Estimation of the Shape and Scale Parameters of the Weibull Distribution

Estimates ? and are proposed for the shape parameter c and the scale parameter b of the Weibull distribution on the assumption that the location parameter is known: ? obtained by first finding an estimate of 1/c, and then setting ? = 1/. When b is unknown, is a consistent and non-negative estimate of d, with a bias which tends to vanish as the sample size increases and with an asymptotic efficiency of about 55%. When b is known, is an unbiased, non-negative and consistent estimate of d, and its efficiency is approximately 84%. An estimate In∧b of In b is found. Its asymptotic efficiency is 95%. It is proposed that exp(In∧b) be used to estimate b.     

Tests for Exponentiality When Origin and Scale Parameters Are Unknown

Several methods are examined for testing for the exponential distribution, using complete samples, when both the scale and location parameters are unknown. Percentage points are given for empirical distribution function (EDF) tests in which both parameters are estimated from the data, and power studies are reported to compare these tests with other goodness-offit techniques for the exponential distribution, particularly those based on regression methods. It is found that the EDF statistics W ² and A ² have overall good power properties, with A ² slightly superior.     

Comparing Rates of Several Independent Weibull Processes

Tests are presented for comparing the scale parameters of Weibull process models when k independent series are available. The application of these tests, together with Crow's maximum likelihood ratio test for comparing shape parameters, is one way of testing that the k series have identical rates.     

Estimation of Parameters in Compound Weibull Distributions

The two-parameter Weibull distribution has been recognized as a useful model for survival populations associated with reliability studies and life testing experiments. In the analysis of atmospheric data, the distributions encountered are often a result of combining two or more component distributions. These compound distributions are consequently of interest to aerospace scientists. Presented is a method for estimation of the parameters of a compound Weibull distribution with two shape parameters, two scale parameters and a proportionality factor.     

Some Percentile Estimators for Weibull Parameters

A percentile estimator for the shape parameter of the Weibull distribution, based on the 17th and 97th sample percentiles, is proposed which is asymptotically about 66% efficient when compared with the MLE (maximum likelihood estimator). A two-observation percentile estimator, based on the 40th and 82nd sample percentiles, for the scale parameter when the shape parameter is unknown is asymptotically about 82y0 efficient when compared with the MLE. The 24th and 93rd sample percentiles yield asymptotically about 41ye jointly efficient percentile estimators for both the scale and shape parameters in a class of two-observation percentile estimators when compared with their MLEs. Some other simple percentile estimators for these parameters are also briefly discussed. Finally, asymptotic properties of these estimators are investigated and their application in statistical inference problems is mentioned.     

Asymptotic Properties of Several Estimators of Weibull Parameters

In this paper several estimators for the scale and the shape parameters of the Weibull law are obtained by postulating a stochastic model aimed at studying the aging process of certain inexpensive industrial products. These estimators are consistent and asymptotically multi-normal.     

Best Linear Invariant Estimation for Weibull Parameters Under Progressive Censoring

Best linear invariant estimators of log reliable life are derived for a model in which failure times have a two-parameter Weibull distribution and removal of some surviving items from life test is allowed at the time of any failure. Weights for obtaining best linear invariant estimates under this model are given in tabular form for all censoring patterns for sample sizes 2 through 6.     

Weibull分布兴趣参数的广义置信区间

Weibull分布可以用来描述疲劳失效、真空管失效和轴承失效等,是重要的寿命分布。本文研究了Weibull分布尺度参数、形状参数、分位数及可靠度函数的广义置信区间问题。利用广义枢轴量给出四个兴趣参数的广义置信区间。证明了由广义枢轴量确定的四个兴趣参数的广义置信区间具有频率意义下的实际置信水平。     

A Graphical Estimation of Mixed Weibull Parameters in Life-Testing of Electron Tubes

It is widely recognized that electron tube failures may be classified into two types: sudden and delayed. A mixture of two Weibull distributions, each representing one type of tube failure, is proposed, and a simple graphical method for estimating the parameters of the mixed Weibull distribution described.     

On the Estimation of Safe Life When the Underlying Life Distribution Is Weibull

The problem of estimating Y ₍₁₎, the smallest of a future sample of k observations from the Weibull distribution, based on an observed sample from the same distribution, is considered. A conditional confidence interval solution is proposed for the estimation of Y ₍₁₎. The results have direct application in reliability theory, where the time until the first failure in a group of k items in service provides a measure of assurance regarding the operation of the items.     

Design of Over-Stress Life-Test Experiments When Failure Times Have the Two-Parameter Weibull Distribution

This paper deals with estimation of reliability parameters when life testing is conducted at stress levels above that which would normally be applied in standard usage. A range of stress for testing is prescribed, and a two-parameter Weibull model for failure times is assumed. The logarithm of the Weibull scale parameter is assumed to be a polynomial function of known degree k of the reciprocal of stress level. The Weibull shape parameter is assumed to be independent of stress level.

The problem considered is that of determining the design for obtaining the least-squares-curve intercept with minimum variance at the nominal testing level. The design obtained specifies the number and location of stress levels in the prescribed range at which the life tests will be conducted and proportion of the total sample of specified size to be randomly allocated to each testing level.     

A Time Scale for Quantum Jumps

Experimental observations of quantum jumps suggest that one can associate a time scale shorter than the usual lifetime with quantum transitions. Two such scales are discussed here, and their relation to experiments and to other theoretical ideas is explored.     

用节约法解决带有时间窗的满载车辆调度问题

建立了具有时间约束的满载VSP问题的线性规划模型,给出了一种基于节约值比较的旨在最小化成本的启发式算法.该算法将满载车辆路线分为三种基本结构,即两点往返、多点连续实载、多点间隔实载,将车辆固定成本和变动成本同时加入到节约值计算中,根据路线结构计算更新节约值,在考虑时间约束的基础上参考节约值最大或机会节约值最大两种策略选择任务连接,得出车辆调度路线.经算例证明,该算法求得优化的调度路线.     

潜水泵参数的综合计量

本文详细介绍了“潜水泵参数综合计量仪”获取技术指标的方法和计量仪电路结构与工作原理。该计量仪自动化程度高。并可实现原始技术指标与归一化指标的转化,提高了计量效率。     

Estimation of Weibull Distribution Shape Parameter When no More than Two Failures Occur per Lot

An estimate, with limits of uncertainty, is given for the shape parameter of the Weibull distribution when failure experience results from lots having different quality levels. The data result from the following situation. Lots are removed from service at some target value, normally after experiencing no failures. Some lots experience one failure, and the remaining non-failed items remain in service until the target value is reached. Finally, there are a few lots in which two failures occur. In this instance, all remaining non-failed items are removed immediately after the second failure occurs. It is assumed that all lots have the same shape parameter, with lot differences, when they exist, appearing as differences in the scale parameter value.     

Tables for Obtaining the Best Linear Invariant Estimates of Parameters of the Weibull Distribution

A censored life-test situation is considered and the assumption of a Weibull distribution for failure times is made. Tables are given for estimating log reliable life, where the estimator is best among linear estimators with expected loss invariant under translations. These best linear invariant (BLI) estimators have uniformly smaller expected loss than the Gauss-Markov best linear unbiased (BLU) estimators and are simple linear functions of the BLU estimators. The preliminary discussion involves a comparison of the BLI estimators with other widely used estimators.     

本地时标评价方法的研究

本地时标UTC(k)运行好坏取决于其与国际标准时间UTC的靠近程度,实际上,本地时标所复现的秒定义与UTC所复现的秒定义之间的一致程度应是更重要的衡量指标。根据国际计量局关于国际标准时间TAI和UTC的定义,提出了相对频率偏差（频率准确度）和时间稳定度是评价本地时标优劣的技术指标。通过对国内外6个守时实验室相对频率偏差、时间稳定度两项指标分析证明了上述观点,并对各实验室时标实现方案进行了简要评述。     

生产要素以不同速度增长情况下的规模经济性

传统经济学中的规模经济理论探讨的是在各种资源以相同速度增长情况下的规模经济性问题。本文则论证了在生产要素以不同速度增长情况下,企业的规模扩张可能导致规模不经济的发生,从而告诫企业在进行规模扩张时,一定要慎重,要取得规模经济,必须尽可能做到各种资源的协调增长。