A Unified Approach for Modeling and Designing Attribute Sampling Plans for Monitoring Dependent Production Processes

In this paper, we consider a probabilistic model to represent some general dependent production processes and present a unified approach for designing attribute sampling plans for monitoring the ongoing production process. This model includes the classical iid model, independent model, Markov-dependent model and previous-sum dependent model, to mention a few. Some important properties of this model are established. We derive the recurrence relations for the probability distribution of the sum of n consecutive characteristics observed from the process. Using these recurrence relations, we present efficient algorithms for designing optimal single and double sampling plans for attributes, for monitoring the ongoing production process. Our algorithmic approach, which uses effectively the recurrence relations, yields a direct and an exact method, unlike many approximate methods adopted in the literature. Several interesting examples concerning specific models are discussed and a few tables for some special cases are also presented. It is demonstrated that the optimal double sampling plans lead to about 42% reduction in average sample number over the single sampling plans for process monitoring. AMS 2000 Subject Classifications: Primary 62P30; Secondary 62E15, 65C60     

高寒草甸地区陆面过程观测及耦合模式研究

对海北高寒草甸地区水热传输过程进行了系统观测,特别考虑了叶片气孔为非饱和水汽条件下的交换情况,结合修正的根系吸水公式,发展了一个多层陆气耦合模式．利用该模式对中国科学院海北高寒草甸生态试验站地区矮嵩草草甸陆气水热交换进行了数值模拟,分析了湍流交换的物理过程,给出了沿高度分布的各物理量．模拟结果与实测值吻合较好．     

A Class of Numerical Algorithms, Conservative at Stabilization, for Modeling Transport Processes

We consider a class of effective two-step symmetrized algorithms for numerical modeling of processes defined by boundary-value problems for transport equations with boundary conditions of the third kind in cases of various approximations of the convection terms of the equation and different ways of writing the difference schemes with respect to time. We prove that the algorithms are unconditionally stable and show that they are economical. We find an approximation for physical conservation laws on grid sets and prove that the difference algorithms are conservative when the process stabilizes.     

CriSP: A Tool for Bump Hunting

We propose a test of multimodality of regression functions and their derivatives. The test statistic is a critical smoothing parameter (CriSP), giving the minimum amount of smoothing necessary to force the regression function to satisfy the null hypothesis. The p values are computed via bootstrapping. Our idea is motivated by Silverman's test concerning the number of modes in the density function. Simulation studies indicate that the test works well, even when testing for bumps in the derivative. We apply CriSP to children's growth data, to study the number of spurts of growth.     

两种液体交叉混合的建模问题

对两种液体的交叉离散混合及连续混合进行了讨论,分别建立了两种液体在等量或等速交叉离散混合条件下的递推数列及微分方程模型.     

CARTscans: A Tool for Visualizing Complex Models

We present CARTscans, a graphical tool that displays predicted values across a fourdimensional subspace. We show how these plots are useful for understanding the structure and relationships between variables in a wide variety of models, including (but not limited to) regression trees, ensembles of trees, and linear regressions with varying degrees of interactions. In addition, the common visualization framework allows diverse complex models to be visually compared in a way that illuminates the similarities and differences in the underlying methods, facilitates the choice of a particular model structure, and provides a useful check for implausible predictions of future observations in regions with little or no data.     

Infinitesimal Perturbation Analysis: A Tool for Simulation

Perturbation analysis is a technique that expedites the process of performing experiments on discrete-event simulation models. This makes it possible to derive sensitivity estimates from one computer execution of a simulation model. Infinitesimal perturbation analysis (IPA) is one class of algorithms used in perturbation analysis. In this paper, the techniques and algorithms used in simulation to perform infinitesimal perturbation analysis are examined. Each algorithm is discussed in detail, with comments concerning implementation problems and examples with experimental results for serial transfer lines. The results of this paper show that for simple systems, IPA can be easily implemented in a general-purpose simulation language such as SIMAN. Unfortunately, for any given system, parameter or performance measure, the algorithm used to generate the gradient may vary. Additionally, algorithms for more complex classes of problems do not yet exist. This problem hampers the current possibility of incorporating IPA into general-purpose simulation languages.     

工程管理的马尔可夫骨架过程建模

在以前,一个工程项目的进程的管理问题在各工段的施工时间为相互独立且都服从负指数分布的假设下通过一个网络图化为对一个马尔可夫链的控制和优化的研究.本文在一般情况下(放弃对各工程段的时间服从负指数分布的假设)把工程项目进程的管理问题化为对一个马尔可夫骨架过程的控制和优化问题.     

Towards Modeling the Curing Processes of Thermosets

This contribution presents a newly developed phenomenological model to describe the curing processes of thermosets undergoing small strain deformations [1]. The governing equations are derived from a number of physical and chemical assumptions. Some numerical examples demonstrate the model's capability to correctly represent the evolution of elastic and inelastic material properties as well as the volume shrinkage taking place during the curing process. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Weak Regeneration in Modeling of Queueing Processes

A survey of recent results on weak regeneration in queueing processes is given in which an embedded process of regeneration points is renewal, but unlike classical regeneration, a dependence between adjacent cycles is allowed. We develop a unified two-step approach to stability analysis based on a characterization of the limit behavior of the forward renewal time. This employs an extended construction (initially proposed by Foss and Kalashnikov [13]), which is widely used to transform an original one-dependent regenerative process into weakly regenerative one. It is shown that the approach simplifies stability analysis of many queuing processes. (The tightness of the queueing processes plays an important role in the proofs.) In particular, we consider both well-known classical queues and multi-server queues with regenerative input and non-identical servers. Included is a stability analysis of a feed-forward network with regenerative input and non-identical servers in the nodes.     

Modeling and Anomalous Cluster Detection for Point Processes Using Process Convolutions

We present a model using process convolutions, which describes spatial and temporal variations of the intensity of events that occur at random geographical locations. An inhomogeneous Poisson process is used to model the intensity over a spatial region with multiplicative spatial and temporal covariate effects. Temporal variation in the structure of the intensity is obtained by employing a time-varying process for the convolution. Use of a compactly supported kernel in the convolution improves the computational efficiency. Additionally, anomalous cluster detection in the event rates is developed based on exceedance probabilities. The methods are demonstrated on data of major crimes in Cincinnati during 2006. Supplementary materials for this article are available online.     

A Review of Goal Programming: A Tool for Multiobjective Analysis

Goal programming is a relatively new tool that has been proposed as a model and approach for the analysis of problems involving multiple, conflicting objectives. In this paper we examine this model, its history, methods of solution and list some recent applications. Hopefully, the reader will appreciate the rather general nature of the field, along with the relative simplicity of model development and solution.     

On Modeling Change Points in Non-Homogeneous Poisson Processes

Failures in repairable systems are often described by means of non-homogeneous Poisson processes, identified by their intensity and mean value functions. Intervention on the systems are likely to modify their reliability, and changes in intensities and mean value functions are therefore induced. We consider different scenarios in which interventions take places and propose models describing each of them. Bayesian analyses, relying on Markov-chain Monte Carlo methods, are illustrated along with applications to simulated and real, widely-known, data.     

Mathematical Modeling of Czochralski Type Growth Processes for Semiconductor Bulk Single Crystals

This paper deals with the mathematical modeling and simulation of crystal growth processes by the so-called Czochralski method and related methods, which are important industrial processes to grow large bulk single crystals of semiconductor materials such as, e. g., silicon (Si) or gallium arsenide (GaAs) from the melt. In particular, we investigate a recently developed technology in which traveling magnetic fields are applied in order to control the behavior of the turbulent melt flow. Since numerous different physical effects like electromagnetic fields, turbulent melt flows, high temperatures, heat transfer via radiation, etc., play an important role in the process, the corresponding mathematical model leads to an extremely difficult system of initial-boundary value problems for nonlinearly coupled partial differential equations. In this paper, we describe a mathematical model that is under use for the simulation of real-life growth scenarios, and we give an overview of mathematical results and numerical simulations that have been obtained for it in recent years.     

Dissimilarity Plots: A Visual Exploration Tool for Partitional Clustering

For hierarchical clustering, dendrograms are a convenient and powerful visualization technique. Although many visualization methods have been suggested for partitional clustering, their usefulness deteriorates quickly with increasing dimensionality of the data and/or they fail to represent structure between and within clusters simultaneously. In this article we extend (dissimilarity) matrix shading with several reordering steps based on seriation techniques. Both ideas, matrix shading and reordering, have been well known for a long time. However, only recent algorithmic improvements allow us to solve or approximately solve the seriation problem efficiently for larger problems. Furthermore, seriation techniques are used in a novel stepwise process (within each cluster and between clusters) which leads to a visualization technique that is able to present the structure between clusters and the micro-structure within clusters in one concise plot. This not only allows us to judge cluster quality but also makes misspecification of the number of clusters apparent. We give a detailed discussion of the construction of dissimilarity plots and demonstrate their usefulness with several examples. Experiments show that dissimilarity plots scale very well with increasing data dimensionality.

Supplemental materials with additional experiments for this article are available online.     

A Markov Property for Set-Indexed Processes

We consider a type of Markov property for set-indexed processes which is satisfied by all processes with independent increments and which allows us to introduce a transition system theory leading to the construction of the process. A set-indexed generator is defined such that it completely characterizes the distribution of the process.     

Mathematical Modeling of Magnetohydrodynamic Processes in an Aluminum Electrolyzer

We model the electrolysis of aluminum in specific electrolysis baths. A model of the physical process is proposed, allowing for the specific bath design, including the state of the bottom surface. The mathematical model utilizes the information capabilities of the Navier–Stokes equations written for the metal and the electrolyte media. The multidimensional system of equations enables us to consider the magnetohydrodynamic processes in two media and the interaction of the media. The problem is solved numerically. The calculations simulate the interface dynamics and the distribution of velocities and currents in the middle layer in both media. The numerical results are compared with physical experiments.     

Multiphase FEM Modeling of Infiltration Processes in Cohesionless Soils

The aim of this work is to develop a continuum multiphase model to describe infiltration processes for cohesionless soils. For this purpose, a Representative Volume Element (RVE) is considered and described by the continuum mixture theory extended by the concept of volume fractions (Theory of Porous Media – TPM). The thermodynamically consistent TPM is a macroscopical multiphase modeling approach, extended from classical single-phase continuum mechanics. Futhermore a 1-dim example for an infiltration problem is presented. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)