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In acceptance sampling, the hypergeometric operating characteristic (OC) function (so called type-A OC) is used to be approximated by the binomial or Poisson OC function, which actually reduce computational effort, but do not provide suffcient approximation results. The purpose of this paper is to examine binomial- and Poisson-type approximations to the hypergeometric distribution, in order to find a simple but accurate approximation that can be successfully applied in acceptance sampling.

The authors present a new binomial-type approximation for the type-A OC function, and derive its properties. Further, the authors compare this approximation via an extensive numerical study with other common approximations in terms of variation distance and relative efficiency under various conditions on the parameters including limiting cases.

The introduced approximation generates best numerical results over a wide range of parameter values, and ensures arithmetic simplicity of the binomial distribution and high accuracy to meet requirements regarding acceptance sampling problems. Additionally, it can considerably reduce the computational effort in relation to the type-A OC function and therefore is strongly recommended for calculating sampling plans.

The newly presented approximation provides a remarkably close fit to the type-A OC function, is discrete and needs no correction for continuity, and is skewed in the same direction by roughly the same amount as the exact OC. Due to less factorials, this OC in general involves lower powers than the type-A OC function. Moreover, the binomial-type approximation is easy to fit to the conventional statistical computing packages.

Gives introductory remarks about chapter 1 of this group of 31 papers, from ISEF 1999 Proceedings, in the methodologies for field analysis, in the electromagnetic community. Observes that computer package implementation theory contributes to clarification. Discusses the areas covered by some of the papers ‐ such as artificial intelligence using fuzzy logic. Includes applications such as permanent magnets and looks at eddy current problems. States the finite element method is currently the most popular method used for field computation. Closes by pointing out the amalgam of topics.

Exponential distribution is widely used in reliability and maintainability studies although it is well known that the constant failure rate assumption may not be valid. The purpose of this paper is to investigate the use of exponential distribution as an approximation. In fact, for components undergoing regular maintenance or replacement, the exponential assumption can be acceptable. In this paper, the exponential approximation for regularly maintained Weibull component is studied. The approximated exponential distribution using the average failure rate is compared with the exact reliability. The asymptotic relative error is derived, which can be used to adjust the exponential approximation when needed. Based on the framework of exponential approximation for Weibull distributed components, the problems of decision‐making regarding the optimal maintenance time and spare allocation are also addressed.

Discusses the 27 papers in ISEF 1999 Proceedings on the subject of electromagnetisms. States the groups of papers cover such subjects within the discipline as: induction machines; reluctance motors; PM motors; transformers and reactors; and special problems and applications. Debates all of these in great detail and itemizes each with greater in‐depth discussion of the various technical applications and areas. Concludes that the recommendations made should be adhered to.

This paper aims to describe a numerical procedure for approximating the potential distribution for a harmonic current point source, which is either buried in horizontally stratified multilayer earth, or positioned in the air. The procedure is very efficient and general. The total number of layers and the source position in relation to the medium model layers are completely arbitrary.

The efficiency of the computation procedure is based on the successful application of the numerical approximation of two kernel functions of the integral expression for the potential distribution within an arbitrarily chosen layer of the medium model. Each kernel function of the observed layer is approximated using a linear combination of 15 real exponential functions. Using these approximations and the analytical integration based on the Weber integral, a simple expression for numerical approximation of potential distribution within boundaries of the observed medium layer is given. Potential retardation is taken into account approximately.

The numerical procedure developed for the approximation of potential distribution for a harmonic current point source, which is positioned arbitrarily in air or in horizontally stratified multilayer earth, is efficient, numerically stable and generally applicable.

Numerical model developed for the harmonic current point source is the basis of a wider numerical models for computation of the harmonic and transient fields of earthing system, which consists of earthing grids buried in horizontally stratified multilayer earth and metallic structures in the air.

This is efficient and numerically stable frequency dependent harmonic current point source model. Potential retardation, which has been neglected at the first step of the approximation, is subsequently added to the potential expression in such a way that the Helmholtz differential equation has been approximately solved without introducing the Sommerfeld integrals.

To present numerical approaches to the solution of physically coupled non‐linear problems, which frequently happen to be characterized by their multi‐domain character.

By adopting coupled solution strategies a considerable attention is devoted, in order to obtain a computationally efficient numerical algorithm, to the selection of appropriate space and time discretization, as well as to a proper discrete approximation method used.

Coupling of two methods, the finite element method and the boundary element method, respectively, has proved to be computationally exceedingly advantageous, particularly in case of moving domains.

As specific case studies computer simulation of an induction heating problem and a mushy‐state forming problem are considered. A thorough discussion on the coupling effects, characterizing the evolutions of respective physical quantities' fields, is given, and their impact on those evolutions is identified.

This paper presents efficient numerical strategies for the solution of a certain class of multi‐physics and multi‐domain problems.

Most documentation systems allocate a variable number of descriptors to their documents. From a consideration of indexing as a stochastic process it is suggested that the distribution of indexing depth in such a system might represent samples of a (truncated) mixed Poisson process. Examination of five different systems showed that indexing depth does appear to be distributed in this manner, since a reasonable fit to negative binomial distributions can be made statistically. Factors in the art of indexing which influence the distribution are discussed. As a first approximation the distribution of indexing depth, i, of a system, or of any subset of descriptors in it, is simple Poisson, p(i) = e−m(mi/i!), where m is the average depth of indexing. The results contradict previous reports that a log‐normal distribution of indexing depth is to be expected.

The main purpose of this paper is to consider the role of discretization of random variables in analyzing statistical tolerancing, and to propose a new discretizing method along with a study on its usefulness.

The approach for discretization of a continuous distribution is based on the concept of moment equalization with the original random variable, conditionally given a set of points of realization. For the purpose of demonstration the normal distribution has been discretized into seven points. Application of the discretization method in approximating the distribution/survival function of a complex system has also been studied. Numerical analysis on two important engineering items has been undertaken and the closeness between the values of the distribution/survival functions obtained by simulation and the proposed method has been examined to indicate the advantage of the proposed approach.

A comparative study with the earlier reported discretizing methods indicates that the proposed method, which is easy to implement, provides better results for most of the cases studied in this work.

Using the proposed approach one can approximate the probability distribution of a complex system with random component values, which cannot be analytically expressed.

This paper is able to provide a new direction in reliability management research, because it can be used for product design of many important engineering items such as solid‐shaft, hollow cylinder, torsion bar, I‐beam etc.

This research gives a new linear method of discretization. It gives better results than the existing discretization methods of Experimental design, Moment equalization, and Discrete Concentration for reliability (survival probability) determination of solid‐shaft and power resistor.

To present a new direct solution method for the Boltzmann‐Poisson system for simulating one‐dimensional semiconductor devices.

A combination of finite difference and finite element methods is applied to deal with the differential operators in the Boltzmann transport equation. By taking advantage of a piecewise polynomial approximation of the electron distribution function, the collision operator can be treated without further simplifications. The finite difference method is formulated as a third order WENO approach for non‐uniform grids.

Comparisons with other methods for a well‐investigated test case reveal that the new method allows faster simulations of devices without losing physical information. It is shown that the presented model provides a better convergence behaviour with respect to the applied grid size than the Minmod scheme of the same order.

The presented direct solution methods provide an easily extensible base for other simulations in 1D or 2D. By modifying the boundary conditions, the simulation of metal‐semiconductor junctions becomes possible. By applying a dimension by dimension approximation models for two‐dimensional devices can be obtained.

The new model is an efficient tool to acquire transport coefficients or current‐voltage characteristics of 1D semiconductor devices due to short computation times.

New grounds have been broken by directly solving the Boltzmann equation based on a combination of finite difference and finite elements methods. This approach allows us to equip the model with the advantages of both methods. The finite element method assures macroscopic balance equations, while the WENO approximation is well‐suited to deal with steep gradients due to the doping profiles. Consequently, the presented model is a good choice for the fast and accurate simulation of one‐dimensional semiconductor devices.

New iteration methods for the calculation of steady magnetic fields in saturable media are presented. These methods converge for any choice of initial approximation, that is they possess global convergence. The convergence conditions and the estimates of convergence rate of these methods are expressed in terms of the physical properties of ferromagnetic media. Each of the proposed methods is deliberately adapted to specific but typical saturation conditions. All these methods together cover the broad area of diverse saturation conditions encountered in practice. The construction and justification of these iteration methods are based on the physical concept of secondary sources and on some mathematical ideas and results arising in the overlapping area of mathematical physics and functional analysis.