Planning of Truncated Sequential Binomial Test via Relative Efficiency

A planning methodology is proposed for the sequential probability ratio test (SPRT) for the purpose of practical application. The SPRT is the most common acceptance test in the field of reliability and quality control. In it, the hypothesis is checked that the percentage of defective items does not exceed a specified value. Truncation is resorted to compensate for the absence of a limit on the test duration, but it complicates the planning process. Moreover, the discreteness and multidimensionality of the characteristics of such tests prevent their direct comparison and optimization. To remedy these drawbacks, quality features of the test are proposed, one of which—the relative efficiency—represents the ratio of the test's weighted average sample number till its stopping and its counterpart for the nontruncated SPRT. It facilitates solution of the problems in automatic planning of the test. Another important advantage of this relative efficiency is that it yields accurate and simple formulas for the stopping boundary. Besides, these formulas permit sound choice of the truncation level already at early stages of the planning process. A planner's algorithm and an industrial example are also included. The proposed methodology can also be applied to exponential SPRT. The advantages of tests based on the proposed methodology over those in IEC‐61123 (the binomial case) and IEC‐61124 (the exponential case) are demonstrated, and revision of the standards is recommended. Copyright © 2012 John Wiley & Sons, Ltd.     

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.     

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

As an extension to the singly truncated case, this article further examines a doubly truncated normal distribution. In this article, we consider both symmetric and asymmetric cases with two truncation points on the left and the right, and develop the tables of a truncated mean, a truncated variance, and a cumulative probability.     

Truncated Linear Gaussian Loss Integrals

The linear Gaussian (normal) loss integral is a well-known technique in economic risk analysis. This integral is easily evaluated with a loss table or standardized normal tables to find an expected cost. Modifications to this basic technique are shown in this paper which increase its versatility with little loss in applicational simplicity. These modifications include a truncation of the cost function and a connected series of linear cost segments. This series modification makes it possible to approximate virtually any nonlinear cost polynomial. Numerical demonstrations are shown.     

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...     

A Sequential Bounding Approach for Optimal Appointment Scheduling

This study is concerned with the determination of optimal appointment times for a sequence of jobs with uncertain durations. Such appointment systems are used in many customer service applications to increase the utilization of resources, match workload to available capacity, and smooth the flow of customers. We show that the problem can be expressed as a two-stage stochastic linear program that includes the expected cost of customer waiting, server idling, and a cost of tardiness with respect to a chosen session length. We exploit the problem structure to derive upper bounds that are independent of job duration distribution type. These upper bounds are used in a variation of the standard L-shaped algorithm to obtain optimal solutions via successively finer partitions of the support of job durations. We present new analytical insights into the problem as well as a series of numerical experiments that illustrate properties of the optimal solution with respect to distribution type, cost structure, and number of jobs.     

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.     

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。     

Sequential Phasemeters

The synthesis and the analysis of the sequential phasemeter based on the polarity?coincidence correlator is described. This phasemeter is devoted to harmonic signal phase-difference measurement in the presence of large random disturbances at the given-accuracy. The realization of the sequential phasemeter and some approximations that seem to be useful are presented as well.     

序列图象目标的一种特殊数字跟踪方法

介绍了在数，模检测相结合的电视跟踪器的一项关键技术－指寅区域的位置和大小的序列图象的实时捕获和处理，并以ＡＤＳＰ２１８１为核心实现了一实际的系统，分析了其中的关键硬件技术介绍了可编程器件ＥＰＬＤ在其中的应用，给出了实时采集处理的结果。     

A Sequential Inspection Plan for Markov Dependent Production Processes

Single sampling plans used for lot acceptance are modified for use in monitoring production processes which exhibit Markov dependence in quality attributes. An augmented Markov chain model is employed for the determination of plan characteristics. Plans for dependent processes are compared with those for independent processes through numerical computations.     

混流生产线车间布置的顺序矩阵方法

为节省混流生产车间的运行成本,通过扩展顺序矩阵模型和分析混流生产线,提出车间布局优化的顺序矩阵方法,并讨论了5种作业关系之间的运算规则,得出普遍适用的作业关系运算规则。     

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     

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。     

Sequential interpolation functions

In the present paper it is shown how to achieve special interpolation functions that can be applied to the finite element method, least squares methods or other related numerical techniques. We call these functions sequential interpolation functions since one of the main characteristics of this technique refers to the fact that the refinement of the solution does not require the redefinition of the interpolation funtions used in a previous step, as the case for instance in the FEM. The present theory and the FEM using an isoparametric element were compared for a plane stress problem. The results show that both have the same degree of accuracy. The choice of the sequential interpolation functions is easier than those used in the finite element formulation and the computer time was reduced by about 50 per cent.     

Sequential Factorial Estimation

Through the use of a “predictor-corrector” equation an experimenter may quickly determine the least squares estimates of all the coefficients in a polynomial model after the conclusion of each run, given that an initial set of orthogonal estimates of the coefficients is available. The analysis of variance may similarly be constructed at the conclusion of each added run. The predictor-corrector equation is subject to mild restrictions which are fully met in the usual application of the 2 ^k and 2 ^k–p factorial designs. Adaptation of the predictor-corrector equation to the case of complimentary blocks of two runs each is described. Examples are given.     

ASRSM: A Sequential Experimental Design for Response Surface Optimization

Most preset response surface methodology (RSM) designs offer ease of implementation and good performance over a wide range of process and design optimization applications. These designs often lack the ability to adapt the design on the basis of the characteristics of application and experimental space so as to reduce the number of experiments necessary. Hence, they are not cost‐effective for applications where the cost of experimentation is high or when the experimentation resources are limited. In this paper, we present an adaptive sequential response surface methodology (ASRSM) for industrial experiments with high experimentation cost, limited experimental resources, and high design optimization performance requirement. The proposed approach is a sequential adaptive experimentation approach that combines concepts from nonlinear optimization, design of experiments, and response surface optimization. The ASRSM uses the information gained from the previous experiments to design the subsequent experiment by simultaneously reducing the region of interest and identifying factor combinations for new experiments. Its major advantage is the experimentation efficiency such that for a given response target, it identifies the input factor combination (or containing region) in less number of experiments than the classical single‐shot RSM designs. Through extensive simulated experiments and real‐world case studies, we show that the proposed ASRSM method outperforms the popular central composite design method and compares favorably with optimal designs. Copyright © 2012 John Wiley & Sons, Ltd.     

A Bayesian Approach to Sequential Optimization based on Computer Experiments

Computer experiments are used frequently for the study and improvement of a process under study. Optimizing such process based on a computer model is costly, so an approximation of the computer model, or metamodel, is used. Efficient global optimization (EGO) is a sequential optimization method for computer experiments based on a Gaussian process model approximation to the computer model response. A long‐standing problem in EGO is that it does not consider the uncertainty in the parameter estimates of the Gaussian process. Treating these estimates as if they are the true parameters leads to an improper assessment of the precision of the approximation, a precision that is crucial to assess not only in optimization but in metamodeling in general. One way to account for these uncertainties is to use bootstrapping, studied by previous authors. Alternatively, some other authors have mentioned how a Bayesian approach may be the best way to incorporate the parameter uncertainty in the optimization, but no fully Bayesian approach for EGO has been implemented in practice. In this paper, we present a fully Bayesian implementation of the EGO method. The proposed Bayesian EGO algorithm is validated through simulation of noisy nonlinear functions and compared with the standard EGO method and the bootstrapped EGO. We also apply the Bayesian EGO algorithm to the optimization of a stochastic computer model. It is shown how a Bayesian approach to EGO allows one to optimize any function of the posterior predictive density. Copyright © 2014 John Wiley & Sons, Ltd.