that the effect of capacitor area on the linear field acceleration parameter, γ, is not statistically significant. Also, it is demonstrated that either a single or a triple DC pulse seriously reduces both the MTTF and γ. Further, the triple DC pulse can change the failure distribution from lognormal to Weibull. The data are also fitted to the reciprocal field model and the predicted failure times under use conditions are too large to be physically reasonable, favoring the linear field model. A graphical method is suggested for discerning between the lognormal and Weibull distributions.This study makes extensive use of statistical methods. One of our goals in this paper is to make the reliability community aware of these powerful techniques so that they may become more widespread.