Construction and selection of tightened–normal–tightened variables sampling scheme of type TNTVSS (n 1, n 2; k)

This paper provides tables for the construction and selection of tightened–normal–tightened variables sampling scheme of type TNTVSS (n ₁, n ₂; k). The method of designing the scheme indexed by (AQL, α) and (LQL, β) is indicated. The TNTVSS (n _T , n _N; k) is compared with conventional single sampling plans for variables and with TNT (n ₁, n ₂; c) scheme for attributes, and it is shown that the TNTVSS is more efficient.     

Orthogonal [k − 1, k + 1]-factorizations in graphs

Let G be a graph. Let F={F₁,F₂,...F_d} be a factorization of G and H be a subgraph of G. If H has exactly one edge in common with F_i for all i = 1,2,…,d, then we say that F is orthogonal to H. In this paper it is proved that for any d-matching M of a [kd − 1, kd + 1]-graphG, there is a [k − 1, k + 1]-factorization of G orthogonal to M where k ⩾ 2 is an integer.     

The mean general residual lifetime of (n − k + 1)-out-of-n systems with exchangeable components

The study of the reliability properties of (n ? k + 1)-out-of-n systems has gained a great deal of attention, from both theoretical and practical perspectives. In this article, we consider (n ? k + 1)-out-of-n systems with exchangeable components and study the stochastic properties of two forms of residual lifetimes of such systems under the following conditions: n ? r + 1 (r ? k) components of the system are operating at time t > 0, and/or the rth (r < k) component has failed, but the system is working at time t. In addition, some results relating to the functions of the mean general residual lifetimes (MGRL) are derived for these systems. Finally, in accordance with the generalized Farlie–Gumbel–Morgenstern model, we present the reliability properties of the general residual lifetime of (n ? k + 1)-out-of-n systems and investigate the asymptotic behavior of the proposed MGRL functions with exponential marginals.     

Aliasing in 2n–k fractions in the absence of within group interactions

It is often known in advance that certain subsets of factors act independently upon a response. Such information can be used to estimational advantage by aliasing low-order effects with such zero interactions. We find the best 2^n–k fractions for the case when the factors can be partitioned into two classes such that non-zero interactions may exist only between classes but not within a class.     

On the exact distribution of the sum of the largest n−k out of n normal random variables with differing mean values

Motivated by an application in Electrical Engineering, we derive the exact distribution of the sum of the largest n?k out of n normally distributed random variables, with differing mean values. Comparisons are made with two normal approximations to this distribution—one arising from the asymptotic negligibility of the omitted order statistics and one from the theory of L-statistics. The latter approximation is found to be in excellent agreement with the exact distribution.     

近似非齐次指数序列的非等间距IANGM(1,1,k)模型构造

针对近似非齐次指数的非等间距数据序列在建模过程中存在灰色微分方程和白化微分方程不匹配、建模后需要对白化微分方程解的时间响应式作累减还原问题,提出利用原始序列与其对应的1-IAGO构建灰色微分方程和白化微分方程相匹配的IANGM(1,1,k)模型新方法,该方法利用模型白化微分方程得到的时间响应函数是关于原始序列的表达式,无需累减还原就可以直接进行模拟预测。通过实例验证了新方法对递增和递减的近似非齐次指数的非等间距序列均具有非常好的模拟和短期预测效果,新方法进一步拓宽了灰色预测模型的适用范围。     

A note on the mean past and the mean residual life of a (n − k + 1)-out-of-n system under multi monitoring

In the study of the reliability of technical systems, k-out-of-n systems play an important role. In the present paper, we consider a (n − k + 1)-out-of-n system consisting of n identical components such that the lifetimes of components are independent and have a common distribution function F. It is assumed that the number of monitoring is l and the total number of failures of the components at time t _i is m _i , i = 1, . . . , l − 1. Also at time t _l (t ₁ < . . . < t _l ) the system have failed or the system is still working. Under these conditions, the mean past lifetime, the mean residual lifetime of system and their properties are investigated.     

Erlang(n)等待时间的两步保费率对偶风险模型

文章考虑在两步保费率策略下等待时间为erlang(n)分布的对偶风险模型,给出了这种风险模型下Gerber-Shiu贴现罚金函数的满足的微积分方程,并得到了方程的解所满足的更新方程。利用此解推导出最终破产概率及破产时间的拉普拉斯变换。最后给出当索赔额分布为指数混合指数分布时破产的两个量的数值结果。     

Many (22, 44, 14, 7, 4) — and (15, 42, 14, 5, 4)-balanced incomplete block designs

A Balanced Incomplete Block Design (BIBD) is a pair (V, B) where V is a v-set and B is a collection of b k-subsets of V, called blocks, such that every element of V occurs in exactly r of the k-subsets and every 2-subset of V occurs in exactly λ of the blocks. The number of non-isomorphic designs of a BIBD (22, 44, 14, 7, 4) whose automorphism group is divisible by 7 or 11 are investigated. From this work, results are obtained on the number of non-isomorphic BIBDs (15, 42, 14, 5, 4).     

Critical values of Mandel’s h and k, the Grubbs and the Cochran test statistic

According to ISO 5725-2 (1994), measurement results obtained in an interlaboratory experiment are inspected for consistency by plotting Mandel’s h and k statistics and for outliers by application of the Grubbs test and the Cochran test. Critical values of these statistics for significance levels α=5% and α=1% and for some numbers p of laboratories and n of repeated measurements in the laboratories are supplied in ISO 5725-2 without reference to methods for their calculation. In this paper, exact formulae for the critical values of Mandel’s h and k and approximate formulae for the critical values of the Single Grubbs test, the Double Grubbs test and the Cochran test are derived.     

改进的以x(1)(n)为初始条件的GM模型

在对以为初始条件的GM模型分析的基础之上,初值的选取对模型的精度有着重要的影响。文章在分析了GM(1,1)模型的预测精度之后,提出了一种修正初值法来提高模型的精度,对以为初始条件的GM模型进行了改进,使所建的模型的精度大为提高,最后通过具体的实例验证了模型的实用性与可靠性。     

On the E-optimality of blocked main effects plans when n ≡ 1(mod4)

ABSTRACT

In this article, we consider experimental situations in which m two-lever factors are to be studied using a two-level main effects plan involving n runs which are partitioned into b blocks of size k =?n/b. For the casen ≡ 1(mod?4) and b???k, we derive some new methods of constructing E-optimal designs which tend to be highly efficient under other optimality criteria as well.     

(,S)联合质量控制图

(?)图、S图和R图是产品质量控制所常用的工具,它们可以从产品组间和组内的变化中发现质量问题。不过在实际应用中,人们不难发现,由于样本数据分布在两张图上((?)图和S图或R图),用起来并不得心应手。究其原因,是因为设制质量控制图是以这样一个假设为前提的,即:样本数据呈正态分布或准正态分布。在这一前提下,由每组样本数据计算的样     

育人十九年,投入十三万(下)

教育成本不再是谜教育成本主要分三大项:一是个人支出。包括教职工工资、福利、社会保障费等;二是公用支出。包括公务费、业务费、设备购置费、修缮费、业务招待费等;三是基建支出。教育成本的主要指标为:生均支出,即平均每个在校学生一年的支出。2002年全国常规教育的生均支出为2192元,其中生均个人支出1245元,占56.8%;公用支出708元,占32.3%;基建支出239元,占10.9%。但由于学级的不同,经费的构成也大不相同。大学生均支出14974元。中专生均支出5455元,高中3693元,初中1534元,小学1172元,幼儿园1702元。除幼儿园外,学级越低生均支出越少,且…     

育人十九年,投入十三万(上)

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