成败型元件串并联系统及并串联系统可靠性置信下限近似解的讨论

本文讨论由相互独立的成败型元件组成的串并联系统及并串联系统可靠性置信下限的近似解。本文利用系统诸元件的试验数据,在一、二阶矩拟合的原则下将其折合为原系统的伪试验数及伪成功数,然后利用单个成败型元件的可靠性的经典精确置信下限作为原系统可靠性置信下限的近似值。本文推导了伪试验数N及伪成功数S的计算公式,并给出了计算实例。     

基于成败型元件试验数据和系统试验数据的串联系统可靠性的置信下限

本文根据成败型元件和系统两者的试验数据来估计串联系统可靠性的置信下限。首先根据元件和系统两者的试验数据,求出系统可靠性的极大似然估计,然后按L-M(Lindstrom-Madden)法给出系统可靠性置信下限的近似值,并提供了数字例子。     

成败型元件可靠性估计及近似置信限

本文基于成败型元件串联系统的成败型试验数据,研究成败型元件可靠性的点估计以及近似置信下限.     

虚拟系统法

本文基于虚拟系统的想法,讨论了设立系统可靠性的置信下限的方法,称为虚拟系统法.该方法克服了Lindstrom和Madden方法的保守性.本文提供的方法的优点是,它具有水平相合性,渐近有效性以及计算的简便.     

成败型并联系统可靠性置信下限的近似解

本文通过大量的模拟计算,对于成败型并联系统可靠性置信下限的四种熟知的近似解法:Madansky法(LR法),AWI法,Maximum Likelihood法(ML法)和AO法进行了分析和比较。据分析比较,认为LR法和AO法是令人满意的。     

可靠性增长试验中一种新的参数估计法

本文在充分利用可靠性增长试验中各阶段试验数据评定现阶段可靠性指标的基础上对成败型和指数寿命型试验下所得的抽样数据,采用一种新的样本空间排序法─字典排序法给出了现阶段可靠性的点估计和置信下限．从理论和实例两个方面论证了它比仅利用现阶段数据的经典方法具有一致的优良性,改进了房祥忠等［４］相应研究中的不足．而文中定理２．４、定理３．４的结论不仅与可靠性增长试验的直观背景相吻合,还大大提高了这种新方法的实际可操作性．     

L—M法置信下限的渐近特性

本文讨论了具有两个串联元件的系统,设系统的可靠性为R,讨论了R的L-M法置信下限的渐近特性。还证明了当置信水平1-α≥1/2时,■_(LM)与常用的最优单调置信下限■_0是渐近等价的。     

双参数指数分布的可靠寿命的广义置信下限

基于双参数指数分布定数截尾数据,利用Weerahanandi给出的广义置信区间的概念,建立了可靠寿命的广义置信下限,并从理论上证明了我们给出的广义置信下限是精确的,即基于广义置信下限的区间估计的覆盖率等于要求的置信水平.广义置信下限需要通过数值方法得到,但是计算方法是简单直接的.在小样本情形下,通过对基于广义置信下限的置信区间与Engelhardt-Bain近似置信区间覆盖率的模拟比较,发现广义置信下限更令人满意.     

K型区间删失数据下参数的置信限

基于K型区间删失数据,利用样本空间排序法给出参数优良的置信下限和计算置信下限的递推公式.     

两成败型元件可靠性之差的经典精确最优置信下限

设有可靠性分别为p1和p2的两成败型元件.第i个元件试验N_次,成功S_次(i=1,2).本文利用样本点排序的方法给出了Q=p1-p2的经典的置信下限,并讨论了所得置信下限的精确性及最优性.     

基于分布矩拟合的小子样二项分布参数P的置信下限

基于分布矩拟合的原则,给出小子样二项分布成功率P的置信下限的一种计算方法,通过与经典置信下限及reformualtion方法计算的置信下限进行比较,得出分布矩拟合方法计算的置信下限是合理和可信的.     

Exact likelihood inference based on Type-I and Type-II hybrid censored samples from the exponential distribution

Chen and Bhattacharyya (1988,Comm. Statist. Theory Methods,17, 1857–1870) derived the exact distribution of the maximum likelihood estimator of the mean of an exponential distribution and an exact lower confidence bound for the mean based on a hybrid censored sample. In this paper, an alternative simple form for the distribution is obtained and is shown to be equivalent to that of Chen and Bhattacharyya (1988). Noting that this scheme, which would guarantee the experiment to terminate by a fixed timeT, may result in few failures, we propose a new hybrid censoring scheme which guarantees at least a fixed number of failures in a life testing experiment. The exact distribution of the MLE as well as an exact lower confidence bound for the mean is also obtained for this case. Finally, three examples are presented to illustrate all the results developed here.     

Assessing process capability based on the lower confidence bound of Cpk for asymmetric tolerances

It has been proved that process capability indices provide very efficient measures of the capability of processes from many different perspectives. At the present time, the C_pk index is used more than any other index for measuring process capability. However, most existing research works for capability testing have focused on processes with symmetric tolerances, but not for asymmetric tolerances. A lower confidence bound estimates the minimum process capability, conveying critical information regarding product quality, which is essential to quality assurance. The sample size determination, which provides the sample sizes necessary to achieve a desired lower confidence bound, is directly related to the cost of the data collection plan. This paper provides explicit formulas with efficient algorithms to obtain the lower confidence bounds and sample sizes required for specified precision of the estimation on C_pk for processes with asymmetric tolerances. A Matlab computer program using a binary search method is developed. For the practitioners to use in their in-plant applications, we tabulate lower confidence bounds for some commonly used capability requirement and the sampling accuracy of C_pk for sample sizes determination. A realistic example of forging process is presented to illustrate the applicability of the proposed method.     

基于随机截尾数据的指数型元件串联系统可靠性的置信限

基于元件的随机定时截尾寿命试验数据 ,给出了指数型元件串联系统可靠性的经典精确置信下限 ,给出了数字例 .     

基于样本空间中序关系构造参数置信限方法的一个注记

，证明了存在样本空间中的一种序关系，使得基于这种序关系构造的参数的上（下）置信限是同一置信水平下的一致最精确上（下）置信限．本文还证明了，多参数指数族中一个参数的一致最精确无偏上（下）置信限也能基于样本空间中的一种序关系构造出来。     

基于置信界及信息附加寻找最大耐受剂量的逐步方法

The primary goal of a phase I clinical trial is to find the maximum tolerable dose of a treatment. In this paper, we propose a new stepwise method based on confidence bound and information incorporation to determine the maximum tolerable dose among given dose levels. On the one hand, in order to avoid severe even fatal toxicity to occur and reduce the experimental subjects, the new method is executed from the lowest dose level, and then goes on in a stepwise fashion. On the other hand, in order to improve the accuracy of the recommendation, the final recommendation of the maximum tolerable dose is accomplished through the information incorporation of an additional experimental cohort at the same dose level. Furthermore, empirical simulation results show that the new method has some real advantages in comparison with the modified continual reassessment method.     

对数正态或正态寿命型元件及系统的贮存可靠性的近似置信下限

本文给出了基于一次性检测数据的对数正态或正态寿命型元件及系统的贮存可靠性的近似置信下限的方法，并对得到的近似置信限的精度作了讨论，结果表明精度符合要求。本文还给出了数字例子。     

Consensus formation of two-level opinion dynamics

Opinion dynamics have received significant attention in recent years. This paper proposes a bounded confidence opinion model for a group of agents with two different confidence levels. Each agent in the population is endowed with a confidence interval around her opinion with radius αd or (1-α)d, where α ∈ (0,1/2] represents the differentiation of confidence levels. We analytically derived the critical confidence bound d_c = 1/(4α) for the two-level opinion dynamics on ?. A single opinion cluster is formed with probability 1 above this critical value regardless of the ratio p of agents with high/low confidence. Extensive numerical simulations are performed to illustrate our theoretical results. Noticed is a clear impact of p on the collective behavior: more agents with high confidence lead to harder agreement. It is also experimentally revealed that the sharpness of the threshold d_c increases with α but does not depend on p.     

逆高斯分布变异系数和尺度参数的统计推断研究

构造了逆高斯分布中变异系数的广义枢轴量,给出了一种参数的区间估计方法,并与MOVOER(method of variance of estimates recovery)和Bootstrap方法进行比较;给出了多总体下尺度参数两两差的同时置信区间.模拟结果表明:在中、小样本情况下,所给的广义置信区间其覆盖概率接近置信水平,平均区间长度较短,优于MOVOER方法与Bootstrap方法;对于多总体下尺度参数两两差的同时置信区间,所给出的三种同时置信区间,其覆盖率在置信水平附近,具有良好的频率性质.     

分数填补下两总体分位数差异的经验似然置信区间

设有两个非参数总体,其样本数据不完全,用分数填补法补足缺失数据,得到两总体的"完全"样本数据,在此基础上构造两总体分位数差异的经验似然置信区间.模拟结果显示,分数填补法可以得到更加精确的置信区间.