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.     

金属夏比缺口(V型)室温冲击试验检测结果不确定度的评定

介绍了测量不确定度在金属夏比（V型缺口）室温冲击试验中的应用，并对影响冲击试验结果的测量不确定度做了详细评定，从试样的形状和尺寸、缺口底部的光洁度、冲击试验机、试验温度、检查试样尺寸量具的最小分度值五方面分析了不确定度的来源，对各分量进行了计算、合成并作出评定。     

Life Tests Under Dependent Competing Causes of Failure

In a life testing situation the failure of an individual, either a living organism or an inanimate object, may be classified into one of k(< 1) mutually exclusive classes, usually causes of failure. One often has dependent causes of failure in actual physical situations, i.e., the theoretical lifetime of an individual failing from one cause may be correlated with the theoretical lifetime of the same individual failing from a different cause. This paper i) discusses some properties of a bivariate Weibull distribution and ii) is concerned with estimating, by the method of maximum likelihood, the unknown parameters of life distributions belonging to two particular parametric families, viz., bivariate normal and bivariate Weibull, when the causes of failure are dependent. An example involving the failure of small electrical appliances is analyzed and compared with an analysis which assumes the causes of failure to be independent.     

Statistical Inference From Censored Weihull Samples

In life testing experiments it is a fairly common practice to terminate the experiment before all items have failed. The Weibull distribution is often used as a model for the observations and when a computer is available maximum likelihood estimation of the parameters is to be recommended. The tables presented in this paper enable one to set confidence limits on the parameters and the reliability based on the maximum likelihood estimates for selected censoring and sample sizes.

It is also observed that, as in the case with no censoring, the maximum likelihood estimator of the reliability is very nearly unbiased and its variance is near the Cramér-Rao lower bound, Unbiasing factors for the maximum likelihood estimator of the shape parameter are given.     

Discussion of “Extreme Vertices Design of Mixture Experiments” by R. A. McLean and V. L. Anderson

Prediction intervals for future observations in life testing situations have been derived by Hewitt (1968), Nelson (1968), Lawless (1971, 1972). Expected-cover tolerance regions have been obtained. Here we give a Bayesian approach to such situations and use the concept of the Bayesian predictive distribution. Both the exponential and the two-parameter exponential distributions are considered.     

Multi-Censored Sampling in the Three Parameter Weibull Distribution

In life and fatique testing, multi-censored samples arise when at various stages of a test, some of the survivors are withdrawn from further observation. Sample specimens which remain after each stage of censoring continue to be observed until failure or until a subsequent stage of censoring. In this paper, maximum likelihood estimators and estimators which utilize the first order statistic are derived for the three parameter Weibull distribution. Estimators are also derived for the special case in which the shape parameter is known, a special case which includes the two parameter exponential distribution. An illustrative example is included.     

Moments,Variances, and Covariances of Sines and Cosines of Arguments which are Subject to Random Error

A simple, unbiased estimator, based on a censored sample, is proposed for the scale parameter of the extreme-value distribution. The exact distribution of the estimator is determined for the cases in which only the first two or only the first three ordered observations are available. The asymptotic distribution is derived, and an approximate distribution for small sample size is also provided. Interval estimation for the scale parameter is developed and a conservative interval estimate for reliability is also obtained.     

A General Approach to the Estimation of Variance Components

A general method of estimation of variance components in random-effects models of the nested and/or classification type is considered. If a given parameter is estimable with respect to some particular experimental design (i.e., an unbiased estimate of the parameter may be obtained from the experiment), then the suggested estimator may be readily computed with only the aid of a desk calculator. The estimates are always unbiased and consistent (with respect to the structure of the experimental design); in the case of balanced experiments, they coincide with those obtained from the analysis of variance.

Secondly, the problem of designing experiments to estimate variance components is briefly discussed from the point-of-view of the suggested estimation procedure. As a result, certain non-balanced designs are seen to yield more efficient estimators of particular parameters in specified situations than the corresponding balanced design using the same number of observations.

Finally, the method of estimation is shown to be applicable to models more general than the variance component one. Again it is readily computed and is unbiased and consistent.     

A Confidence Interval for the Availability Ratio

A method is given for establishing an exact confidence interval for availability under the assumption that the time between failures and the time to repair are independent, exponential and lognormal random variables respectively. The method requires computations of the distribution of

The cumulative distribution of W is tabled for selected values of W and the parameters.     

One-Sided Prediction Intervals to Contain at Least m out of k Future Observations

Factors for constructing one-sided prediction intervals to contain k out of m future observations from normal and exponential populations are presented. An application involving prediction intervals is also given.     

Optimising the palletisation of cylinders in cases

Summary This paper is concerned with the analysis of the packing arrangements of cylindrical objects into a rectangular case with respect to the palletisation efficiency of the resultant case. A set of regular arrangements are considered. The size and shape of the surrounding case depends not only on the number of rows and the number of cylinders per row but also on the angle between the centres of cylinders in adjacent rows. Previous theoretical results on the palletisation of rectangular boxes are used to develop an algorithm for determining the optimal angle for any arrangement. Arrangements with angles of 0° or 30° are often used in practice as they are easy to load. The expected optimality of this practice is investigated by an empirical study.     

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.     

Some Complete and Censored Sampling Results for the Weibull or Extreme-Value Distribution

A simple, unbiased estimator, based on a censored sample, has been proposed by Rain [1] for the scale parameter of the Extreme-value distribution. This estimator was shown to have high efficiency and to be approximately distributed as a chi-square variable if substantial censoring occurs. Further small sample and asymptotic properties of this estimator are considered in this paper. The estimator is modified so that it is more applicable to the complete sample case and a close chi-square approximation is established for all cases. The estimator is also shown to be related to the maximum likelihood estimator.     

加载速率对Al2O3陶瓷弯曲切口强度及其概率分布的影响

测定了 Al2 O3陶瓷在不同恒位移加载速率作用下的弯曲强度和弯曲切口强度。结果表明 ,不同切口的实际应力速率可由试验记录的载荷 -时间曲线确定。在实验的四种加载速率下(0 .0 5,0 .5,5和 50 mm/min) ,其弯曲强度、弯曲切口强度均同时符合正态分布、对数正态分布和Weibull分布。加载速率在 0 .0 5～ 5mm/min,其弯曲强度、弯曲切口强度符合本文给出的陶瓷材料切口强度的表达式。从而实现了用光滑试件的断裂强度及其概率分布预测切口强度及其概率分布 ,这对陶瓷材料的强度设计与可靠性评估具有指导意义     

International Journal of Computer Mathematics

The performances of three procedures for treatment of outliers in normal samples are evaluated. The first procedure is the sequential application of the usual maximum residual test. The largest observation is declared an outlier if the largest studentized residual exceeds a predetermined value. If one outlier is detected, the test is repeated on t.he remaining observations, the process continuing until no further outliers are detected. In the second procedure the two largest observations are declared outliers if the sum of the two largest studentized residuals exceeds a predetermined value. In the third procedure the two largest observations are considered outliers if the ratio of the corrected sum of squares omitting these values to the total corrected sum of squaresis less than a critical ratio. The performances of these procedures are evaluated for samples in which two of the observations have means different from the common mean of the remainder of the sample.     

Maximum Likelihood Estimation For Multi-Risk Model

In this paper we discuss a probabilistic model of failure due to competing causes of failure operating on a unit during its lifetime. Following Cox we term this the Multi-Risk Model. We impose some well-known parametric forms on the underlying distributions of the model and obtain maximum likelihood estimates for the parameters of the distributions. The asymptotic variance-covariance matrix of the estimates is derived. We give examples using the exponential and Weibull distributions. The theory is applied to data published by Mendenhall and Hader, who studied a Single-Risk Model.     

出口电梯的运输包装设计

在确定滇通环境的基础上，对出口电梯进行了运输包装设计。其中包括产品防护设计及木箱结构设计。     

Note on an Application of Four-Moment Inequalities To a Problem in Queues

Examples of numerical bounds are given for the distribution of the duration of the busy period in the context of a single server queue with random arrivals and (special) Erlanginn service time. The computations are based on Tchebycheff type inequalities using the first four moments of the busy period distribution. The computations are intended to illustrate an approach to a difficulty cited by D. R. Cox.     

Charts for the Interpretation and Estimation of the Second Order Autoregressive Model

The second order autoregressive model (AR(2)) is examined to cast light on its physical interpretation and to facilitate its use. A number of AR(2) series are simulated and charts are presented which relate the characteristics of these series to the parameters of the model and their roots and the associated correlation, partial correlation and forecast functions. Charts are also developed for the estimation of the parameters of the model and the construction of confidence regions for the estimates. An example is given to demonstrate the use of the charts.     

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.