逐步增加的Ⅱ型截尾下冷贮备串联系统可靠性指标的Bayes估计

在逐步增加的Ⅱ型截尾模型下,研究部件寿命服从双参数指数分布的冷贮备串联系统可靠性指标的Bayes估计。在超参数未知的情形下,分别在平方损失(SE),LINEX损失和熵(General Entropy,GE)损失函数下给出两个参数及可靠性指标的Bayes估计;对于超参数的确定,给出一种新的方法;最后利用随机模拟方法进行比较,并对结果进行了讨论。     

竞争失效场合Weibull产品的可靠性分析

在竞争失效场合下,建立了Weibull产品的具有二项移走的逐步Ⅱ型截尾寿命试验模型.针对一般近似算法在小样本情形下精度较低的问题,以Gamma分布综合产品的先验信息,采用Gibbs抽样建立了参数的Bayes估计.利用Bootstrap方法、Bayes后验分布法分别构造了参数的置信区间.最后,利用随机模拟方法对估计结果进行了比较,结果表明在小样本情形下,Bayes比MLEs估计效果更好.     

基于隐蔽的系统成败型数据的元件可靠性的极大似然估计和区间估计

考虑由３个独立工作的成败型元件组成的串联系统，利用隐蔽的系统寿命试验数据求元件可靠性的极大似然估计和区间估计，给出了数值例子。     

威布尔分布的环保型电子节能灯寿命的极大似然估计

提出了一种利用改进的极大似然估计法对基于威布尔分布的环保型电子节能灯寿命数据进行分析的方法.该方法利用加速寿命实验获取环保型电子节能灯使用寿命的数据,利用统计学的方法和威布尔分布模型,实现高应力下的实验时间的等效折算.采用改进的极大似然估计,有益于对环保型电子节能灯的寿命数据进行分析.     

无信息先验下几种不同Bayes估计的比较

讨论了在二项分布场合关于成功率的不同无信息先验分布下的Bayes估计，并从Bayse风险的角度对它们进行了比较。     

威布尔分布场合下无失效数据的Bayes分析

通过对分布函数进行变换，使变换后的函数成为凹函数，利用凹函数性质给出了各检测时刻失效概率的Bayes估计，进而得到了产品可靠性指标的估计。最后，通过对实际数据进行计算，验证了方法的稳定性。     

无失效数据下失效概率的多层Bayes和E Bayes估计的性质

高可靠性产品的可靠性试验很难获得样品失效的数据,可靠性参数估计涉及无失效数据分析,Bayes方法是处理无失效数据分析的有力方法。多层Bayes参数估计涉及到Beta函数比的积分。利用Gamma函数比不等式,导出Beta函数比不等式及Beta函数比的积分不等式,证明了无失效数据下失效概率的EBayes估计与多层Bayes估计渐近相等,且给出多层Bayes估计值小于EBayes估计值的一个充分条件。     

双参数Rayleigh分布环境因子的经验Bayes估计及应用

本文针对Rayleigh分布位置参数已知的情形,给出了Rayleigh分布环境因子的极大似然估计和经验Bayes估计,并将环境因子的估计结果应用于Rayleigh部件的可靠性评估,给出了该部件可靠度函数与失效率的估计。最后的随机模拟例子表明,经验Bayes估计优于极大似然估计,并且在考虑环境因子的情形下,Rayleigh部件可靠性指标的估计优于未考虑环境因子时的估计。     

一类具有椭球误差的多无线性模型参数的Bayes估计

本文讨论下列线性模型Ｙｍ×ｎ＝βｍ×ｐＸｐ×ｎ＼＋βｍ×ｎ其中ε服从一类特殊的矩阵椭球分布，特征矩阵为。给出了在Σ＞０已知；Ｖ＞０，已知，Σ＝σ２Ｉｎ，σ２＞０未知；Ｖ＞０未知三种情形下参数矩阵β的Ｂａｙｅｓ估计。     

一类单边截断型分布族参数的双侧经验Bayes检验问题

讨论一类单边截断型分布族参数的双侧经验Bayes(EB)的检验问题，构造了参数的EB判决函数，证明它具有渐近最优性，并且获得了收敛速度。     

Progressively Censored Reliability Sampling Plans for the Weibull Distribution

This article presents progressively censored variable sampling plans for the Weibull distribution. Approximate maximum likelihood estimators are developed for estimating the parameters of interest. In the construction of sampling plans, asymptotic distribution theory is used to determine the sample size and the acceptance constant. Sampling plans are tabulated for selected progressive censoring patterns and specifications, for demonstration and comparison. A Monte Carlo experiment, conducted to investigate the accuracy of the asymptotic normal approximation, has shown that the procedure is sufficiently accurate for practical purposes. An example, based on data reported by Montanari and Cacciari from progressively censored aging tests on XLPE-insulated cable models, is given for illustration.     

Conditional Control Charts for Monitoring the Weibull Shape Parameter under Progressively Type II Censored Data

In this paper, (i) we propose new conditional Shewhart‐type control charts for monitoring the shape parameter of the Weibull distribution under a progressively type II censoring strategy, and (ii) we generalize the control charts proposed by Guo and Wang¹ for the progressively type II censoring case. We provide a comparison between these control charts in terms of the out‐of‐control average run length obtained by simulation for both the known and unknown parameter cases. A real example consisting of data from breaking stress of carbon fibers is also presented for illustration and comparison of the proposed control charts. Copyright © 2014 John Wiley & Sons, Ltd.     

Linear Order Statistic Estimation for the Two-Parameter Weibull and Extreme-Value Distributions from Type II Progressively Censored Samples

Point estimation for the scale and location parameters of the extreme-value (Type I) distribution by linear functions of order statistics from Type II progressively censored samples is investigated. Four types of linear estimators are considered: the best linear unbiased (BLU), an approximation to the BLU, unweighted regression, and a linearized maximum likelihood. Linear transformations of the estimators are also considered for reducing mean square errors. Exact bias, variance, and mean square error comparisons of the estimators are made for several censoring patterns. Since the natural logarithms of Weibull variates have extreme-value distributions, the investigation is applicable to estimation for Weibull distributions.     

A Stochastic EM Algorithm for Progressively Censored Data Analysis

Progressive censoring technique is useful in lifetime data analysis. Simple approaches to progressive data analysis are crucial for its widespread adoption by reliability engineers. This study develops an efficient yet easy‐to‐implement framework for analyzing progressively censored data by making use of the stochastic EM algorithm. On the basis of this framework, we develop specific stochastic EM procedures for several popular lifetime models. These procedures are shown to be very simple. We then demonstrate the applicability and efficiency of the stochastic EM algorithm by a fatigue life data set with proper modification and by a progressively censored data set from a life test on hard disk drives. Copyright © 2013 John Wiley & Sons, Ltd.     

Bayesian Estimation of Constant-Stress Life Test Model Using Type-I Censored Data from the Linear Failure Rate Distribution

Strength of Materials - This paper considers both likelihood and Bayesian estimations of a constant-stress partially accelerated life test model with type-I censored data from the linear failure...     

删失数据下一类回归模型的参数估计

考虑一类回归模型,在右删失数据下构造了参数的最小二乘估计和加权最小二乘估计,证明了估计量具有渐近正态性。模拟结果表明加权最小二乘估计比最小二乘估计有优良的性质。     

截尾数据下一类半参数回归模型的估计

讨论了一类半参数回归模型y =x′β+g(t′α) +e .假定y被随机变量T右侧截尾 ,T与y独立 ,T～G。在G已知和未知两种情况下 ,构造了α、β和g(·) 的强相合估计     

Maximum Likelihood Estimation in the Weibull Distribution Based On Complete and On Censored Samples

This paper is concerned with the two-parameter Weibull distribution which is widely employed as a model in life testing. Maximum likelihood equations are derived for estimating the distribution parameters from (i) complete samples, (ii) singly censored samples and (iii) progressively (multiple) censored samples. Asymptotic variance-covariance matrices are given for each of these sample types. An illustrative example is included.     

Monitoring the Weibull Shape Parameter with Type II Censored Data

In this article, we introduce a method for monitoring the Weibull shape parameter β with type II (failure) censored data. The control limits depend on the sample size, the number of censored observations, the target average run length, and the stable value of β. The method assumes that the scale parameter α is constant during each sampling period, which is true under rational subgrouping. The proposed method utilizes the relationship between Weibull and smallest extreme value distribution. We propose an unbiased estimator of σ = 1/β as the monitoring statistic. We derive the control limits for one‐sided and two‐sided charts for several stable process average run lengths. We discuss two schemes, namely, the control‐limits‐only scheme and the control‐limits‐with‐warning‐lines scheme. The stable process average run length performance of the proposed charts is studied and compared with those of other charts for monitoring β under similar assumptions. Copyright © 2014 John Wiley & Sons, Ltd.     

Model Calibration With Censored Data

The purpose of model calibration is to make the model predictions closer to reality. The classical Kennedy–O’Hagan approach is widely used for model calibration, which can account for the inadequacy of the computer model while simultaneously estimating the unknown calibration parameters. In many applications, the phenomenon of censoring occurs when the exact outcome of the physical experiment is not observed, but is only known to fall within a certain region. In such cases, the Kennedy–O’Hagan approach cannot be used directly, and we propose a method to incorporate the censoring information when performing model calibration. The method is applied to study the compression phenomenon of liquid inside a bottle. The results show significant improvement over the traditional calibration methods, especially when the number of censored observations is large. Supplementary materials for this article are available online.