对数正态分布场合恒加试验的数据分析与容忍限

本文在寿命分布为对数正态分布场合,对恒定应力加速寿命试验的数据分析进行了讨论。利用加速应力水平下的寿命数据给出了正常工作应力水平下产品寿命的容忍限,并以一数值例加以说明。     

几何分布产品全样本场合步进应力加速寿命试验TFR模型下的统计分析

讨论了几何分布产品在步进应力加速试验TFR模型下寿命分布.给出了其寿命分布函数步进形式,在全样本场合利用极大似然估计方法和矩估计方法求出了未知参数的点估计,最后利用计算机模拟说明本文方法的可行性.     

几何分布截尾样本场合步进应力加速寿命试验TFR模型下的统计分析

讨论了几何分布产品在步进应力加速试验TFR模型下寿命分布.给出了其寿命分布函数步进形式,在截尾样本场合利用极大似然估计方法和拟矩估计方法求出了未知参数的点估计,最后利用计算机模拟考察了说明本文方法的可行性.     

幂函数模型下恒加寿命试验的非参数贝叶斯分析

线性加速模型常用于恒定应力加速寿命试验的统计分析,这与实际不完全相符.本文建立幂函数加速模型,给出了不同恒定加速应力水平间寿命分位数的关系,利用最小二乘法估计了加速模型的参数及特征标系数向量,从而实现不同应力水平间寿命数据的相互转换.采用Dirichlet过程先验,分别在完全数据情形和截尾数据情形下,得到可靠度函数的后验分布与非参数贝叶斯估计,并证明了后验估计的一致性.最后,通过一个金属氧化物半导体电容寿命实例说明了所建模型的效果.     

极值Ⅰ型分析步加应力寿命试验统计分布

本文在极值 型分布场合 ,非除形状参数与加速应力无关的限制 ,进行步加应力寿命试验统计分析 ,给出了正常应力水平寿命分布的参数及变异系数估计 .     

Weibull分布下多组序进应力加速寿命试验的统计分析

给出了多组序进应力加速寿命试验下指数分布的极大似然估计的存在和唯一的一个充要条件;模拟比较了一组与二组序进应力加速寿命试验下有关参数估计的差异:对Weibull分布给出了有关参数的联合置信域.     

Weibull分布步进应力加速寿命试验的Bayes估计

本文研究了定时和定数截尾情形CE模型下Weibull分布场合步进应力加速寿命试验的Bayes估计.利用加速系数和加速方程将各种加速应力水平下的尺度参数换算为正常应力水平下的尺度参数,从而获得含正常应力下尺度参数的似然函数.在参数先验的选取时,尺度参数和加速系数分别取共轭先验和无信息先验,当形状参数m<1和m>1时分别取Beta分布和Gamma分布作为其先验.在平方损失下,利用Gibbs抽样和切片抽样给出了该模型参数的Bayes估计.最后,通过Monte Carlo模拟表明该Bayes估计是有效的.     

固体钽电介电容器序进应力加速寿命试验

一、引言固体钽电解电容器是一种高可靠产品,在正常工作条件下进行寿命试验常常不会发生失效,即使使用恒定应力加速寿命试验(恒加试验)也需要较长时间,为此需要探索新的加速寿命试验的方法。序进应力加速寿命试验(序加试验)是指所施加的应力水平随时间增长的一种加速试验,这种试验不仅能克服恒加试验中的上述缺点,且可大量减少试验样品,缩短试验时间,但使用序加试验会遇到二大困难:一是需要有专门设备,二是要有好的统计分析方法。1987年LinZhengning和Fei Heliang对寿命分布为威布尔分布,加速模型为逆幂律,应力水平增长     

Weibull分布恒定应力加速寿命试验的Bayes估计

对定时和定数截尾样本情形CE模型下Weibull分布场合恒定应力加速寿命试验进行了Bayes统计分析,利用Laplace方法给出了该模型的近似Bayes估计.最后通过模拟实例表明该Bayes估计是有效的.     

极值Ⅰ型分析步加应力寿命试验统计分布

本在极值Ⅰ型分布场合,非除形状参数与加速应力无关的限制,进行步加应力寿命试验统计分析,给出了正常应力水平寿命分布的参数及变异系数估计。     

混合加速寿命试验模型及其统计分析

本文结合序进应力加速寿命试验和恒定应力加速寿命试验提出了一种混合加速寿命试验,讨论了这种加速寿命试验的模型及其在寿命分布为指数分布和对数正态分布时的参数估计,导出了参数的最大的似然估计。     

Optimal Robust Design of Step Stress Accelerated Life Test Scheme under Weibull Distribution

The traditional accelerated life test scheme is necessary to give the rough values of some model parameters in advance, but the influence of fluctuation on the stability of test scheme is irregulared. Based on the prior life test information, this paper aims to minimize the mean and variance of asymptotic variance of $p$-quantile life estimate under normal test stress level, using maximum likelihood estimation theory and Nelson cumulative failure principle, the optimal robust design mathematical model of step stress accelerated life test scheme with uncertainty parameters under Weibull distribution is established. The results of optimal robust design of step stress accelerated life test scheme for electrical connectors show that: comparing with the optimal design of step stress test scheme in the literature, the optimal robust design scheme is not sensitive to the uncertainty of model parameters when the asymptotic variance of median life estimate is basically the same; Comparing with the optimal design of constant accelerated life test scheme, when the statistical accuracy of test data is basically the same, the number of samples required can be reduced by 1/5, and the test time can be reduced by about 1/4.     

定数截尾恒定应力加速寿命试验的最优设计

本文讨论了在指数分布下K个应力情况满足条件（3．3）的恒加试验，并给出它的最优设计。     

Statistical analysis of progressive stress accelerated life test for the product of two-parameter Laplace BS fatigue life distribution under inverse power law model

Based on the product of two-parameter Laplace Birnbaum-Saunders fatigue life distribution, its failure distribution mode is theoretically derived under the progressive stress accelerated life test with inverse power law model, and then three-parameter generalized Laplace Birnbaum-Saunders fatigue life distribution is introduced. The basic properties of three-parameter generalized Laplace Birnbaum-Saunders fatigue life distribution are analyzed, and the image characteristics of its density function, failure rate function and average failure rate function are investigated. Meanwhile, the point estimate method is given for three parameters, and then the point estimates of parameters are obtained for the product of two-parameter Laplace Birnbaum-Saunders fatigue life distribution under the progressive stress accelerated life test with inverse power law model. In addition, the practical example and simulation examples are illustrated to show the feasibility of the proposed method.     

一种新的恒加试验下双参数指数型产品的可靠性分析

针对双参数指数型产品,在具有二项移走(即在每个观测时刻产品的移走数服从二项分布)的分组寿命试验下,研究了分组时刻的确定方法,推导出门限参数、寿命参数和移走概率的极大似然估计。进而,讨论了双参数指数型产品在具有二项移走的恒加寿命分组试验下的可靠性分析问题。利用加速寿命方程,给出了双参数指数型产品的可靠性估计。最后给出随机模拟例子验证了结论的正确性。     

Diagnostics in Birnbaum–Saunders accelerated life models with an application to fatigue data

In industrial statistics, there is great interest in predicting with precision lifetimes of specimens that operate under stress. For example, a bad estimation of the lower percentiles of a life distribution can produce significant monetary losses to organizations due to an excessive amount of warranty claims. The Birnbaum–Saunders distribution is useful for modeling lifetime data. This is because such a distribution allows us to relate the total time until the failure occurs to some type of cumulative damage produced by stress. In this paper, we propose a methodology for detecting influence of atypical data in accelerated life models on the basis of the Birnbaum–Saunders distribution. The methodology developed in this study should be considered in the design of structures and in the prediction of warranty claims. We conclude this work with an application of the proposed methodology on the basis of real fatigue life data, which illustrates its importance in a warranty claim problem. Copyright © 2012 John Wiley & Sons, Ltd.     

Weibull分布基于恒加试验的参数估计

讨论了Weibull分布场合恒加寿命试验的参数估计,在文[1]对参数估计改进的基础上作了进一步改进,从而使改进后的参数估计更优.     

Optimum step-stress partially accelerated life tests for the truncated logistic distribution with censoring

This paper deals with the optimal designing of step-stress partially accelerated life tests (PALTs) in which items are run at both accelerated and use conditions under censoring. It is assumed that the lifetime of the items follow truncated logistic distribution truncated at point zero. Truncated distributions arise when sample selection is not possible in some sub-region of the sample space. The logistic distribution is considered inappropriate for modeling lifetime data because left hand side of its distribution extends to negative infinity, and this could conceivably result in modeling negative times-to-failure. This has necessitated the use of truncated logistic distribution truncated at point zero for modeling lifetime data. Unlike the widely studied exponential, Weibull and lognormal life distributions, the failure rate of truncated logistic distribution is increasing and more realistically bounded below and above by non-zero finite quantity. The optimal change-time for the step PALT is determined by minimizing either the generalized asymptotic variance of maximum likelihood estimates (MLEs) of the acceleration factor and the hazard rate at use condition or the asymptotic variance of MLE of the acceleration factor. Inferential procedure involving model parameters and acceleration factor are studied. Sensitivity analysis is also performed.     

Optimum ramp-stress accelerated life test for m identical repairable systems

This paper proposes optimum ramp accelerated life test (ALT) of m identical repairable systems using non-homogeneous power law process (PLP) under failure truncated case. An ALT with linearly increasing stress is a ramp test. In particular, a ramp test with two different linearly increasing stresses is a simple ramp test. The optimum ramp test with different stress rates is formulated by determining the proportions of test systems allocated to each stress rate using D-optimality criterion. D-optimality criterion minimizes the reciprocal of the determinant of the Fisher information matrix of the model parameters. The method developed is illustrated using two stress rates and three stress rates. It has been found that it takes much longer to obtain same estimated expected no. of failures at baseline condition than at stress levels.     

A NEW WAY TO ESTIMATE THE PARAMETERS IN THE PROGRESSIVE STRESS ACCELERATED LIFE TESTING

Among the three types of accelerated life testing, that is, the constant stress accelerated life testing, the step stress accelerated life testing, and the progressive stress accelerated life testing, the last one is the most effective and economical way to get the failure times of products in a short period of time. In this artiele a deficiency inthe classical approach is pointed out and a new method for the statisticul analysis of lifedata, especially for electronic products, under progressive stress (voltage) V(t)=Kt is given. Using the Bayesian method, for certain choices of the prior distribution, several forms of estimators of the parameters in the noraml stress We|bull distribution and the htverse power law model are derived. In particular, when the new shape parameter computers. The formulations are given for the general case and are illustrated for a special sitnpio case. comparison with the classical approach using pseudorandom dataas well as real data on solid tantatum electrolytic capacitors shows that the proposed method is better and more effective.