Electrical surface resistivity of conductive polymers - A non-Gaussian approach for determination of confidence intervals

Polyanilines doped with different acids (HCl, H₂SO₄ and dodecylbenzenesulfonic acid, DBSA) were prepared and their surface electrical conductivities were characterized in a four-probe device, connected to a real-time data acquisition board. Collected data were synchronized and conductivity calculations were performed. The conductive behavior of the polyanilines was investigated along the electrification time. This allowed for introduction of a non-Gaussian technique for determination of the confidence intervals of surface resistivity data. It is shown that the distribution of experimental surface resistivity data does not follow a normal probability distribution function (PDF). Thus, ordinary assumptions related to normal distribution of the experimental errors are wrong and must be corrected for proper determination of the confidence limits of measured resistivity values. It is shown here that confidence limits of resistivity values are asymmetrical and that distribution of experimental values can follow multimodal distributions.     

A new linear ordering of fuzzy numbers on subsets of {{\mathcal F}({\pmb{\mathbb{R}}}})

We introduce a novel linear order on every family of fuzzy numbers which satisfies the assumption that their modal values must be all different and must form a compact subset of . A distinct new feature is that our linear determined procedure employs the corresponding order of a class interval associated with a confidence measure which seems intuitively anticipated. It is worthy noting that although we start from an entirely different rationale, we introduce a fuzzy ordering which initially coincides with the one established earlier by Ramik and Rimanek. However, this fuzzy ordering does not apply when the supports of the fuzzy numbers overlap. In order to cover such cases we extent this initial fuzzy ordering to the “extended fuzzy order” (XFO). This new XFO method includes a possibility and a necessity measure which are compared with the widely accepted PD and NSD indices of D. Dubois and H. Prade. The comparison shows that our possibility and necessity measures comply better with our intuition.     

第三讲:Weibull分布和对数正态分布情形的可靠性评定

对于产品寿命服从Weibull分布或对数正态分布的情形,针对几种不同类型的数据(例如随机截尾,定数截尾情形出现的数据),分别给出了可靠性参数(可靠度、可靠寿命)的点估计或置信下限。特别是在定时截尾出现零失效情形,给出了可靠性参数的置信下限的计算公式。     

参数法和非参数法估计组合样中被测组分含量的置信区间

本文以散装生铁块的随机样本分析结果为基础,应用Ｍｏｎｔｅ Ｃａｒｌｏ模拟法考察了组合样本中Ｓｉ、Ｍｎ,Ｃ,Ｓ,Ｐ含量（或份样平均值）的分布情况,研究了组分含量的置信区间,对参数法和非参数法的结果进行了比较。结果表明,对近似符合正态分布的原始总体或当组合样中的份样数目较多时,两种方法所估计的置信区间相近。但对偏离正态分布（或ｔ－分布）的总体且组合样中的份样数目较少时,非参数法较参数法的结果更符合实际     

非线性随机效应模型的置信域

本文对非线性随机效应模型,建立了微分几何框架,推广了Bates＆Wates关于非线性模型几何结构．在吡基础上,我们导出了关于固定效应参数和子集参数的置信域的曲率表示,这些结果是BatesandWates(1980),Hamilton(1986)与Wei(1994)等的推广．     

数据变换参数的渐近置信域的曲率表示

该文首次用几何方法研究回归模型中数据变换参数及其子集参数的渐近置信域问题．由于文中讨论的是一般的数据变换多参数的渐近置信域的曲率表示，从而有关结论适用于各种数据变换如著名的Box-Cox变换、带有漂移参数的幂变换等变换中变换参数的渐近置信域的曲率表示．     

Fixed-width confidence intervals for contrasts in the means

The sequential procedure developed by Bhargava and Srivastava (1973, J. Roy. Statist. Soc. Ser. B, 35, 147–152) to construct fixed-width confidence intervals for contrasts in the means is further analyzed. Second-order approximations for the first two moments of the stopping time and the coverage probability associated with the sequential procedure, are obtained. A lower bound for the number of additional observations after stopping is derived, which ensures the mxact probability of coverage. Moreover, two-stage, three-stage and modified sequential procedures are proposed for the same estimation problem. Relative advantages and disadvantages of these sampling schemes are discussed and their properties are studied.     

Statistical validation of classification and calibration models using bootstrapped Latin partitions

Unbiased evaluation of classification and calibration methods is important, especially as these methods are applied to increasingly complex data sets that are under-determined. Precision bounds, such as confidence intervals, are required for interpreting any experimental result. Using bootstrapped Latin partitions to evaluate classification and calibration models, bounds on the average predictions were obtained. These bounds characterize sources of variation attributed to building the model and the composition of the training set with respect to the test set. Furthermore, precision bounds on the average of the model-variable loadings allow the significance of characteristic features to be estimated. The procedure for bootstrapped Latin partitions is given and demonstrated with synthetic data sets for classification using linear discriminant analysis and fuzzy rule-building expert systems, and for calibration using partial least squares regression with one and three properties. All analyses were implemented on a personal computer with the longest evaluation requiring 6-h processing time. Analysis of variance and matched sample t-tests were also used to demonstrate the statistical power of these tests.     

Inner and outer fuzzy approximations of confidence intervals

We extend the notion of confidence region to fuzzy data, by defining a pair of fuzzy inner and outer confidence regions. We show the connection with previous proposals, as well as with recent studies on hypothesis testing with low quality data.     

关于MIL—HDBK—781中的保证试验

美国军用标准 MIL— H DBK— 781中的保证试验以其所需的试验时间短而引起可靠性工程界的广泛关注。本文指出这种试验方案存在不合理之处 ,并提出了避免不合理因素的修正方案 ,还从贝叶斯统计角度论证了这种修正方案是有道理的 ,值得实际工作中采用。