An investigation of transformation-based prediction interval for the Weibull median life

Statistical inference based on the Weibull distribution, a distribution widely used in reliability and survival analysis, is usually difficult as it often involves numerical computation and approximation. However, this distribution can be transformed to near-normality by a simple power transformation. Based on this transformation, a prediction interval (PI) for its median can be easily constructed through an inverse transformation. The procedure for selecting the best power transformation through minimizing Kullback-Leibler information is described. The property of this transformation-based PI is investigated. Simple correction factors are also proposed. It is shown that the transformation-based PI with corrections performs well, irrespective of the sample size and parameter values. Simulation results show that the new PI generally outperforms the existing PI. Numerical examples are given for illustration.     

潜油电泵泵轴寿命可靠性分析

统计了大庆油田近五年应用的4123套潜油电泵机组，针对248件失效泵轴的寿命进行分布检验分析，验证了其符合威布尔分布规律,并进行了可靠性评定。应用编制的工程软件可计算不同样本下泵轴寿命的概率分布规律，确定其可靠性指标，实现对泵轴使用可靠性的定性分析和定量评定，为进一步开展潜油电泵机组可靠性研究提供必要的基础数据和数据处理手段。     

A practical solution to the problem of ultimate ruin probability

Abstract

It was the Swiss actuary Chr. Moser who, in lectures at Bern University at the turn of the century, gave the name “self-renewing aggregate” to what Vajda (1947) has called the “unstationary community” of lives, namely where deaths at any epoch are immediately replaced by an equivalent number of births. It was Moser too (1926) who coined the expression “steady state” for the stationary community in which the age distribution at any time follows the life table (King, 1887). With such a distinguished actuarial history, excellently summarized by Saxer (1958, Ch. IV), it behoves every actuary to know at least the definitions and modus operandi of today's so-called renewal (point), or recurrent event, processes.     

Analysis of Instantaneous and Early Failures in Weibull Distribution

There are many situations in life testing experiment where an item fail instantaneously and hence the observed lifetime is reported as zero. The items that fail prematurely are called early failures. We propose a modified Weibull distribution as a suitable model to represent such situations by mixture of a singular distribution at zero and a two parameter Weibull distribution. We obtain the maximum likelihood estimates of the parameters and their asymptotic distributions. The methods are illustrated on drying of woods under different experiments and schedules reported by Vanmann (Research report, 1991:2).     

Shrinkage estimation of the exponentiated Weibull regression model for time-to-event data

The exponentiated Weibull distribution is a convenient alternative to the generalized gamma distribution to model time-to-event data. It accommodates both monotone and nonmonotone hazard shapes, and flexible enough to describe data with wide ranging characteristics. It can also be used for regression analysis of time-to-event data. The maximum likelihood method is thus far the most widely used technique for inference, though there is a considerable body of research of improving the maximum likelihood estimators in terms of asymptotic efficiency. For example, there has recently been considerable attention on applying James–Stein shrinkage ideas to parameter estimation in regression models. We propose nonpenalty shrinkage estimation for the exponentiated Weibull regression model for time-to-event data. Comparative studies suggest that the shrinkage estimators outperform the maximum likelihood estimators in terms of statistical efficiency. Overall, the shrinkage method leads to more accurate statistical inference, a fundamental and desirable component of statistical theory.     

售后服务数据的有效利用

文章通过对大量售后服务数据的分析,建立基于传统GM(1,1)的退后GM(1,1)模型和Weibull分布模型,找出表中的不合理数据,提出制表建议,并对横向和纵向的未来数据进行预测,最后对质量管理方面的决策和生产组织运送方面提出一些想法。     

基于整体性的制造企业供应链可靠性分析

制造企业要获得高的市场反应能力和效益,必须要有高的供应链系统可靠性做保障。针对制造企业供应链系统,结合GO法,建立出基于威布尔分布的制造企业供应链系统GO模型。运用定量分析法,研究系统的整体可靠度函数与失效率函数的表达式和图形,通过实例对表达式和图形进一步证明。结果表明:通过将GO法运用于制造企业的供应链系统可以清晰、直观地表达出供应链系统的可靠度及失效率的变化情况,并从表达式和图形中可以追溯出影响制造企业供应链系统整体可靠性的关键因素,为制造业供应链系统制定出相关可靠性管理措施提供科学的依据。     

逐次定数截尾下Weibull分布参数的逆矩估计

基于逐次定数截尾样本下,讨论了两参数Weibull分布的参数估计,得到了两参数的逆矩估计.并利用模拟方法与极大似然估计作比较,模拟结果表明逆矩估计优于极大似然估计。     

SKEWNESS FOR THE WEIBULL FAMILY

Abstract. The skewness of the Weibull family of distributions is discussed for all values of the shape parameter. This class includes unimodal probability densities for which the coefficient of skewness μ₃/o³ is positive, but the order of the mean, median and mode is μ < m < M. For values of the shape parameter used in practice the distributions are skewed to the right by a well accepted definition of skewness.     

航空惯导系统核心器件寿命测定方法

本文采用一种新方法对航空惯导系统核心器件进行加速寿命试验,试验中采用的加速电流超过了一般加速寿命试验所选取的加速电流,通过对试验数据的分析讨论了该方法的可行性,在加速寿命试验中,对加速电流的上限进行了确定。