On the Confidence Limits of Bernoulli Parameter in Any Sequential Case

Let x 1,x 2,… be independent identically distributed (i.i.d.) random variables, in which x n=0 or 1 and the probability of ｛x n=1｝ is p. Here p is unknown. Let τ be any finite stopping time for (x n,n1). For any sequential sample (x 1,x 2,…,x τ ) and γ∈(0,1), we have given an optimal confidence limit of p with confidence level γ . Some related problems are also discussed.

Statistical Properties and Confidence Limits about the Mean Time between the Failures (MTBF) in Failure-free Period Life Test (FFPLT)

On the basis of strict mathematical description about Failure_Free Period Life Test (FFPLT), the statistical properties of the tests and optimal confidence limit of the parameter are discussed in detail and corresponding calculating formulae are found out.

Reliability Analysis of Wind Turbine Gearbox Based on the Optimal Confidence Limit Method

Based on the zero-failure data of 30 Chinese 1. 5 MW wind turbine gearboxes( WTGs),the optimal confidence limit method was developed to predict the reliability and reliability lifetime of WTG. Firstly,Bayesian method and classical probability estimation method were introduced to estimate the value interval of shape parameter considering the engineering practice. Secondly,taking this value interval into the optimal confidence limit method,the reliability and reliability lifetime of WTG could be obtained under different confidence levels. Finally,the results of optimal confidence limit method and Bayesian method were compared. And the comparison results show that the rationality of this estimated range.Meantime, the rule of confidence level selection in the optimal confidence limit method is provided, and the reliability and reliability lifetime prediction of WTG can be acquired.

Confidence limit calculation for antidotal potency ratio derived from lethal dose 50

AIM:To describe confidence interval calculation for antidotal potency ratios using bootstrap method.METHODS:We can easily adapt the nonparametric bootstrap method which was invented by Efron to construct confidence intervals in such situations like this.The bootstrap method is a resampling method in which the bootstrap samples are obtained by resampling from the original sample.RESULTS:The described confidence interval calculation using bootstrap method does not require the sampling distribution antidotal potency ratio.This can serve as a substantial help for toxicologists,who are directed to employ the Dixon up-and-down method with the application of lower number of animals to determine lethal dose 50 values for characterizing the investigated toxic molecules and eventually for characterizing the antidotal protections by the test antidotal systems.CONCLUSION:The described method can serve as a useful tool in various other applications.Simplicity ofthe method makes it easier to do the calculation using most of the programming software packages.

Confidence Interval Estimation of the Correlation in the Presence of Non-Detects

This article deals with correlating two variables that have values that fall below the known limit of detection (LOD) of the measuring device;these values are known as non-detects (NDs). We use simulation to compare several methods for estimating the association between two such variables. The most commonly used method, simple substitution, consists of replacing each ND with some representative value such as LOD/2. Spearman’s correlation, in which all NDs are assumed to be tied at some value just smaller than the LOD, is also used. We evaluate each method under several scenarios, including small to moderate sample size, moderate to large censoring proportions, extreme imbalance in censoring proportions, and non-bivariate normal (BVN) data. In this article, we focus on the coverage probability of 95% confidence intervals obtained using each method. Confidence intervals using a maximum likelihood approach based on the assumption of BVN data have acceptable performance under most scenarios, even with non-BVN data. Intervals based on Spearman’s coefficient also perform well under many conditions. The methods are illustrated using real data taken from the biomarker literature.

小样本加速寿命试验设计与评估方法

针对工程上加速寿命试验仍然存在时间长、试样多的问题,提出一种小样本加速寿命试验设计与评估方法。该方法只需在两个加速应力水平下进行加速寿命试验,即可对产品在正常使用应力水平下高置信度、高可靠度的可靠寿命进行评估。文中首先利用工程上常用的线性加速模型(如阿伦尼斯模型、逆幂律模型和指数模型等)建立了正常使用应力水平下可靠寿命的单侧置信下限与两个加速应力水平下的可靠寿命置信限之间的数学关系式,给出了正常使用应力水平下高置信度、高可靠度的可靠寿命单侧置信下限评估方法。然后分别对指数分布、两参数Weibull分布和对数正态分布的定数截尾加速寿命试验情况进行了详细讨论,给出了相应的正常使用应力水平下高置信度、高可靠度的可靠寿命单侧置信下限计算公式。该方法计算简单,而且对完全数据、不完全数据以及各种分布均适用。大量工程算例和Monte Carlo模拟验证表明,与需要在多个加速应力水平下进行寿命试验的传统方法相比,本文方法不但可以节省大量试样和试验时间,而且理论上更加严谨,精度更高。

固体激光器可靠性评估技术研究

主要介绍了在获得固体激光器的失效数据下,利用AIC、BIC信息量最小准则的分布类型选择方法,确定固体激光器的失效分布类型,再利用已有的数据,对其可靠性进行有效的评估,得到固体激光器MTBF的点估计和不同置信度下的MTBF置信下限,为该产品设计定型和生产决策提供管理信息。

串联系统小样本可靠度直接评估方法

建立了一种串联系统小样本可靠度直接评估方法,能够根据子系统的可靠度置信限直接给出串联系统的可靠度置信限,解决了目前常用的LM法和MML法等传统方法需将信息量较大的连续型分布的子系统试验数据转换为信息量较小的成败型数据,造成试验信息大量丢失,导致可靠度评估精度不高或偏于危险的问题。在此基础上,针对工程上许多成败型试验转计量型试验的机构都是正态分布串联系统的情况,建立了正态分布串联系统小样本可靠度直接评估方法,该方法能够根据子系统的小样本计量型数据对串联系统可靠度进行高精度评估。大量的Monte Carlo模拟验证和实例计算结果表明,传统方法在小样本情况下误差较大,甚至无法满足置信度要求,本文方法则不仅能够满足置信度要求,而且评估精度更高。此外,本文方法对工程上常用的指数分布、 Weibull分布和正态分布等连续分布均适用。

多应力小样本加速寿命试验设计与评估方法

针对目前多应力加速寿命试验需要的组合应力水平多、时间长、费用高的问题,提出一种多应力小样本加速寿命试验设计与评估方法。该方法建立了正常使用应力水平下可靠寿命的单侧置信下限与加速应力水平下的可靠寿命置信限之间的数学关系式,给出了正常使用应力水平下高置信度、高可靠度的可靠寿命单侧置信下限计算公式。文中首先针对工程上最常用的双应力情况,分别建立了无耦合和有耦合的双应力小样本加速寿命试验设计与评估方法,它只需在三个(无耦合)或四个(有耦合)组合应力水平下进行加速寿命试验,即可对产品在正常使用应力水平下高置信度、高可靠度的可靠寿命进行评估。然后针对一般的m种应力情况,建立了基于多应力线性加速模型的小样本加速寿命试验设计与评估方法,它只需在m+1个组合应力水平下进行加速寿命试验,即可求得产品在正常使用应力水平下高置信度、高可靠度的可靠寿命单侧置信下限。该方法计算简单,而且对完全数据、不完全数据以及各种分布均适用。大量工程算例和Monte Carlo模拟验证表明,与传统多应力加速寿命试验方法相比,本文方法不但可以节省大量试样和试验时间,而且理论上更加严谨,精度更高。

Weibull和正态分布不完全数据可靠性评估方法

提出一种两参数Weibull分布和正态分布定数截尾数据可靠性评估方法,建立了其高置信度下的可靠寿命和可靠度单侧置信限计算公式。同时,给出一种能够充分开发利用以往试验数据,并与当前试验数据有机融合进行可靠性评估的方法,由于增大了信息量,从而可以显著提高当前产品可靠性评估精度。在此基础上,还进一步将上述方法推广用于两参数Weibull分布和正态分布的定时截尾数据、无失效数据以及一般不完全数据的可靠性评估,从而实现了不完全数据情况机电产品高精度小样本可靠性评估。与传统的需查表计算的BLUE和BLIE等方法相比,本文方法不但理论上更加严谨,而且评估精度更高,工程计算也更加便捷。

洁净室洁净度分级标准探究

鉴于科技的进步和实验经验,ISO/TC 209出台ISO14644-1:2015《按粒子浓度划出空气洁净度等级》Classification of air cleanliness by particle concentration比ISO14644-1:1999《空气洁净度等级》Classification of air cleanliness技术概念更清晰,使用更方便;实事求是,更赋灵活性:分级表中,所有浓度值都是累积,包括所有大于等于关注粒径(Considered particle size)的粒子的最大允许浓度值(Maximun allowable concentration siae),浓度限值。区域粒子浓度太高,浓度限值不适用;或者由于低浓度时采样和统计方法的局限性区域分级不适用。按统计学技术概念,决定检测洁净度最少采样点数N_(L);N_(L)值与洁净度无直接关联。作为标准应用的补充,超净环境检测需关注超高过滤器滤材最易穿透粒径MPPS,Most penetrating particle size。

三参数威布尔分布的参数估计及置信限计算方法

针对三参数威布尔分布参数估计及置信限计算精度较低问题,提出了相关-回归法的参数估计及置信限计算方法。所提方法充分利用了相关系数法(简称“傅氏法”)对三参数威布尔分布参数估计的便捷性,以及非线性回归法的优良估计效果,将傅氏法和非线性回归法二者优势相结合。为验证其有效性,将相关-回归法应用于某合金强度值数据三参数威布尔分布的参数估计及置信限计算,并将不同样本量情况下的计算结果与傅氏法、极大似然估计与经验公式相结合的方法(简称“MMPDS法”)进行比较。结果表明,相关-回归法具有较高的参数估计和置信限计算精度,当样本量小于100时优势更为显著,能够准确计算威布尔分布的参数及置信限。

基于元器件应力法的微波等离子体质谱仪控制系统可靠性预计

在微波等离子体质谱仪控制系统的设计阶段,元器件应力法是一种有效的获取设计方案可靠性指标的预计方法,然而,元器件应力法直接求和获取同类型元器件总失效率的方法会导致总失效率标准差的线性上升,给预计结果带来不确定性。本文根据总失效率及其标准差采用基于置信上限的估计方法,使预计结果具有更高的置信水平,最后实现了控制系统的可靠性预计,并根据预计结果提出了优化方案。

M-BAYESIAN CREDIBLE LIMIT METHOD OF PARAMETER AND ITS APPLICATION

This article develops a new method, named M-Bayesian credible limit method, to estimate reliability parameter. In the article, the M-Bayesian credible limit method of failure rate is derived for zero-failure data from products with exponential distribution. Relations between M-Bayesian credible limit and other classical confidence limits are discussed. Finally, the new method is applied to a real zero-failure data set, and as can be seen, it is both efficient and easy to operate.

基于灰色预测理论和最优置信限法的核主泵机械密封可靠性分析

为了解决无失效数据情形下核主泵机械密封的可靠度评估问题,分析了大亚湾核主泵机械密封的运行数据,确定了其可靠度分布;利用MATLAB求取了定时截尾时间,建立了结合灰色预测理论和最优置信限法的可靠度分析模型;预测了无失效数据下核主泵机械密封的可靠度。研究表明:所建模型可以有效评估核主泵机械密封的可靠度,且在同等的置信水平下,形状参数范围已知时计算出的可靠度与真实值之间的相对误差较形状参数未知时降低10%。研究成果对无失效数据下核主泵机械密封的可靠性分析具有指导意义。

优化决策树预测大学生体质健康的模型构建研究

目的:为了方便、快速、高效地预测大学生体质健康状况。方法:按照我国六大行政区划,在全国范围内选取12所高等院校,筛选在校男性大学生共计104530名的体质健康测试数据,基于互信息量与机器学习决策树方法,研究了大学生体质健康状况预测精度。结果:不同特征对于体质健康状况预测贡献度具有明显差异;其中,七特征组合“1000米+引体向上+立定跳远+50米+坐位体前屈+体重+肺活量”对于体质健康状况的预测效果最好,预测精度可达95.0%。与粗略决策树、中等决策树、精细决策树相比,优化决策树对于体质健康状况的预测效果最好,预测精度可达95.1%。对于三种分类规则,最大程度减少偏差分类规则对于体质健康状况预测效果最好;对于不同替代决策分裂类型,关闭、打开、全部搜索状态对于体质健康预测效果未有明显区别。对于贝叶斯、网格搜索、随机搜索三种优化器而言,在各优化器下均有一种超参数组合和其他优化器下的最优超参数预测效果相当超参数组合。结论:优化决策树对于大学生体质健康状况相较于传统决策树有较好的预测效果.

The computation of Buehler confidence limits

In medicine and industry, small sample size often arises owing to the high test cost. Then exact confidence inference is important. Buehler confidence limit is a kind of exact confidence limit for the function of parameters in a model. It can be always defined if the order in sample space is given. But the computing problem is often difficult, especially for the cases with high dimension parameter or with incomplete data. This paper presents an algorithm to compute the Buehler confidence limits by EM algorithm. This is the firsttime usage of EM algorithm on Buehler confidence limits, but the algorithm is often used for maximum likelihood estimate in literatures. Three computation examples are given to illustrate the method.

Confidence limits for the mean of exponential distribution in any time-sequential samples

We present the general results determining confidence limits for the mean of exponential distribution in any time-sequential samples, which are obtained in any sequential life tests with replacement or without replacement. Especially, we give the best lower confidence limits in the case of no failure data.

Standardized Distance from the Mean to the Median as a Measure of Skewness

The normal distribution, which has a symmetric and middle-tailed profile, is one of the most important distributions in probability theory, parametric inference, and description of quantitative variables. However, there are many non-normal distributions and knowledge of a non-zero bias allows their identification and decision making regarding the use of techniques and corrections. Pearson’s skewness coefficient defined as the standardized signed distance from the arithmetic mean to the median is very simple to calculate and clear to interpret from the normal distribution model, making it an excellent measure to evaluate this assumption, complemented with the visual inspection by means of a histogram and a box-and-whisker plot. From its variant without tripling the numerator or Yule’s skewness coefficient, the objective of this methodological article is to facilitate the use of this latter measure, presenting how to obtain asymptotic and bootstrap confidence intervals for its interpretation. Not only are the formulas shown, but they are applied with an example using R program. A general rule of interpretation of ∓0.1 has been suggested, but this can only become relevant when contextualized in relation to sample size and a measure of skewness with a population or parametric value of zero. For this purpose, intervals with confidence levels of 90%, 95% and 99% were estimated with 10,000 draws at random with replacement from 57 normally distributed samples-population with different sample sizes. The article closes with suggestions for the use of this measure of skewness.

基于等级置信度的灾后初期多阶段时限派遣模型

大规模地震灾害发生后,快速有效的实现救援队伍的合理调配是应急救援工作开展的前提和基础,同时也是减少受灾点人员伤亡和财产损失的重要保障。针对震后初期应急救援队伍派遣问题,考虑到应急救援过程中的动态连续性、应急时限性以及震后初期受灾及救援信息的未知不确定性,本文引入ER理论构建震后多阶段时限应急救援派遣模型,根据受灾点的初始受灾信息,通过扩展证据推理的权重维度来构建救援队伍针对于受灾点的效率矩阵;在此基础上,以救援时间约束构建各阶段救援子方案,考虑相邻阶段子方案间的动态可行性,以整个救援过程救援效率最大化为目标建立多阶段动态时限优化模型,并针对模型特点给出了求解算法。最后,通过算例确定了求解过程及最佳派遣方案,由此验证了模型及算法的可行性和有效性。下一步将对救援力量不足情况下考虑救援优先等级的连续动态指派问题进行研究。