On a class exhibiting trend change in average failure rate

Abstract

Weak convergence and moment convergence issues are investigated for the New Better than Average Failure Rate (NBAFR) family (introduced by Loh (1984 Loh, W. Y. 1984. A new generalization of the class of NBU distributions. IEEE Transactions on Reliability R-33 :97–113[Crossref], [Web of Science ®] , [Google Scholar])). We explore the validity of these results in the context of a more general ageing class that we introduce. We prove some new properties of this class and derive its interrelationships with other non-monotonic ageing families. Reliability and moment bounds are obtained and an interesting characterization of exponentiality is proved. Special cases of our results lead to new theorems for the NBAFR class. Finally weak convergence and related issues are established for this class.     

The residual effect of a growth-decay mechanism and the distributions of covariance structures

The product of two independent or dependent scalar normal variables, sums of products, sample covariances, and general bilinear forms are considered. Their distributions are shown to belong to a class called generalized Laplacian. A growth-decay mechanism is also shown to produce such a generalized Laplacian. Sets of necessary and sufficient conditions are derived for bilinear forms to belong to this class. As a generalization, the distributions of rectangular matrices associated with multivariate normal random vectors are also discussed.     

指数级数的增长性和值分布

本文研究了随机狄里克莱级数 在随机变量序列{Xn}独立（可不同分布）以及满足等条件时的增长性以及值分布,得到了一些新的结果.     

Book Reviews

Books reviewed:
M Hollander and D Wolfe, Nonparametric Statistical Methods
T Leonard and J.S.J Hsu, Bayesian Methods     

ERP在钢铁贸易企业的应用研究

以上海宝钢技术经济发展公司为对象,根据公司对提升内部管理及业务流程规范化的要求,研究了公司建立ERP系统的定位及目标,提出应建立以钢材贸易和钢铁产品深加工为主业的ERP体系,实现流通过程中的价值增值.在分析存在的主要问题的基础上,提出了ERP的模式、流程设计及采购业务、库存业务的解决方案.     

一类带有分布参数系统的最佳控制

本文给出一类非均匀弦的横向振动的最佳控制，推广了P C Park的结果。这一结果同样适用于同类型振动问题。     

Simple detection of outlying short time series

Sets of relatively short time series arise in many situations. One aspect of their analysis may be the detection of outlying series. We examine the performance of standard normal outlier tests applied to the means, or to simple functions of the means, of AR(1) series, not necessarily of equal lengths. Although unequal lengths of series implies that the means have unequal variances, that are only known approximately, it is shown that nominal significance levels hold good under most circumstances. Thus a standard outlier test can usefully be applied, avoiding the complication of estimating the time series' parameters. The test's power is affected by unequal lengths, being higher when the slippage occurs in one of the longer series     

黑龙江（汉族）民歌衍变过程探析——对黑龙江、河北（汉族）民歌的比较

黑龙江汉族民歌的衍变历经了数百年的岁月沧桑，它与民族迁徙、人口变迁以及文化传统等存在着极为密切的联系。通过对黑龙江民歌与河北、山东、河南、山西民歌进行比较，表明黑龙江民歌与河北民歌之间存在着较近的亲缘关系。因此，文章试图在对较有代表性的几首黑龙江与河北民歌比较研究的基础上进一步探究黑龙江民歌衍变的影响因素。     

Robustness of a Class of Partial Diallel Cross Designs to the Unavailability of a Complete Block of Observations

Complete and partial diallel cross designs are examined as to their construction and robustness against the loss of a block of observations. A simple generalized inverse is found for the information matrix of the line effects, which allows evaluation of expressions for the variances of the line-effect differences with and without the missing block. A-efficiencies, based on average variances of the elementary contrasts of the line-effects, suggest that these designs are fairly robust. The loss of efficiency is generally less than 10%, but it is shown that specific comparisons might suffer a loss of efficiency of as much as 40%.