基于 Weibull 分布的航空装备部件寿命预测研究

针对现代航空装备的 PHM 需求,为提高 Weibull 分布在寿命预测中的精确度,提出了综合运用最小二乘法及平均秩次法对预测模型进行参数估计的方法,在此基础上建立了航空装备部件的寿命预测模型。对某型歼击机上航电系统中15个相同的核心部件进行了实验,分别用近似中位秩公式和平均秩次法处理实验数据,并对二者的拟合效果进行对比分析,结果显示平均秩次法的估计精度较高。寿命预测的结果表明,设备工作到3106．2 h 后可靠度下降到50％以下,与实际维护中平均每3000 h 进行一次检修或更换部件的情况基本相符。     

Weibull分布下基于MAM的白光OLED寿命预测

为了得到白光有机发光二极管(OLED)寿命信息,降低试验成本,开展了三组恒定电流应力加速寿命试验。采用Weibull函数描述其寿命分布,基于图分析法(MAM)和MATLAB绘制的Weibull概率双坐标纸,描点作图并估计形状参数和尺度参数,实现了白光OLED的寿命预测。数值结果表明,白光OLED样品在各加速应力下失效机理保持不变,加速模型满足逆幂定律,精确计算的加速参数使得OLED寿命快速估算成为可能。     

Weibull分布下基于MLE的红外发光二极管寿命预测

为了对红外发光二极管(LED)恒定及步进应力加速寿命试验的数据进行统计分析,应用Weibull分布函数描述了其寿命分布,利用极大似然法(MLE)及其迭代流程图估计出形状参数和尺度参数,通过最小二乘法确定了红外LED加速寿命方程,对红外LED寿命是否符合威布尔分布进行了Kolmogorov-Smirnov检验,并利用自行开发的寿命预测软件计算出平均寿命和中位寿命。数值结果表明,红外LED的寿命服从Weibull分布,加速寿命方程符合逆幂定律,所估计出的红外LED的寿命对生产厂商和用户有很强的指导意义。     

定数截尾Weibull分布下恒定应力加速寿命试验统计分析

设产品寿命服从Weibull分布，尺度参数为η＞0，形状参数为m＞0，在加速应力水平Si下，加速方程为Inηi=a＋bφ（Si）（i=1，2，…，k）本文绘出了定数截尾Weibull分布各应力下形状参数mi的极大似然估计的一种改进迭代算法，利用[1]类似的方法对各应力下所得估计进行修正，后对各应力下mi的估计值进行加权平均得m的近似无偏估计；利用定数截尾Weibull分布尺度参数ηi的极大似然估计，通过Weibull分布与指数分布之间不关系以及指数分布的性质，求得各应力下尺度参数的自然对数Inηi的近似无偏估计，利用Inηi的估计值与加速方程，建立线性模型，利用Gauss－Markov定理得加速方程系数a和b的近似最佳线性无偏估计值．通过模型由此可求出正常应力S0下各种可靠性特征量的估计．模拟结果表明本方法是具有较高的精度，且本方法计算比较简单，在工程上比较适用．     

三参数Weibull分布下基于BRM的LED照明灯寿命预测

为了在短时间内准确获得LED照明灯的寿命信息,以3组恒定加速应力的试验数据为基础,采用三参数Weibull函数描述其寿命分布,基于双线性回归法(BRM)对试验数据进行处理分析,并利用自行开发的寿命预测软件较为精确地得出LED照明灯在正常工作应力下的寿命。数值结果表明,LED照明灯的寿命服从三参数Weibull分布,其加速模型符合Arrhenius方程,精确预测的LED照明灯寿命为工程技术人员关于产品的可靠性设计提供技术参考。     

Weibull分布变差系数的抽样检验

本文给出了二参数Weibull分布变差系数的计量型抽样验收方案、     

恒加试验下LED照明灯的三参数Weibull分布的参数估计

三参数Weibull分布拟合LED照明灯寿命的优势较为明显,但要得到三参数Weibull分布参数较为精确的点估计较为困难。目前常用的参数估计方法有极大似然法、矩估计法、Bayes估计法等,由于其计算的方程复杂,导致软件编程繁琐,不易掌握,而且也不一定能得到参数估计。鉴于此,文章针对恒加试验提出一种简便地求解三参数Weibull分布参数估计的方法,该方法不涉及超越方程的求解问题,软件编程相当简单,且统计思想清晰。通过LED照明灯恒加试验下的几个案例数据说明方法的应用,并与已有的方法做了对比分析。     

继电器的耐久性寿命试验及其寿命分布规律

本文以某一继电器的耐久性寿命试验为例,探索了继电器的寿命分布规律,用最小二乘法按威布尔分布进行了拟合,并进行了假设检验,然后用最好线性无偏估计(BLUE)得出了该继电器寿命特征的估计值。     

新一代天气雷达寿命预测方法

详细阐述了雷达剩余物理寿命、剩余经济寿命和剩余使用寿命3种不同概念及各自在应用中的指导意义。剩余物理寿命和剩余经济寿命分别从技术和经济角度为雷达的退役更新提供参考,而剩余使用寿命则和雷达的故障周期密切相关,能指导雷达的维护维修工作。同时,还从理论上提出了3种不同概念的雷达寿命的预测方法,并对各种方法的难点、存在的问题和改进措施进行了深入的剖析。     

基于Weibull分布2.5D封装热疲劳可靠性评估

针对2.5D立体封装中热膨胀系数及结构尺寸均存在较大差异、极易在热应力作用下产生热疲劳失效的可靠性问题,开展多芯片硅基集成封装互连界面温度循环加速试验,并基于Weibull分布对2.5D封装互连界面热适配性能进行评估分析,实现了2.5D封装可靠性指标的评估和失效率鉴定方案的制定.     

基于威布尔分布的某半导体器件贮存寿命分布规律初探

对有机电致发光二极管（Organic Light-Emitting Diode,OLED）微型显示器件进行90℃、80℃、70℃的高温贮存试验,获得产品的失效数据。基于威布尔分布模型,采用最小二乘法进行参数估计,对失效数据分析,获得OLED微型显示器件失效分布函数。应用经典可靠性理论,计算产品在90℃、80℃、70℃的特征寿命、可靠寿命及平均故障间隔时间（Mean Time Between Failure,MTBF）。采用Arrhenius模型,依据90℃、80℃、70℃的贮存特征寿命,获得常温下产品的贮存特征寿命。分析结果表明,该方法合理、简便、有效,数据结果可以进一步应用到推导产品常温贮存寿命。     

Estimation of Mixed Weibull Parameters in Life Testing

This paper deals with estimating parameters from a mixture of two Weibull distributions. The weighted least-squares method is used to estimate the parameters of the mixed model when data are grouped and censored. Simulation study of the variations of the weighted least-squares estimator has been carried out. A few examples have also been provided. Based on the simulation study, the weighted least-squares estimators are robust with respect to the number of intervals for the grouped data. The estimators of the scale parameters are quite sensitive to the censoring time, but those of the shape parameters are not as sensitive. This method provides a good alternative to the commonly used maximum likelihood estimators which are difficult to obtain and are frequently intractable. The techniques could easily be extended to a mixed model of more than two Weibull distributions and ungrouped and/or uncensored samples.     

Empirical Bayes Estimation in the Weibull Distribution

In part I empirical Bayes estimation procedures are introduced and employed to obtain an estimator for the unknown random scale parameter of a two-parameter Weibull distribution with known shape parameter. In part II, procedures are developed for estimating both the random scale and shape parameters. These estimators use a sequence of maximum likelihood estimates from related reliability experiments to form an empirical estimate of the appropriate unknown prior probability density function. Monte Carlo simulation is used to compare the performance of these estimators with the appropriate maximum likelihood estimator. Algorithms are presented for sequentially obtaining the reduced sample sizes required by the estimators while still providing mean squared error accuracy compatible with the use of the maximum likelihood estimators. In some cases whenever the prior pdf is a member of the Pearson family of distributions, as much as a 60% reduction in total test units is obtained. A numerical example is presented to illustrate the procedures.     

Maximum Likelihood Estimation For The 2-Parameter Weibull Distribution Based On Interval-Data

MLE techniques are presented for estimating time-to-failure distributions from interval-data. Interval-data consist of adjacent inspection times that surround an unknown failure time. Censored interval-data bound the unknown failure time with only a lower time. The 2-parameter Weibull distribution is examined as the failure distribution. Parameter estimates from interval-data and from the midpoints of the intervals are compared for 6 shapes of the Weibull distribution. The results from Monte Carlo simulation runs are used to examine the s-bias and S-variability of the parameter estimates.     

威布尔分布下竞争性故障装备的可靠性分析

利用外场故障数据,对威布尔竞争性故障装备进行了可靠性分析。首先对外场故障数据进行处理和失效模式分析,分别为各部件建立威布尔分布模型,得到其形状参数和尺度参数。进而在竞争性故障下,得到装备的可靠度函数和失效率函数。最后给出了一个陀螺仪算例来说明该分析方法的有效性。研究表明,该分析方法更符合装备的故障规律。     

Estimation of the Parameters of the Weibull Distribution from Multicensored Samples

Monte Carlo simulations are used to investigate the maximum likelihood estimators for the parameters of the Weibull distribution using multicensored samples. For the case of unequal number of items censored, a single situation is considered. When the same number of items are removed at each test, several different estimators are compared for several values of the parameters.     

Simultaneous Estimation of Location and Scale Parameters of the Weibull Distribution

This paper deals with the simultaneous estimation of the location parameter ? and the scale parameter ? of the Weibull distribution when both are unknown and the shape parameter ? is known. The best linear unbiased estimate (BLUE) (?, ?) based on a subset of k optimum ordered observations selected from the whole sample is compared with 1) Ogawa's asymptotically best linear estimate (ABLE) (?*, ?*) based on k ordered observations whose ranks are approximated by an asymptotic optimum selection, and 2) the BLUE based on the ranks in 1). Tables facilitating the computation of (?, ?) based on k = 3, 4 optimum ordered observations are provided.