A Copula Markov CUSUM Chart for Monitoring the Bivariate Auto‐correlated Binary Observations

Although in the statistical process control (SPC) literature, there are considerable number of researches related to the multivariates variables control charting (focusing on the variable quality characteristics), fewer investigations could be found regarding the multivariate attributes control charts (relying on the attribute quality characteristics). More specifically considering the multivariate attributes control charting, it would be more interesting to monitor the auto‐correlated data, since the real‐world processes usually include the data based on an auto‐correlation structure. Ignoring the auto‐correlation structure in developing a multivariate control chart increases the type I and type II errors simultaneously and consequently reduces the performance of the chart. The most important difficulty with developing multivariate attributes control charts is the absence of the joint distribution for the quality characteristics. This deficiency can be dispelled through the use of the copula approach for developing the joint distribution. In this paper, we use the Markov approach for modeling the auto‐correlated data. Then, the copula approach is used to make the joint distribution of two auto‐correlated binary data series. Finally, based on this joint distribution, we develop a cumulative sum (CUSUM) chart. Hence, the proposed chart is entitled the copula Markov CUSUM chart. The proposed control chart is compared with the most recent and effective existing one in the literature. Based on the average number of observations to signal (ANOS) measure, it is considered that the developed control chart performs better than the other one. In addition, a real case study related to two correlated diseases such as the Type 2 Diabetes Mellitus and the Obesity, in which each has an auto‐correlated structure, is investigated to verify the applicability of the control chart. Copyright © 2012 John Wiley & Sons, Ltd.     

On Enhanced Interquartile Range Charting for Process Dispersion

A careful monitoring of process dispersion is necessary to get optimum output from any process. Control charts are very important process monitoring tools of Statistical Process Control toolkit. Interquartile range (IQR) is a famous dispersion measure that is used to monitor process dispersion in quality control literature. In this study, a set of auxiliary information‐based Shewhart‐type IQR charts are proposed for efficient monitoring of process dispersion under bivariate normal, t and gamma distributed processes. The control structures of the proposed charts are developed, and their performances are evaluated in terms of Average Time to Signal (ATS), Average Extra Quadratic Loss and Average Ratio to ATS. Comparisons are made among different charts to establish their superiorities for a quicker detection of process changes. An illustrative example is also provided to elaborate the procedural details of the proposed IQR charts using a real data set. Copyright © 2013 John Wiley & Sons, Ltd.     

基于双变量泊松点过程的无线Ad Hoc网络的保密广播传输容量分析

本论文利用双变量泊松点过程对无线ad hoc广播网络和非法窃听网络共存的网络场景进行建模,运用随机几何工具,研究了无线ad hoc网络的保密广播传输容量,其定义为未发生窃听中断的广播发送节点密度、广播发送节点的相邻接收节点数量的平均值与保密速率的乘积.针对一般衰落和瑞利衰落信道条件,论文推导了造成保密中断的相邻窃听节点数量的平均值和保密广播传输容量的表达式.分析结果表明,与不存在相关性的网络场景相比,广播网络和窃听网络间的相关性会带来的保密广播传输容量的损失.     

Bayesian estimates of covariance components between lactation curve parameters and disease liability in Danish Holstein cows

In the present work, covariance components for milk yield and disease liability were estimated with bivariate random regression test-day sire models using a Bayesian approach and implemented via the Gibbs sampler. The data consist of 8075 first-parity Danish Holstein (DH) cows, from 1259 sires, performing in 57 herds from 1992 to 1997. Treatments associated with five different type of diseases were pooled into a single general disease liability for each cow. Two models were fitted to the data. First, using a bivariate model, milk yield is modeled via a random regression, and disease liability via a repeatablility model. Second, using a bivariate model, both milk yield and disease liability are modeled using random regressions. A comparison based on a Bayes factor provides very strong support for the bivariate random regression model. Posterior means of heritabilities for each of the traits were estimated for five different points in time throughout lactation. Across models, heritabilities for milk yield are lowest in the beginning of the lactation (0.19) and highest at the end of the lactation (0.35). Posterior means of heritabilities of disease liability range from 0.04 to 0.10 for test days, and is equal to 0.20 for the whole lactation. Heritability of persistency measures estimated from the two models are 0.20 and 0.21. Estimates of posterior means of genetic correlations between single test-day milk yield and single test-day disease liability are in the range of 0.31 to 0.57. The estimates of posterior mean and of the 95% posterior interval of the genetic correlation between persistency and (total) disease liability using the model with the highest posterior probability are -0.12 and (-0.44; 0.20), respectively. Even though the largest proportion of the posterior probability mass is spread along negative values of the correlation (indicating that individuals with a flatter lactation curve tend to have lower disease liability), a value of zero of the genetic correlation falls comfortably within the 95% posterior interval. Thus the prospects of reducing incidence of disease by manipulating persistency as defined in this work remain inconclusive.     

二维紧支撑正交多尺度函数的构造

提出了由二维单正交的尺度函数构造二维紧支撑正交的多尺度函数的构造方法,并给出相应组合系数应满足的条件.研究表明,二维正交多尺度函数可由所给二维单正交的尺度函数的线性组合而成,这种由正交的单尺度函数构造出来的多尺度函数不是惟一的,但其平移伸缩构成的空间与相应单尺度函数的平移伸缩生成的子空间相同.     

Bivariate population balance model of ethanol‐fueled spray combustors

We present a bivariate population balance‐based formulation of the performance of well‐mixed adiabatic combustors fed by ethanol (EtOH)‐containing sprays of prescribed droplet size distribution (DSD) and composition. Our historically interesting example is the fuel‐cooled V‐2 chemical rocket—using 75 wt % EtOH + H₂O solution, and oxidizer O₂(L). Of special interest are the predicted combustion “intensity” (GW/m³) and efficiency (EtOH fraction vaporized) at each ratio of combustor mean residence time to feed‐droplet characteristic vaporization time. Our formulation exploits a quasi‐steady, gas‐diffusion‐controlled individual droplet evaporation rate law, and the method‐of‐characteristics to solve the associated first‐order population balance partial differential equation governing the joint distribution function n(m₁, m₂) of the fuel spray exiting such a chamber, where m₁ = EtOH mass/droplet, and m₂ = H₂O mass/droplet. Besides the combustor efficiency and intensity, this bivariate distribution function enables predictions of corresponding unconditional DSD, and the joint distribution function(diam., droplet temperature)—perhaps measurable. Our numerically exact formulation/results also provide valuable test cases for convenient approximate methods (bivariate moment and spectral/weighted residual) to predict these “correlated” bivariate distribution functions in more complex situations. © 2011 American Institute of Chemical Engineers AIChE J, 2011     

Image denoising with anisotropic bivariate shrinkage

This paper presents a novel image denoising algorithm based on the modeling of wavelet coefficients with an anisotropic bivariate Laplacian distribution function. The anisotropic bivariate Laplacian model not only captures the child-parent dependency between wavelet coefficients, but also fits the anisotropic property of the variances of wavelet coefficients in different scales of natural images. With this statistical model, we derive a closed-form anisotropic bivariate shrinkage function in the framework of Bayesian denoising and a new image denoising approach with local marginal variance estimation based on this newly derived shrinkage function is proposed in the discrete wavelet transform (DWT) domain. The proposed anisotropic bivariate shrinkage approach is also extended to the dual-tree complex wavelet transform (DT-CWT) domain to further improve the performance of image denoising. To take full advantage of DT-CWT, a more accurate noise variance estimator is proposed and the way the anisotropic bivariate shrinkage function applied to the magnitudes of DT-CWT coefficients is presented. Experiments were carried out in both the DWT and the DT-CWT domain to validate the effectiveness of the proposed method. Using a representative set of standard test images corrupted by additive white Gaussian noise, the simulation results show that the proposed method provides promising results and is competitive with the best wavelet-based denoising results reported in the literature both in terms of peak signal-to-noise ratio (PSNR) and in visual quality.     

Probabilistic surrogate models for uncertainty analysis: Dimension reduction-based polynomial chaos expansion

This paper presents an approach for efficient uncertainty analysis (UA) using an intrusive generalized polynomial chaos (gPC) expansion. The key step of the gPC-based uncertainty quantification ( UQ) is the stochastic Galerkin (SG) projection, which can convert a stochastic model into a set of coupled deterministic models. The SG projection generally yields a high-dimensional integration problem with respect to the number of random variables used to describe the parametric uncertainties in a model. However, when the number of uncertainties is large and when the governing equation of the system is highly nonlinear, the SG approach-based gPC can be challenging to derive explicit expressions for the gPC coefficients because of the low convergence in the SG projection. To tackle this challenge, we propose to use a bivariate dimension reduction method (BiDRM) in this work to approximate a high-dimensional integral in SG projection with a few one- and two-dimensional integrations. The efficiency of the proposed method is demonstrated with three different examples, including chemical reactions and cell signaling. As compared to other UA methods, such as the Monte Carlo simulations and nonintrusive stochastic collocation (SC), the proposed method shows its superior performance in terms of computational efficiency and UA accuracy.     

Composition control through pH and ionic strength during acrylic acid/acrylamide copolymerization

The possibility of controlling the composition of acrylic acid/acrylamide copolymers by controlling the pH and the ionic strength of the reaction medium is investigated. The reactivity ratios of charged monomers depend on the pH of the medium, acrylic acid is the more reactive monomer below pH 3 and acrylamide above pH 4. The working pH was set at 3.6, a candidate for the crossover point, where no composition drift is expected. Copolymerization kinetics is investigated at this pH at various ionic strengths and a reaction without composition drift up to 80% conversion was achieved. All the chains produced in this reaction contain 30% ± 3% acrylic acid. Copolymer conversions, molecular weights, and composition distributions were measured through Automatic Continuous Online Monitoring of Polymerization (ACOMP) system. The copolymerization data were analyzed by a recent error in variables method (EVM) and reactivity ratios are calculated. The results show that in salt free conditions, the reactivity ratios depend on the ionic monomer concentration (ionic strength) in addition to the pH of the reaction medium. The effect of polyelectrolytic interactions on the reactivity ratios and the resulting composition drift during the reaction, sequence length distribution, and Stockmayer bivariate distribution are discussed in detail. © 2012 Wiley Periodicals, Inc. J. Appl. Polym. Sci., 2013     

Damage informatics concept for plant life-cycle management

‘Damage informatics’ means here a total life-cycle management methodology including event scenario making, statistical damage analyses and risk-based maintenance decision-making. Event scenarios are expressed in terms of event trees for various components in steam turbines and gas turbines. The field damage data of specific machine types are analysed statistically and the probability of damage or failure can be expressed through the bivariate distribution function of total start-up cycles and operation time. For gas turbine nozzle cracking data, a damage evolution law for low cycle fatigue cracking is applied and the nozzle position dependence is clarified as the major cause of data dispersion. The risks are obtained by the product of probability and consequence of damage/failure and then shown to provide the basis of maintenance decision-making.