Tables of a Truncated Standard Normal Distribution: A Singly Truncated Case

A normal distribution has a unique position in many engineering fields, and the standard normal distribution table has been widely used for more than a century. There are many situations, however, in which a truncated normal distribution needs to be considered. Although the theoretical foundations of the truncated normal distribution are well established, there has been little work on tabulating the characteristics associated with the truncated normal distribution, such as a cumulative probability, a truncated mean, and a truncated variance. In this article, we provide tables for a singly truncated normal distribution, which may be useful for quality practitioners.     

Truncated Gröbner Bases for Integer Programming

 The toric ideal I _A of a matrix A=(a ₁, . . . ,  a _n )∈ℤd ^× n is the kernel of the monoid algebra map π^ _A  : k[x ₁, . . . ,  x _n ]→k[t ^±1 ₁, . . . ,  t ^±1 _d ], defined as x _j ?t ^aj . It was shown in [4] that the reduced Gr?bner basis of I _A , with respect to the weight vector c, can be used to solve all integer programs minimize {cx : Ax=b, x∈ℕ ⁿ }, denoted IP _A,b,c,= , as b varies. In this paper we describe the construction of a truncated Gr?bner basis of I _A with respect to c, that solves IP _A,b,c,= for a fixed b. This is achieved by establishing the homogeneity of I _A with respect to a multivariate grading induced by A. Depending on b, the truncated Gr?bner basis may be considerably smaller than the entire Gr?bner basis of I _A with respect to c. For programs of the form maximize{cx : Ax≦b, x≦u, x∈ℕ  ⁿ } in which all data are non-negative, this algebraic method gives rise to a combinatorial algorithm presented in [17]. Received: April 10, 1995; revised version: February 6, 1996     

石油螺纹量规中截顶参数测量方法的讨论

JJF 1108-2012中增加了测量石油螺纹量规截顶的要求,但是给出的测量方法并不能准确反映螺纹牙型轮廓的加工误差。本文详细分析了规范中所给方法的不周全的地方,并给出了使用三坐标测量机测量螺纹截顶的方法和计算过程。     

INFINITE DOMAIN CORRECTION FOR IN-PLANE BODY WAVES IN A TWO-DIMENSIONAL BOUNDARY ELEMENT ANALYSIS

A method is described in this article to correct for the error that arises with the discretization of domains that include boundaries that extend to infinity. Typically when open domains are discretized, part of the boundary is excluded from the calculation resulting in a truncated region. Of particular interest in this article are earthquake wave amplification problems through zoned media. In these type of problems, the boundary element discretization scheme typically results in truncated regions. Correction for truncation in anti-plane wave problems has already been addressed in a previous article by Heymsfield. In this article, truncation correction for in-plane body waves in a damped material will be discussed. To prove the validity of the proposed technique, the method is checked by calculating the soil amplification of a unit in-plane SV wave through a soil layer resting on a rock half-space. Since an analytic solution exists for this problem, the problem serves as a good basis to compare results with and without the corrections for truncation. Results for this particular problem compare the analytic solution with the numerical solution considering (1) no truncation correction, (2) only layer correction, and (3) both layer and half-space corrections. © 1997 by John Wiley & Sons, Ltd.     

Truncated branch-and-bound,schedule-construction,and schedule-improvement procedures for resource-constrained project scheduling

We present heuristic procedures for approximately solving large project scheduling problems with general temporal and resource constraints. In particular, we propose several truncated branch-and-bound techniques, priority-rule methods, and schedule-improvement procedures of types tabu search and genetic algorithm. A detailed experimental performance analysis compares the different heuristics devised and shows that large problem instances with up to 1000 activities and several resources can efficiently be solved with sufficient accuracy.

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Received: July 26, 2000 / Accepted: May 15, 2001     

A Truncated Sequential t-Test

A truncated sequential t-test is developed and is compared with Barnard's one-sided (one-tailed) non-truncated sequential t-test and the fixed sample-size procedure. Empirical results indicate that, in part of the parametric region between the null and alternative hypotheses, the proposed test, as compared to Barnard's procedure, leads to improvement in ASN and appreciable reduction in sample size variability. In addition, it seems to have uniformly lower ASN Values than those of its fixedsample counterpart. The proposed test is then extended to a two-sided procedure and compared with the truncated t-test of Schneiderman and Armitage.     

Development of measures to estimate truncation error in fault tree analysis

The fault tree quantification uncertainty from the truncation error has been of great concern for the reliability evaluation of large fault trees in the probabilistic safety analysis (PSA) of nuclear plants. The truncation limit is used to truncate cut sets of the gates when quantifying the fault trees. This paper presents measures to estimate the probability of the truncated cut sets, that is, the amount of truncation error. The functions to calculate the measures are programmed into the new fault tree quantifier FTREX (Fault Tree Reliability Evaluation eXpert) and a Benchmark test was performed to demonstrate the efficiency of the measures.The measures presented in this study are calculated by a single quantification of the fault tree with the assigned truncation limit. As demonstrated in the Benchmark test, lower bound of truncated probability (LBTP) and approximate truncation probability (ATP) are efficient estimators of the truncated probability. The truncation limit could be determined or validated by suppressing the measures to be less than the assigned upper limit. The truncation limit should be lowered until the truncation error is less than the assigned upper limit. Thus, the measures could be used as an acceptability of the fault tree quantification results. Furthermore, the developed measures are easily implemented into the existing fault tree solvers by adding a few subroutines to the source code.     

厚截锥壳结构的自由振动

本文对基于Mindlin理论所导出的厚截锥壳的一阶基本微分方程组采用了子结构离散变量法,求解了这类结构的固有频率和相应的振型。文中给出了算例,其结果与试验结果和有限无法计算结果相比是令人满意的。     

Adaptive Radial Based Sampling for Reliability and Reliability Sensitivity Analysis Involving Truncated Correlated Normal Variables

The reliability and reliability sensitivity (RS) models are presented for the engineering problem involving truncated correlated normal variables (CNV),and in the case an adaptive radial based sampling is used to analyze the reliability and the RS.In the presented models,the truncated CNV is transformed to general CNV,and the value domains of the truncated CNV are treated as multiple failure modes,then the reliability and the RS with the truncated CNV are transformed to the general cases,on which an efficie...     

Reliability Estimation of the Truncated Exponential Model

This paper deals with the minimum variance unbiased estimation of the reliability function of the one parameter exponential model, truncated from above at a known point, on the basis of a full and a censored sample. The techniques used are those of Barton [2], Laurent [9], and Basu [3] combined with results by Tukey [17] and Smith [14]. The derivations are direct applications of these techniques.     

On the upper truncated Weibull distribution and its reliability implications

The characteristics and application of the truncated Weibull distribution are studied in this paper. This distribution is applicable to the situation where the test data are bounded in an interval because of test conditions, cost and other restrictions. An important property of the truncated Weibull distribution is that it can have bathtub-shaped failure rate function. In this paper, the parametric analysis and parameter estimation methods of the distribution are investigated. Both the graphical approach and the maximum likelihood estimation are considered. The applicability of this distribution to modeling lifetime data is illustrated by an example and the results of comparisons to other competitive models in modeling the given data are also presented. Moreover, the possible application of the distribution to modeling component or system failure is discussed.     

Desingularized meshless method for solving Laplace equation with over-specified boundary conditions using regularization techniques

The desingularized meshless method (DMM) has been successfully used to solve boundary-value problems with specified boundary conditions (a direct problem) numerically. In this paper, the DMM is applied to deal with the problems with over-specified boundary conditions. The accompanied ill-posed problem in the inverse problem is remedied by using the Tikhonov regularization method and the truncated singular value decomposition method. The numerical evidences are given to verify the accuracy of the solutions after comparing with the results of analytical solutions through several numerical examples. The comparisons of results using Tikhonov method and truncated singular value decomposition method are also discussed in the examples.     

Minimum Variance Unbiased Estimation of Reliability for the Truncated Exponential Distribution

This note derives the unique minimum variance unbiased estimate (MVUE) of the reliability function associated with the one-parameter exponential distribution which is truncated from above at a known point using the method of integral transforms.     

Modulation of Truncated Periodic Targets in Partially Coherent Light

Formulae have been developed for computing the diffraction images of partially coherent truncated one-dimensional periodic targets. The modulations in the images of these objects are compared with those of an infinite cycle target. The intensity distributions in the limiting case of coherent light imagery are also shown. Both sine-wave and square-wave targets have been considered.     

Tables for Maximum Likelihood Estimates: Singly Truncated and Singly Censored Samples

In a previous paper in Technometrics, Vol. 1, 1959, the author derived the maximum liklihood estimates of the mean and variance for simply truncated or simply censored samples drawn from a Normal distribution. This paper extends considerably the tables originally published, and contains a further worked example.     

A Binomial Error Model with a Truncated Latent Distribution and its Application

Behaviormetrika - A binomial error model which has a truncated beta distribution as its latent trait distribution is proposed for the analysis of test scores. This model can be used when the...     

复合材料层合开顶扁球壳在集中冲击下的非线性动力屈曲

研究了具有刚性中心的复合材料层合开顶扁球壳在中心集中冲击载荷作用下的非线性动力屈曲问题。通过增加横向转动惯量项得到中心集中冲击下复合材料层合开顶扁球壳非线性稳定性的控制方程，采用Galerkin方法得到以刚性中心位移表达的冲击动力响应方程，并用Runge-Kutta方法进行数值求解，应用Budiansky-Roth准则（简称B—R准则）确定冲击屈曲的临界荷载；讨论了壳体几何尺寸对复合材料层合开顶扁球壳冲击屈曲的影响。     

Buckling of functionally graded conical panels under mechanical loads

This paper presents an analytical approach to investigate the linear buckling of truncated conical panels made of functionally graded materials and subjected to axial compression, external pressure and the combination of these loads. Material properties are assumed to be temperature-independent, and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of constituents. Equilibrium and linear stability equations in terms of displacement components for conical panels are derived by using the classical thin shell theory. Approximate analytical solutions are assumed to satisfy simply supported boundary conditions and Galerkin method is applied to obtain closed-form relations of bifurcation type buckling loads. An analysis is carried out to show the effects of material and geometrical properties and combination of loads on the linear stability of conical panels.     

四边简支方形幕壳的基频计算

本文引用А.Г.Назаров关于用转折角θ表示脉冲曲率的建议,推导出四边简支方形幕壳基频的近似理论计算公式。同时在大量模型试验基础上,推导出半经验公式。前者在幕角α_0≤20°,顶跨比 b/a≥0.5的范围内,后者在幕角α_o≤30°,顶跨比 b/a≥0.25的范围内,与实验数据对比,误差不超过5%,故可作为工程设计参考。     

Simplified Estimators for the Normal Distribution When Samples Are Singly Censored or Truncated

Easily computed estimates of the mean and variance of a Normal distribution obtained from samples which are truncated or censored are described. The estimates require only a single auxiliary function which is conveniently tabulated. Worked examples are given for sample data subject to left and right truncation. Additional examples are given for left and right censoring for the two cases in which either the point of censoring is fixed or the number of censored items is known.