应用威布尔过程模型统计分析中的几个问题

对威布尔过程应用中的若干问题作了进一步探讨:如威布尔过程与威布尔分布;具有切断的故障数据处理;威布尔过程的拟合优度检验;可修系统可靠性评估参数;多个同型系统参数一致性检验等.     

基于更新过程的多阶段备件需求模型

正态分布、威布尔分布是常用的备件寿命模型,但是正态分布和威布尔分布的记忆性会导致多阶段需求量预测的相关性.利用更新过程理论,将叠加的更新过程分解和拼接,建立单阶段多项备件需求模型;通过将年龄转移到下个阶段,建立了多阶段不可修备件需求模型;采用加权平均法对多阶段需求模型进行了修正.仿真表明,这种模型能有效预测多阶段需求的波动.     

机械系统可靠性分段寿命试验的统计验证

针对复杂机械系统的使用特点,提出了可靠性分段寿命试验的思想,并运用威布尔过程模型AMASS,对典型车辆故障数据进行统计分析,具体证明了这种思想的合理性.     

威布尔过程模型在机械系统可靠性中的应用

为了研究复杂可修系统的规律,应用威布尔过程模型,得出这样结果,即提出一种定量描述预防性维修质量的方法,并对MTBF进行了分析。可以这样认为,模型参数在实际工作中有很广泛的应用。     

三参数威布尔分布在寿命分析中的参数估计

威布尔分布在可靠性工程中已得到了广泛的应用.在对己给定的寿命试验数据进行可靠性分析与评估中,因简单易解多采用二参数威布尔分布,但参数估计会带来较大误差.对具有以损耗失效为特征的某些机械零部件,采用三参数威布尔分布进行拟合及参数估计,可以得到更高的精度,因而较二参数威布尔分布,更能反映产品可靠性的实际情况.     

基于竞争失效建模的导弹贮存寿命评估方法

为了提高导弹贮存寿命估计的准确性,提出了一种基于退化失效与突发失效竞争的导弹贮存寿命估计方法。基于建模假设,建立导弹竞争失效模型;采用赤池信息准则(AIC)来确定导弹退化过程的最优随机过程模型,进而建立其退化失效模型;采用威布尔分布和比例危险模型,建立基于退化量影响的突发失效模型;采用极大似然估计算法,求解模型未知参数。结合实例分析,验证了所建模型的正确性和优势。     

某新型榴弹引信加速寿命试验设计

通过对影响某新型榴弹引信长储失效的主要环境因素（温度和湿度）分析,得出其寿命服从威布尔分布,双环境应力下满足阿伦尼斯模型。用恒定应力加速寿命试验方法计算出双环境应力下威布尔分布的过渡参数、形状参数、尺寸参数等值,从而估算出某新型榴弹引信长储失效规律。     

基于威布尔过程模型的坦克部署期可靠性研究

通过对某新研坦克部署期故障情况进行具体而全面的统计分析,并采用基于随机点过程的可修系统理论中的威布尔过程模型(AMSAA模型),得出该型坦克部署期的可靠性特点与规律,对于研究新装备可靠性规律和提高新装备的部署保障水平,具有重要的借鉴作用.     

基于贝叶斯模型的装备剩余寿命预测研究

为了解决武器装备日益复杂及维修工作日趋繁重的问题,运用贝叶斯模型预测装备修理后的剩余寿命,为合理安排其修理计划提供依据。替代传统的指数分布,用威布尔分布描述系统寿命特征,并运用极大似然方法和贝叶斯方法估计威布尔分布的两个未知参数,给出其置信区间。在此基础上,对先验样本和后验样本两种不同情况,分别运用贝叶斯模型预测装备修理后的剩余寿命,并给出实例。结果表明了该方法的有效性。     

基于年龄更换策略的威布尔分布备件需求计算方法

备件需求量预测在装备保障工作中发挥着重要作用。预防性维修可以消除装备潜在的故障或避免装备发生故障后所导致的严重后果,从而使装备始终处于期望状态。预防性维修策略下备件需求量建模能够以可预见的可靠性数据为基础进行,其关键问题是最佳更换间隔时间的确定。针对威布尔分布装备备件,采用年龄更换策略,确定最佳更换间隔时间,并在此基础上导出威布尔型备件需求计算模型,为备件需求量的预测提供了一种简单有效的方法。     

Nonparametric bayesian lifetime data analysis using dirichlet process lognormal mixture model

We propose a nonparametric Bayesian lifetime data analysis method using the Dirichlet process mixture model with a lognormal kernel. A simulation‐based algorithm that implements the Gibbs sampling is developed to fit the Dirichlet process lognormal mixture (DPLNM) model using rightly censored failure time data. Five examples are used to illustrate the proposed method, and the DPLNM model is compared to the Dirichlet process Weibull mixture (DPWM) model. Results indicate that the DPLNM model is capable of estimating different lifetime distributions. The DPLNM model outperforms the DPWM model in all the examples, and the DPLNM model shows promising potential to be applied to analyze failure time data when an appropriate parametric model for the data cannot be specified. © 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013     

一种新的Weibull分布恒定应力加速寿命试验分析方法

分析了Weibull分布恒定应力加速寿命试验常用的二步分析方法存在的不足 ,建立了一种新的构造数据分析方法。考虑到分布参数的相关性 ,该方法引入了Weibull分布特征寿命参数的二次估计 ,在模型拟合优度上高于原来的二步分析方法 ,使分析精度得到了改善。同时 ,该方法避免了原来二步分析方法的查表过程 ,便于软件实现和工程实际应用。     

Heuristic modeling of supply availabilities in large networks

The objective of this article is to describe heuristic solutions to the problem of modeling inventories at each node of a large network in the context of a computer simulation model of that network. The heuristic solutions are compared with the mathematical solution which is too unwieldy for use in a simulation model. The Weibull cumulative distribution is used as an approximation for the heuristic models. We question whether the good performance of the Weibull is coincidence or perhaps mathematically justifiable.     

Power series expansions for the distribution and mean value function of a geometric process with Weibull interarrival times

The geometric process is considered when the distribution of the first interarrival time is assumed to be Weibull. Its one‐dimensional probability distribution is derived as a power series expansion of the convolution of the Weibull distributions. Further, the mean value function is expanded into a power series using an integral equation. © 2014 Wiley Periodicals, Inc. Naval Research Logistics, 61: 599–603, 2014     

考虑外场差异的步进加速寿命数据可靠性评估方法

针对寿命服从双参数Weibull分布的机电产品,进行单应力、定时转换的步进加速寿命试验,研究加速寿命试验数据下的可靠性评估问题。考虑到外场多应力环境与实验室单一应力环境之间的差异性,构建基于修正系数的分布参数计算模型;开展步进加速寿命试验过程的统计分析,建立各应力下的累计分布函数关系;构建极大似然函数,运用数值迭代法,求解未知参数估计;结合某型机电产品进行仿真方案设计,采用Monte Carlo仿真方法产生样本数据,通过对比分析说明所提出的模型评估精度更高。     

Normal and weibull distributions

Numerous applications of the Weibull distribution in diverse fields of human endeavor are well known today. Nevertheless, it is not uncommon to find applications of the normal distribution in such fields of studies as agriculture, biology, chemistry, engineering, physics, sociology and others. At the present time we have at our disposal many more refined statistical techniques for analyzing the normal rather than the Weibull data. Consequently, it is important for applied statisticians to know if some of their data which can be described by the Weibull distribution can also be described by the normal distribution. The present investigation of the author reveals that the normal distri,bution can be considered to be a good approximation to the Weibull distribution as long as its shape parameter is in the open interval (3.25, 3.61). This fact enables them to perform a refined statistical analysis of their data. Conversely, they can now easily compute the desired normal cumulative probabilities from the Weibull distribution function, which would be especially helpful for those standard normal deviates whose cumulative probabilities cannot be read from the available tables of normal cumulative probability. In a similar situation they can also use the Weibull distribution to obtain an approximation to any desired normal deviate for a given normal probability which may be better than those obtained by the linear interpolation method.     

FRC/钢嵌入式T型接头疲劳试验及可靠性分析

为了研究FRC/钢嵌入式T型连接接头疲劳特性,采用真空成型工艺(VARTM)及缝合技术制作T型连接接头,利用Letry疲劳试验机对接头开展拉-拉疲劳试验。根据疲劳试验结果,研究了T型接头在拉-拉疲劳载荷作用下初始损伤特性及损伤演变规律;基于两参数Weibull分布模型,开展T型连接接头疲劳可靠性分析,拟合得到接头在不同应力水平下的疲劳寿命分布规律,给出接头在不同应力水平下疲劳可靠度函数,以及接头在指定可靠度下应力/寿命双对数曲线关系式(R-lnS-lnN曲线)。结果表明,ln ln[1/R(N)]与lnN呈现良好的线性关系,T型接头疲劳寿命服从Weibull分布;疲劳寿命可靠度双对数方程建立了可靠度、疲劳寿命以及疲劳应力的关系,可指导接头疲劳可靠性设计和工程应用。     

Mean hazard rate and its application to the normal approximation of the weibull distribution

It is important for applied statisticians to know if data that can be described by the Weibull distribution can also be described by the normal distribution. Some investigations have been published on this subject. In this article, we review the results in papers related to the above problem. Next, we define the mean hazard rate. We then investigate the properties of the mean hazard rate for the Weibull distribution and the normal distribution, respectively. Finally, we discuss the method of approximating the normal distribution by the Weibull distribution using the mean hazard rate.     

Bounds on the availability function

This paper gives bounds on the availability function for an alternating renewal process with exponential failure and general repair times. A bound on the error is also given. Several of the bounds with greatest practical consequence are worked out and illustrated. Repair distributions for which a lower bound on availability is easily computed are gamma (integer shape parameter), log normal, and Weibull. Finally, some simulation results for log normal repair versus gamma repair are given.