Accelerated Life Test Planning With Independent Weibull Competing Risks With Known Shape Parameter

This article presents methodology for accelerated life test (ALT) planning when there are two or more failure modes, or competing risks which are dependent on one accelerating factor. It is assumed that the failure modes have respective latent (unobservable) failure times, and the minimum of these times corresponds to the product lifetime. The latent failure times are assumed to be s-independently distributed Weibull with known, common shape parameter. Expressions for the Fisher information matrix, and test plan criteria are presented. The methodology is applied to the ALT of Class-H insulation for motorettes, where temperature is the accelerating factor. Two-level, and 4:2:1 allocation test plans based on determinants, and on estimating quantiles or hazard functions, are presented. Sensitivity of optimal test plans to the specified Weibull shape parameter is also studied     

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。     

定时截尾Weibull分布的双参数的矩估计

讨论了在定时截尾情形下,将Weibull分布转化成指数分布数据或均匀分布,利用平均剩余寿命构造样本矩．从而得出参数的矩估计。并通过大量的Monte-Garlo数值模拟试验证实了所给方法的可行性。     

Complete Sample Estimation Techniques for Reparameterized Weibull Distributions

The Weibull distribution, frequently employed to assign probabilities to the lifetimes of components and systems operating under stress, is habitually characterized by a pair of positive parameters, termed the scale and shape parameters. Two fundamental reparameterizations of the Weibull probability density function are proposed. The first reparameterization replaces the shape parameter by its inverse, the resulting positive parameter thereafter termed the shaping parameter. This permits a more facile exposition of the properties of parameter estimates, derived in the event that a complete random sample from the Weibull distribution is available. The characteristics of these parameter estimation techniques are then reviewed and compared, and their variances and distributional properties are delineated whenever possible. A second reparameterization extends the parameter space so as to include nonpositive values of the shape parameter. This extension augments the utility and applicability of the Weibull distribution without requiring radical alteration of the standard parameter estimation procedures applicable to the original parameter space.     

Analysis of Incomplete Data in Competing Risks Model

Parametric and nonparametric estimation methods are proposed for reliability characteristics of one failure mode under competing risks with incomplete data; some of the failure times are observed without observing the cause of failure. The efficiencies of these methods are discussed.     

Estimation of P[Y

Kundu  D. Gupta  R.D. 《Reliability, IEEE Transactions on》2006,55(2):270-280

Estimation of the stress-threshold for the Weibull inverse powerlaw

Lifetime data on stress rupture of copper joints made with certain lead-free solders suggest that specimens under `stress below a certain threshold' run indefinitely without failure. A commonly used model for this type of data is the Weibull inverse power law that includes a threshold. If the threshold is unknown, this estimation problem presents several difficulties for statistical treatment. The largest problem is: as the threshold approaches the minimum of the data (stresses) the likelihood approaches infinity, thus there is no global maximum. A modified maximum likelihood approach, in the spirit of Cohen is used to resolve this problem. The method is similar to Cohen's, but interesting differences occur for censored data. The results show that modifications of the Cohen method produce estimates of the parameters in the Weibull inverse power threshold law     

Competing causes of failure and reliability tests for Weibull lifetimes under type I progressive censoring

For many high reliability products where very few items are expected to fail during the test period, testing under normal conditions is not feasible. Further, the requirement for high reliability increases the need for test procedures which yield valuable degradation and other useful information for improving product reliability. Thus in some manufacturing and other experiments, various types of failure censored and accelerated life tests are commonly employed for life testing. In this paper we discuss Type I progressively censored variable-sampling plans for Weibull lifetime distributions under competing causes of failure. The proposed procedure is attractive as it yields useful degradation-related information for improving product quality. In addition, the procedure is useful when a test is conducted under severe time constraint and/or when the experimenter wishes to save costly specimens or scarce test facilities for other use.     

零均值独立复杂噪声背景下二维谐波估计的时间平均矩方法

对于零均值独立乘性噪声背景下二维谐波的三次非线性耦合估计问题,由于缺乏理论支持及有效的计算方法,至今尚无有效的解决办法.本文首先分析了不同的噪声模型对谐波耦合分析所产生的影响,通过对原始采样数据进行平方预处理,改变了采样信号的信噪模型,利用新模型下噪声的统计特性及噪声间的相关特性,通过定义一种特殊四阶时间平均矩,首次解决了零均值独立噪声背景下谐波频率的二维三次非线性耦合问题.数学推导了该特殊四阶时间平均矩的矩多谱,理论证明了相应估计子渐进无偏性和一致性.理论分析和试验结果表明,该方法用于二维谐波的三次耦合分析时,不再需要对噪声的统计特性及噪声间的相关特性作任何限制.     

零均值复杂噪声背景下二维谐波的三次非线性耦合分析

该文利用一种四阶时间平均矩谱,通过对原始数据取平方的办法,改变了原始信号中噪声的统计特性,首次对零均值独立噪声背景下的二维谐波的三次耦合问题给出了解决方法,文中给出了详细的理论分析和证明。由于该方法也适合于非零均值噪声下的谐波耦合问题,因此这种方法不再需要对噪声的均值、颜色和分布作任何限制。仿真结果表明了该方法的有效性。     

Estimation of Weibull Parameters With Competing-Mode Censoring

Existing results are reviewed for the maximum likelihood (ML) estimation of the parameters of a 2-parameter Weibull life distribution for the case where the data are censored by failures due to an arbitrary number of independent 2-parameter Weibull failure modes. For the case where all distributions have a common but unknown shape parameter the joint ML estimators are derived for i) a general percentile of the j-th distribution, ii) the common shape parameter, and iii) the proportion of failures due to failure mode j. Exact interval estimates of the common shape parameter are constructable in terms of the ML estimates obtained by using i) the data without regard to failure mode, and ii) existing tables of the percentage points of a certain pivotal function. Exact interval estimates for a general percentile of failure-mode-j distribution are calculable when the failure proportion due to failure-mode-j is known; otherwise a joint s-confidence region for the percentile and failure proportion is calculable. It is shown that sudden death endurance test results can be analyzed as a special case of competing-mode censoring. Tabular values for the construction of interval estimates for the 10-th percentile of the failure-mode-j distribution are given for 17 combinations of sample size (from 5 to 30) and number of failures.     

竞争失效产品步进加速寿命试验的优化设计

对weibull分布竞争失效产品的步进加速寿命试验进行优化设计,首先选取产品正常应力下中位寿命的极大似然计估渐近方差的估计值作为优化目标函数,并对优化目标函数进行统计推断.然后利用目标函数的连续性,提出基于离散数据的函数拟合方法,将试验优化设计转化为显函数的约束极值求解问题,同时将智能优化算法应用到步进加速寿命试验的优...     

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.     

Estimation of system reliability for independent series componentswith Weibull life distributions

The reliability of a series system with independent components is estimated based on random samples from Weibull failure distributions with parameters &thetas;_i and β_i. It is assumed that the β_i's are known, which reduces the reliability of the system to a function, γg(&thetas;), of &thetas;=(&thetas;₁, . . ., &thetas;_p). An estimate of γ(&thetas;) which is better than the MVUE of γ(&thetas;) in terms of mean square error is determined. The predicted reliability and the percentage improvement for this estimator is computed and compared with the usual MVUE of γ(&thetas;). The predicted reliability using the improved estimator is numerically closer to the true system reliability     

Sample Size for Selecting the Better of Two Weibull Populations

Suppose an experimenter wishes to select the better of two Weibull populations. In a life testing situation he may have some time t* for which the device must perform properly and he would consider the better population to be the one with the larger reliability at time t*. It is reasonable for the experimenter to test n items from each of the two populations until there are r(r < n) failures from each and then select as better the population for which the maximum likelihood estimate of the reliability at time t* is the larger. This paper presents the sample sizes needed to achieve a desired level for the probability of correct selection with such a decision rule.     

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.     

宽带独立信号和相干信号的DOA估计

当独立信号和相干信号共存时,传统四阶累积量方法无法估计出宽带相干信号的来波方向(DOA),针对这个问题提出了一种新方法。该方法首先通过离散傅里叶变换,将宽带阵列接收数据分解为若干个窄带信号,构造出各个窄带频率处的自相关矩阵,再通过MUSIC(Multiple Signal Classification)算法估计出各个窄带信号的DOA,将各个窄带信号的空间谱相加求平均,通过谱峰搜索得到宽带独立信号的DOA;然后分离出独立信号的信息,构造出一个只包含宽带相干信号信息的矩阵,最后通过稀疏重构的方法估计出相干信号的DOA。计算机仿真结果证明该算法的正确性和有效性。     

One-Order-Statistic Estimation of the Scale Parameters of Weibull Populations

This paper calculates the minimum-variance unbiased one-order-statistic estimator of the parameter of a one-parameter exponential population. The estimator is given for N = 2(1)20 along with its efficiency with respect to an unbiased M-order-statistic estimator for a sample of N items which is truncated after M items have failed. Furthermore, it is shown that by using the estimator for exponential populations one can obtain a consistent estimator for the scale parameter of Weibull populations with any known shape parameter and with ## location parameter zero. A section on the use of the tabled data and a numerical example are included.