Bayesian analysis for step‐stress accelerated life testing under progressive interval censoring

A step‐stress accelerated life testing model is considered for progressive type‐I censored experiments when the tested items are not monitored continuously but inspected at prespecified time points, producing thus grouped data. The underlying lifetime distributions belong to a general scale family of distributions. The points of stress‐level change are simultaneously inspection points as well while there is the option of assigning additional inspection points in between the stress‐level change points. In a Bayesian framework, the posterior distributions of the parameters of the model are derived for characteristic choices of prior distributions, as conjugate‐like and normal priors; vague or noninformative. The developed approach is illustrated on a simulated example and on a real data set, both known from the literature. The results are compared to previous analyses; frequentist or Bayes.     

恒应力加速寿命试验中无失效数据的处理

对恒应力加速寿命试验中W eibu ll分布无失效数据,合理地构造了失效概率的两种先验分布,并结合现场试验数据,利用极大似然方法和Bayes方法对该组无失效数据进行了处理,所得结果表明本文给出的方法是正确可行的.     

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.     

恒定应力加速寿命试验的非参数统计分析

研究了恒定应力加速寿命试验(简称恒加试验)的非参数统计方法，给出了恒加试验的矩估计和最小二乘估计，并研究了它们的优良性。     

A new estimate of the parameters in linear mixed models

In linear mixed models, there are two kinds of unknown parameters: one is the fixed effect, the other is the variance component. In this paper, new estimates of these parameters, called the spectral decomposition estimates, are proposed, Some important statistical properties of the new estimates are established, in particular the linearity of the estimates of the fixed effects with many statistical optimalities. A new method is applied to two important models which are used in economics, finance, and mechanical fields. All estimates obtained have good statistical and practical meaning.     

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.     

Weibull 分布基于恒加试验尺度参数估计

对 Weibull 分布场合恒加寿命试验的参数估计进行了讨论,在现有参数估计的基础上作了进一步改进,从而使改进后的参数估计更优.     

Inference of constant-stress accelerated life test for a truncated distribution under progressive censoring

Accelerated life test (ALT) provides a feasible and efficient way to obtain information quickly on lifetime of products by testing them at higher-than-use operating conditions. In this paper, the lifetime of products is assumed to follow a lower truncated family of distributions, when both resilience and threshold parameters are nonconstant and affected by operating stress, inference is discussed for simple constant-stress ALT under progressive Type-II censoring. Point estimates for unknown parameters are presented based on maximum likelihood and pivotal quantities based estimation methods. Meanwhile, generalized, asymptotic and bootstrap confidence intervals for the parameters of interest are constructed as well. Simulation studies and illustrative examples are carried out to investigate the performance of the proposed methods.     

A new approach to determine tensile stress states from the parameters of longitudinal waves

In this paper, an experiment is proposed to select longitudinal ultrasonic waves as the physical agent in the detection of tensile stress states. The delay time in the back-wall echo travel presents a relation with the strain usually considered in tensile tests. From an algebraic manipulation procedure, this time interval is the fundamental quantity in the proposed method. The theoretical development initiates from the sound velocity in the unstressed state and employs a perturbative method to quantify the changes in the time-of-flight due to both the dimension modifications and the acoustoelastic effect. In addition to Armco iron and rail steel, this study applies its mathematical model to metal-matrix composites of aluminium and SiC particles at different temperatures. The scheme requires one transducer to perform the corresponding measurements to evaluate if a metallic material is under tensile stress.     

Transmission of macroeconomic shocks to risk parameters: Their uses in stress testing

In this paper, we are interested in evaluating the resilience of financial portfolios under extreme economic conditions. Therefore, we use empirical measures to characterize the transmission process of macroeconomic shocks to risk parameters. We propose the use of an extensive family of models, called General Transfer Function Models, which condense well the characteristics of the transmission described by the impact measures. The procedure for estimating the parameters of these models is described employing the Bayesian approach and using the prior information provided by the impact measures. In addition, we illustrate the use of the estimated models from the credit risk data of a portfolio.     

Bayesian accelerated life testing under competing log-location-scale family of causes of failure

This article provides Bayesian analyses of data arising from multi-stress accelerated life testing of series systems. The component log-lifetimes are assumed to independently belong to some log-concave location-scale family of distributions. The location parameters are assumed to depend on the stress variables through a linear stress translation function. Bayesian analyses and associated predictive inference of reliability characteristics at usage stresses are performed using Gibbs sampling from the joint posterior. The developed methodology is numerically illustrated by analyzing a real data set through Bayesian model averaging of the two popular cases of Weibull and log-normal, with the later getting a special focus in this article as a slightly easier example of the log-location-scale family. A detailed simulation study is also carried out to compare the performance of various Bayesian point estimators for the log-normal case.     

A new estimate for the topological degree

We establish a new estimate for the topological degree of continuous maps from the sphere ${\mathbb{S}}^N$ into itself, which answers a question raised in Bourgain, Brezis, and Mironescu [Commun. Pure Appl. Math. 58 (2005) 529–551] and extends some of the results proved there, as well as in recent work by these authors (Lifting, degree, and distributional Jacobian revisited, http://ann.jussieu.fr/publications). To cite this article: J. Bourgain et al., C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

A new way to evaluate the Probability and Fresnel integrals

In this article, we show how Laplace Transform may be used to evaluate variety of nontrivial improper integrals, including Probability and Fresnel integrals. The algorithm we have developed here to evaluate Probability, Fresnel and other similar integrals seems to be new. This method transforms the evaluation of certain improper integrals into evaluation of improper integrals of the corresponding Laplace transform, which in many cases are much easier.     

Estimating the parameters of Weibull distribution and the acceleration factor from hybrid partially accelerated life test

This article considers the estimation of parameters of Weibull distribution based on hybrid censored data. The parameters are estimated by the maximum likelihood method under step-stress partially accelerated test model. The maximum likelihood estimates (MLEs) of the unknown parameters are obtained by Newton–Raphson algorithm. Also, the approximate Fisher information matrix is obtained for constructing asymptotic confidence bounds for the model parameters. The biases and mean square errors of the maximum likelihood estimators are computed to assess their performances through a Monte Carlo simulation study.     

A stochastic programming model to find optimal sample sizes to estimate unknown parameters in an LP

An LP is considered where the technology coefficients are unknown and random samples are taken to estimate them. A stochastic programming problem is formulated to find the optimal sample sizes where it is required that a confidence interval should cover the unknown deterministic optimum value by a given probability and the cost of sampling be minimum.     

关于Smarandache函数的一个新的下界估计

利用初等方法研究Smarandache函数在某些特殊值上的下界估计,给出了Smarandache函数在某些特殊值上的一个较强的下界估计,证明了估计式S(2p+1)≥6p+1,其中P≥7为任意素数.     

A new approach to the linearity of testing planarity of graphs

In testing planarity of graphs, there are many criteria. The earliest one as known is the Kuratowski's theorem, then Whitney's, Maclane's, and so forth. Since the early sixties, people have begun researches on algorithms. Up to 1974, Hopcroft and Tarjan found an algorithm with a computing time being a linear function of the order of a graph. This is the linearity concerned here.This paper presents a new approach to the linearity by means of transforming the problem of testing planarity of a graphG into that of finding a spanning tree on another graphH, called an auxiliary graph ofG, with the order ofH being a linear function of that ofG. And moreover, we can also make the size ofH be a linear function of that ofG. The whole procedure is based on the building up of a theory of linear equations onGF (2) related toG.This was a report invited by RUTCOR, The State University of New Jersey, Rutgers, U. S. A. in 1984. And, the main part of this paper was completed during the author's stay at the Department of C & O, University of Waterloo, Canada.