Estimating the limits for statistical process control charts: A direct method improving upon the bootstrap

This paper considers the problem of finding limits for a statistical process control (SPC) chart for the process mean, when the process distribution is unknown. The bootstrap method estimates these limits relying on Monte Carlo methods, which are subject to simulation errors. Therefore this paper develops a computationally efficient enumeration method for exact calculations of the control limits.     

Invariance principle for biased bootstrap random walks

Our main goal is to study a class of processes whose increments are generated via a cellular automata rule. Given the increments of a simple biased random walk, a new sequence of (dependent) Bernoulli random variables is produced. It is built, from the original sequence, according to a cellular automata rule. Equipped with these two sequences, we construct two more according to the same cellular automata rule. The construction is repeated a fixed number of times yielding an infinite array ($\{?K,\dots ,K\}\times \mathbb{N}$) of (dependent) Bernoulli random variables. Taking partial sums of these sequences, we obtain a $(2K+1)$-dimensional process whose increments belong to the state space ${\{?1,1\}}^{2K+1}$.The aim of the paper is to study the long term behaviour of this process. In particular, we establish transience/recurrence properties and prove an invariance principle. The limiting behaviour of these processes depends strongly on the direction of the iteration, and exhibits few surprising features. This work is motivated by an earlier investigation (see Collevecchio et al. (2015)), in which the starting sequence is symmetric, and by the related work Ferrari et al. (2000).     

Weighted Multivariate Mean Square Error for processes optimization: A case study on flux-cored arc welding for stainless steel claddings

A mathematical programming technique developed recently that optimizes multiple correlated characteristics is the Multivariate Mean Square Error (MMSE). The MMSE approach has obtained noteworthy results, by avoiding the production of inappropriate optimal points that can occur when a method fails to take into account a correlation structure. Where the MMSE approach is deficient, however, is in cases where the multiple correlated characteristics need to be optimized with varying degrees of importance. The MMSE approach, in treating all responses as having the same importance, is unable to attribute the desired weights. This paper thus introduces a strategy that weights the responses in the MMSE approach. The method, called the Weighted Multivariate Mean Square Error (WMMSE), utilizes a weighting procedure that integrates Principal Component Analysis (PCA) and Response Surface Methodology (RSM). In doing so, WMMSE obtains uncorrelated weighted objective functions from the original responses. After being mathematically programmed, these functions are optimized by employing optimization algorithms. We applied WMMSE to optimize a stainless steel cladding application executed via the flux-cored arc welding (FCAW) process. Four input parameters and eight response variables were considered. Stainless steel cladding, which carries potential benefits for a variety of industries, takes low cost materials and deposits over their surfaces materials having anti-corrosive properties. Optimal results were confirmed, which ensured the deposition of claddings with defect-free beads exhibiting the desired geometry and demonstrating good productivity indexes.     

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以平衡程序Jsolver 为基础开展了紧凑型聚变裂变混合堆先进等离子体平衡位形设计,重点研究了反剪切运行模式,并在此位形下研究了自举电流的计算、分布及份额。     

Pinkness of the North Atlantic Oscillation signal revisited

The long episode of negative values in the North Atlantic Oscillation (NAO) index during the winter season 2009-2010 has attracted more attention to its predictability. Previous analyses (Fernández et al. (2003) [16] and Caldeira et al. (2007) [25]) by this same author group have established that the NAO signal behaves as a slightly red noise and therefore the prediction of the phenomenon must rely upon a deeper understanding of the underlying Physics. In this paper the authors address a predictability study of the NAO index by applying the “detrended fluctuation analysis” (DFA) to a composite series, completed with a bootstrap spectral analysis. The DFA provides a quantitative measure of predictability by computing several piecewise fits, either linear or higher degree polynomial ones, to a cumulative series of fluctuations associated to the original series. These newer measurements agree with the previous results.     

平滑转换向量误差修正模型的非线性协整SupLM检验

本文考虑平滑转换向量误差修正模型的非线性协整检验问题,相对于传统的两步检验法,给出已知协整向量下的直接检验非线性协整的SupLM检验方法,通过定义平滑转换协整模型,给出SupLM检验统计量,在原假设下得到检验统计量的渐近分布和相关的bootstrap算法,模拟结果和实例计算表明了该方法的有效性。     

Better saddlepoint confidence intervals via bootstrap calibration

Confidence interval construction for parameters of lattice distributions is considered. By using saddlepoint formulas and bootstrap calibration, we obtain relatively short intervals and bounds with coverage errors, in contrast with and coverage errors for normal theory intervals and bounds when the population distribution is absolutely continuous. Closed form solutions are also provided for the cases of binomial and Poisson distributions. The method is illustrated by some simulation results.

     

删截分布未知的多维随机删截数据的PP拟合优度检验

文[5]在假定删截分布已知的条件下,用投影寻踪（PP）技巧讨论了多维随机删截数据的PP拟合优度检验问题．本文讨论截尾分布未知时,多维随机删截数据的拟合优度检验问题,得到了检验统计量在零假设成立时的渐近分布,并讨论了其Bootstrap逼近．     

进口铁矿砷量特征的内核密度分析与Bootstrap代表值估计

对进口铁矿中的砷量进行了总体统计分析, 在数据统计分布特征研究基础上, 使用内核密度估计对进口铁矿砷量进行数据多态性分析, 使用bootstrap对原始数据样本值重复取样以获得稳健的砷量代表值估计及标准偏差, 证明以bootstrap重新取样样本分布的均值与标准偏差作为有限单次样本代表值是合理、有效的.     

样本均值Bootstrap逼近的收敛速度

本文进一步研究Ｂｏｏｔｓｔｒａｐ逼近的收敛速度，在随机变量的（２＋δ）阶矩（０≤δ＜２）有限的情况下，讨论标准化样本均值的分布与它的Ｂｏｏｔｓｔｒａｐ逼近之间差的一致收敛速度，以及这种逼近与正态分布之间差的一致收敛速度。