Reliabilities for (n,f, k (i,j)) and ⟨n,f, k (i,j)⟩ Systems

The (n,f,k(i,j)):F(? n,f,k(i,j)?:F) system consists of n components ordered in a line or circle, while the system fails if, and only if, there exist at least f failed components OR (AND) at least k consecutive failed components among components i,i + 1,…,j ? 1,j. In this article, we present the system reliability formulae for these systems with product of matrices by means of a two-stage finite Markov chain imbedding approach, a technique first used by Cui et al. (2002 Cui , L. R. , Kuo , W. , Xie , M. ( 2002 ). On (f,g)-out-of-((i,j),n) systems and its reliability . In: Third International Conference on Mathematical Methods in Reliability Methodology and Practice , June 17–20 , Norway , Trondheim , pp. 173 – 176 . [Google Scholar]). In addition, their dual systems, denoted by (n,f,k(i,j)):G and ? n,f,k(i,j)?:G, are also introduced. Two numerical examples are given to illustrate the results.     

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.     

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.     

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.     

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。     

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.     

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.     

A stochastic restricted k–d class estimator

In this paper, we introduce a stochastic restricted k–d class estimator for the vector of parameters in a linear model when additional linear restrictions on the parameter vector are assumed to hold. The stochastic restricted k–d class estimator is a generalization of the ordinary mixed estimator and the k–d class estimator. We show that our new biased estimator is superior in the mean squared error matrix sense to the k–d class estimator [S. Sakall?o?lu and S. Kaçiranlar, A new biased estimator based on ridge estimation, Statist. Papers 49 (2008), pp. 669–689] and the stochastic restricted Liu estimator [H. Yang and J.W. Xu, An alternative stochastic restricted Liu estimator in linear regression, Statist. Papers 50 (2009), pp. 639–647]. Finally, a numerical example is given to show the theoretical results.     

Preisindikatoren für Wohnimmobilien in Deutschland

Zusammenfassung: Vermögenspreise im Allgemeinen und Immobilienpreise im Besonderen gewannen in den zurückliegenden Jahren mehr und mehr an Bedeutung. Während sie in den späten 80er Jahren (nach dem Börsencrash im Herbst 1987) und im vergangenen Jahrzehnt vornehmlich unter dem Schlagwort asset-price inflation/deflation betrachtet wurden, stehen neuerdings die Tragfähigkeit und Bestandsfestigkeit der Finanzsysteme im Vordergrund. In den Ausführungen geht es vor allem um die Frage, warum, seit wann und aufgrund welcher Grunddaten die Deutsche Bundesbank auf diesem Gebiet der Preisstatistik tätig geworden ist. Dabei wird nicht nur auf das hohe Maß an Unsicherheit in den vorgelegten Angaben hingewiesen, sondern auch der Second–Best–Charakter der Berechnungen hervorgehoben.

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Summary: Asset prices in general and property prices in particular have gained increasing importance in recent years. Whereas in the late 1980s (after the stock market crash in autumn 1987) and in the last decade these prices mainly came under the heading of asset-price inflation/deflation, the focus has recently shifted to sustainable and viable financial systems. The notes primarily explain why the Bundesbank is involved in this area of price statistics, when this involvement began and what underlying data the Bundesbank uses. At the same time, they not only indicate the large degree of uncertainty in the reported data but also highlight the second-best nature of the calculations.

*Vortrag anlässlich der 9. Konferenz Messen der Teuerung am 17./18. Juni 2004 in Marburg. Der Verfasser gibt seine persönliche Auffassung wieder, die nicht unbedingt mit derjenigen der Deutschen Bundesbank übereinstimmen muss.     

用n还是用n-1?

(本刊今年第3期刊登了《如何使用多功能计算器》一文后,不少读者来信反映文中有错。我们深查后才发觉是有些读者没弄清σ与S的意义所致。这里仅就这一问题作一简单说明)在不少电子计算器上,其统计功能键中有两个计算标准差的键,其中一个是σ,一个是S。这两个键的主要差别在于:σ是以n为分母来计算标准差的,     

基于局部均值k近邻和密度峰值的实例约简

实例约简的目的是移除训练集中的冗余样本。大多数实例约简算法保留了许多内部样本,且难以处理非球形的数据。为此,文章提出了一种基于局部均值k近邻和密度峰值聚类的实例约简算法（IRLMDP）。首先,设计了一种基于局部均值k近邻的裁剪方法LMEM来移除噪声;其次,设计了一种基于局部均值k近邻和密度峰值聚类的压缩方法CMLMDP来保留代表性的边界样本;最后,实验证明,就KNN分类器而言,IRLMDP在分类正确率和样本压缩率上优于6个流行的实例约简算法。     

Reverse Foldovers for Blocked 2 m−k Fractional Factorial Designs

Two-level regular fractional factorial designs are often used in industry as screening designs to help identify early on in an experimental process those experimental or system variables which have significant effects on the process being studied. When the experimental material to be used in the experiment is heterogenous or the experiment must be performed over several well-defined time periods, blocking is often used as a means to improve experimental efficiency by removing the possible effects of heterogenous experimental material or possible time period effects. In a recent article, Li and Jacroux (2007 Li , F. , Jacroux , M. (2007). Optimal foldover plans for blocked 2 ^m?k fractional factorial designs. J. Statsist. Plann. Infer 137:2434–2452. [Google Scholar]) suggested a strategy for constructing optimal follow-up designs for blocked fractional factorial designs using the well-known foldover technique in conjunction with several optimality criteria. In this article, we consider the reverse foldover problem for blocked fractional factorial designs. In particular, given a 2^(m+p)?(p+k) blocked fractional factorial design D, we derive simple sufficient conditions which can be used to determine if there exists a 2^{(m+p?1)?(p?1+k+1)} initial fractional factorial design d which yields D as a foldover combined design as well how to generate all such d. Such information is useful in developing an overall experimental strategy in situations where an experimenter wants an overall blocked fractional factorial design with “desirable” properties but also wants the option of analyzing the observed data at the halfway mark to determine if the significant experimental variables are obvious (and the experiment can be terminated) or if a different path of experimentation should be taken from that initially planned.     

基于可加常量方法的"k倍回答法"

本文通过对Himmelfarb和Edgell可加常量方法深入考察,分析了其固有的局限及优点,并在其基础上提出了"k倍回答法",挖掘了使估计量在无偏的情况下,采用"k倍回答法"时提高估计量精度的规律,从而有效地提高了估计量的精度.     

线性代数简介——六、n维向量

§8 n维向量(一)n维向量的定义和运算定义8.1 由n个数构成的有序数组(a_1,a_2,…a_n)称为一个n维向量;a_1,a_2,…a_n叫做向量的分量.我们常用黑体小写拉丁字母a,b,c,O,…等表示向量如a=(a_1,a_2.…a_n),有时也写成竖列形     

The power of the fisher permutation test in 2 × k tables

The power of the Fisher permutation test extended to 2 × k tables is evaluated unconditionally as a function of the under-lying cell probabilities in the table. These results are then applied in assessing the sensitivity of two-generation cancer bioassays in which a fixed number of pups from each litter born in the first generation are selected to continue on test in the second generation. In this case, the two rows of the table correspond to two treatment groups and the k columns correspond to the number of animals responding in a litter. The cell probabilities in this application are based on a suitable beta-binomial superpopulation model.     

On selecting from k finite populations the population with the largest α -quantile

Several procedures for ranking populations according to the quantile of a given order have been discussed in the literature. These procedures deal with continuous distributions. This paper deals with the problem of selecting a population with the largest α-quantile from k ≥ 2 finite populatins, where the size of each population is known. A selection rule is given based on the sample quantiles, where he samples are drawn without replacement. A formula for the minimum probability of a correct selection for the given rule, for a certain configuration of the population α-quantiles, is given in terms of the sample numbers.     

r − k Class estimator in the linear regression model with correlated errors

Autocorrelation in errors and multicollinearity among the regressors are serious problems in regression analysis. The aim of this paper is to examine multicollinearity and autocorrelation problems concurrently and to compare the r ? k class estimator to the generalized least squares estimator, the principal components regression estimator and the ridge regression estimator by the scalar and matrix mean square error criteria in the linear regression model with correlated errors.