Estimating a transformation and its effect on Box-CoxT-ratio

This article concernsi) the stochastic behavior of the Box-Cox transformation estimator andii) the effect of estimating a transformation on the Box-CoxT-ratio used for the post-transformation analysis. It is shown that the transformation estimator depends on three factors: the model structure, the mean-spread and the error standard deviation σ₀. In general, a structured model is able to estimate the transformation very well; an unstructured model can do well also unless the mean-spread and σ₀ are both small; and a one-mean mode can give a poor-estimate if σ₀ is small. When the sample is not large, it is shown that the unconditional effect of estimating a transformation on the Box-CoxT-ratio is generally small, and the “conditional” effect is also negligible in most of the situations except the case of one-way ANOVA with small σ₀. Extensive Monte Carlo simulations are performed to support the theoretical findings.     

一种非高斯随机振动过程数值模拟方法

目的 考虑真实随机振动的非高斯特性,提出一种根据已知信息生成与其相符的非高斯随机振动过程的数值模拟方法。方法 基于均值、方差、偏斜度、峭度及功率谱密度函数（或自相关函数）等约束条件,对非高斯随机振动进行模拟。根据功率谱获取非高斯过程的自相关矩阵;通过Hermite多项式的正交性质和多项式混沌展开方法推导出的公式,构造满足标准正态分布随机过程的协方差矩阵,并对其进行谱分解和主成分分析;最后,利用Karhunen-Loeve展开和多项式混沌展开来表示所模拟的非高斯振动过程。结果 随着采样点个数的增加,实测数据与模拟数据之间的误差越来越小,该方法具有较好的模拟精度。结论 应用多项式混沌展开、Karhunen-Loeve展开以及蒙特卡洛等方法,可生成非高斯随机振动过程,并得到准确有效的各项统计参数模拟值。     

Non-Gaussian simulation using Hermite polynomial expansion: convergences and algorithms

Mathematical justifications are given for a Monte Carlo simulation technique based on memoryless transformations of Gaussian processes. Different types of convergences are given for the approaching sequence. Moreover an original numerical method is proposed in order to solve the functional equation yielding the underlying Gaussian process autocorrelation function.     

A spectral representation based model for Monte Carlo simulation

A new model is proposed for generating samples of real-valued stationary Gaussian processes. The model is based on the spectral representation theorem stating that a weakly stationary process can be viewed as a superposition of harmonics with random properties. The classical use of this theorem for Monte Carlo simulation is based on models consisting of a superposition of harmonics with fixed frequencies but random amplitude and phase. The resulting samples have the same period depending on the discretization of the frequency band. In contrast, the proposed model consists of a superposition of harmonics with random amplitude, phase, and frequency so that different samples have different periods depending on the particular sample values of the harmonic frequencies.

A band limited Gaussian white noise process is used to illustrate the proposed Monte Carlo simulation algorithm and demonstrate that the estimates of the covariance function based on the samples of the proposed model are not periodic.     

Capacity investment decision by Monte Carlo approach in a cooperation network

This paper proposes a Monte Carlo approach to make the capacity investment decision. The environment concerns the capacity expansion issue for independent plants operating in a collaborative network. The plants that compose the network can share capacity through a negotiation protocol in order to balance under and over utilisation due to the customer demand. The plants apply the capacity expansion process following a periodic review policy. The generic plant makes the decision using a Monte Carlo approach that takes into account the information of the plant and the information of the collaboration with the plants of the network. The Monte Carlo simulator provides the information to each plant to support the capacity investment decision. The proposed approach is compared with a case characterised by information sharing among the plants proposed in literature and a case without information sharing. A simulation environment based on the JAVA package has been developed in order to test the approach in several market conditions. Several customer demand scenarios have been tested. The simulation results highlight these main findings: the robustness of the proposed approach; the reduction of the capacity investment keeping the same level of total profit performance; and the higher utilisation of the cooperation with the other plants of the network.     

一种新的散射电子空间输运坐标转换方法

提出一种新的随动坐标系矢量转换方法，给出用于转换散射电子空间输运坐标的矩阵方程，该方程具有递推的形式，计算方便，并且只涉及乘法运算，不会引起计算上的困难，将其用于PMMA－Si中电子散射过程的Monte Carlo模拟，结果表明可以有效节约机时，提高模拟效率，明显优于习惯上使用的静态坐标系方程。     

Tables for a Treatments Versus Control Multiple Comparisons Sign Test

Tables are presented for a multiple comparisons sign test comparing each treatment with a control. An illustration of the test procedure is provided, and the tables are also used to construct non-parametric joint confidence intervals. It is also shown how t.o find the per-comparison error rate for a given experimentwise error rate and vice versa.     

A multi-failure additive dependability model for transit system effectiveness analysis

Dependability has been recognized in the transportation reliability literature as an effective measure of transit system service quality. Dependability models link system dependability with reliability and maintainability characteristics of subsystems, incorporating special operating characteristics and recovery policy from failure of each particular transit system. In this paper a new transit system dependability model is proposed, which considers the possibility that a passenger may be delayed by the occurrence of more than one failure in a trip. The mathematical difficulties associated with the algebra of random variables are overcome by using the Monte Carlo method. The results of the proposed model are compared with those relative to different modelling approaches in the literature, by applying the model to a common test scenario.     

A stochastic simulation method for uncertainty quantification in the linearized inverse conductivity problem

This paper considers the inverse problem in electrical impedance tomography with non‐informative prior information on the required conductivity function. The problem is approached with a Newton‐type iterative algorithm where the solution of the linearized approximation is estimated using Bayesian inference. The novelty of this work focuses on maximum a posteriori estimation assuming a model that incorporates the linearization error as a random variable. From an analytical expression of this term, we employ Monte Carlo simulation in order to characterize its probability distribution function. This simulation entails sampling an improper prior distribution for which we propose a stable scheme on the basis of QR decomposition. The simulation statistics show that the error on the linearized model is not Gaussian, however, to maintain computational tractability, we derive the posterior probability density function of the solution by imposing a Gaussian kernel approximation to the error density. Numerical results obtained through this approach indicate the superiority of the new model and its respective maximum a posteriori estimator against the conventional one that neglects the impact of the linearization error. Copyright © 2011 John Wiley & Sons, Ltd.     

A plausible strategy for modeling fatigue life variation

In this paper stochastic modeling is used to predict fatigue life uncertainty by simulating small variations in strain-life material constants. The Monte Carlo method,^[1] using either known cumulative distribution functions (CDFs) for the material constants and/or postulated CDFs, provides the mechanism to generate a set of failure data. These data are analyzed, using ordinary statistical techniques, to develop the Weibull CDF for cycles to failure. It is seen that small variations (∼±15%) in values of the strain-life constants result in large variations (∼600%) in predicted fatigue life at moderate strain. The often-observed phenomenon that spread in fatigue data is greater at lower strain is also described by the stochastic model.     

A Distribution‐free Control Chart for the Joint Monitoring of Location and Scale

Traditional statistical process control for variables data often involves the use of a separate mean and a standard deviation chart. Several proposals have been published recently, where a single (combination) chart that is simpler and may have performance advantages, is used. The assumption of normality is crucial for the validity of these charts. In this article, a single distribution‐free Shewhart‐type chart is proposed for monitoring the location and the scale parameters of a continuous distribution when both of these parameters are unknown. The plotting statistic combines two popular nonparametric test statistics: the Wilcoxon rank sum test for location and the Ansari–Bradley test for scale. Being nonparametric, all in‐control properties of the proposed chart remain the same and known for all continuous distributions. Control limits are tabulated for implementation in practice. The in‐control and the out‐of‐control performance properties of the chart are investigated in simulation studies in terms of the mean, the standard deviation, the median, and some percentiles of the run length distribution. The influence of the reference sample size is examined. A numerical example is given for illustration. Summary and conclusions are offered. Copyright © 2011 John Wiley & Sons, Ltd.     

Decision making in health care using robust parameter design with conditions‐based selection of regression estimators

Health care professionals often use regression methods to quantitatively describe the functional relationships between predictors and outcomes. However, little research investigates the appropriateness of tool application for response‐surface‐based design of experiments, the choice of regression estimators under different environments, and the impact of the determination of optimum conditions, or optimal factor‐level settings, to achieve desirable target outcomes. Robust parameter design (RPD) is an established methodology for determining optimum conditions for a process to achieve specified process targets while minimizing variability of the outcomes. Underlying assumptions for RPD modeling and process conditions should be taken into account when selecting a regression estimator for developing fitted models. If these assumptions are incorrect, then a direct use of estimates obtained has the potential to be problematic, and the results may be potentially catastrophic, particularly when applied to the health care field. Many approaches to RPD in existing literature use ordinary least squares to obtain response functions by assuming normality and moderate variability in the underlying process. Given that some biologic processes are often highly variable and inherently asymmetric, a conditions‐based approach for the selection of a regression estimate technique needs to be explored. This paper examines alternative approaches to regression estimation when the process data indicates that asymmetry or a high degree of process variability exists. The performance of select alternative regression methods is compared using Monte Carlo simulation and numerical analysis.     

Space–time extreme value statistics of a Gaussian random field

This paper describes a new method for estimating the extreme values of a Gaussian random field in both space and time. The method relies on the use of data provided by measurement or Monte Carlo simulation combined with a technique for estimating the extreme value distribution of a recorded time series. The time series in question represents the spatial extremes of the random field at each point in time. The time series is constructed by sampling the available realization of the random field over a suitable grid defining the domain in question and extracting the extreme value. This is done for each time point of a suitable time grid. Thus, the time series of spatial extremes is produced. This time series provides the basis for estimating the extreme value distribution using available techniques for time series, which results in an accurate practical procedure for solving a very difficult problem. This is demonstrated by comparison with the results obtained from analytically derived expressions for the extreme values of a Gaussian random field. Properties of these analytical formulas are also discussed.     

A new model with non-spherical interactions for dense polymer systems

Summary We introduce a new general model for the simulation of dense macromolecular systems. It consists of basic ellipsoidally shaped units stringed together to form chains, including branched and side chains. The ellipsoidally shaped unit can vary in its principal axes, allowing for flexible modeling of a chain. The variation in the main principal axis is used for the intramolecular potential of the bond type. Intramolecular units interact through a harmonic bond-angle potential and the intermolecular interaction is modelled by a confocally decreasing Lennard-Jones potential. We present the model for the special case of a polycarbonate and indicate the generalization to other cases.     

A polynomial dimensional decomposition for stochastic computing

This article presents a new polynomial dimensional decomposition method for solving stochastic problems commonly encountered in engineering disciplines and applied sciences. The method involves a hierarchical decomposition of a multivariate response function in terms of variables with increasing dimensions, a broad range of orthonormal polynomial bases consistent with the probability measure for Fourier‐polynomial expansion of component functions, and an innovative dimension‐reduction integration for calculating the coefficients of the expansion. The new decomposition method does not require sample points as in the previous version; yet, it generates a convergent sequence of lower‐variate estimates of the probabilistic characteristics of a generic stochastic response. The results of five numerical examples indicate that the proposed decomposition method provides accurate, convergent, and computationally efficient estimates of the tail probability of random mathematical functions or the reliability of mechanical systems. Copyright © 2008 John Wiley & Sons, Ltd.     

A new methodology for Bayesian history matching using parallel interacting Markov chain Monte Carlo

This paper presents an innovative application of a new class of parallel interacting Markov chains Monte Carlo to solve the Bayesian history matching (BHM) problem. BHM consists of sampling a posterior distribution given by the Bayesian theorem. Markov chain Monte Carlo (MCMC) is well suited for sampling, in principle, any type of distribution; however the number of iteration required by the traditional single-chain MCMC can be prohibitive in BHM applications. Furthermore, history matching is typically a highly nonlinear inverse problem, which leads in very complex posterior distributions, characterized by many separated modes. Therefore, single chain can be trapped into a local mode. Parallel interacting chains is an interesting way to overcome this problem, as shown in this paper. In addition, we presented new approaches to define starting points for the parallel chains. For validation purposes, the proposed methodology is firstly applied in a simple but challenging cross section reservoir model with many modes in the posterior distribution. Afterwards, the application to a realistic case integrated to geostatistical modelling is also presented. The results showed that the combination of parallel interacting chain with the capabilities of distributed computing commonly available nowadays is very promising to solve the BHM problem.     

Monitoring process variation using modified EWMA

A new control chart, namely, modified exponentially weighted moving average (EWMA) control chart, for monitoring the process variance is introduced in this work by following the recommendations of Khan et al.¹⁵ The proposed control chart deduces the existing charts to be its special cases. The necessary coefficients, which are required for the construction of modified EWMA chart, are determined for various choices of sample sizes and smoothing constants. The performance of the proposed modified EWMA is evaluated in terms of its run length (RL) characteristics such as average RL and standard deviation of RL. The efficiency of the modified EWMA chart is investigated and compared with some existing control charts. The comparison reveals the superiority of proposal as compared with other control charts in terms of early detection of shift in process variation. The application of the proposal is also demonstrated using a real-life dataset.     

真空校准室内分子流场分布的理论分析与计算

在动态流量校准系统中,气体分子流场分布非均匀性是造成被校规测量值出现偏差的原因,也是校准装置系统误差的来源。介绍校准室内分子流场分布的理论计算方法,这种方法不仅能分析分子流场分布的非均匀性,还能够直接计算被校规室内的分子密度,给出规室内分子密度与进入校准室气体流量之间的函数关系。计算时考虑了校准室的几何结构,最大限度的减小了校准室结构设计对分子流场分布带来的影响。对返流比β和有效抽速Seff的计算方法,为动态流量校准装置系统参数的蒙特卡罗模拟提供了理论依据。     

A new transformation technique for evaluating nearly singular integrals

Accurate evaluation of nearly singular integrals plays an important role in the overall accuracy of the Boundary Element Method (BEM). A new approach for the evaluation of nearly singular integrals particularly those with severe near singularity is described in this paper. This method utilizes a degenerate mapping to first reduce near singularity and then employs a variable transformation to further smooth out the resultant integrand. The accuracy and efficiency of the method are demonstrated through several examples that are commonly encountered in the applications of the BEM. Comparison of this method with some of the existing methods is also presented.     

A particle code for plasma technological applications

The 2D Direct Simulation Monte Carlo code LasVegas was originally developed and used for the simulation of atmospheric re-entry and the flow around plasma wind tunnel probes. This code is reviewed regarding its applicability to appropriate plasma technological applications. The main DSMC theory and the code structure, features and properties are described in order to classify the LasVegas code in regard to these applications. General restrictions, model uncertainties and geometrical considerations of the DSMC method itself as well as of the LasVegas code put the focus on the vacuum spray process. As proof of concept, results of a supersonic free stream simulation in a vacuum chamber with typical inflow properties are presented and discussed. Appropriate code extensions such as the flow-particle interaction, ionization model and parallel computation capability were identified, thus indicating future numerical works.