Robustness to non-normality and autocorrelation of individuals control charts

This paper studies the effects of non-normality and autocorrelation on the performances of various individuals control charts for monitoring the process mean and/or variance. The traditional Shewhart X chart and moving range (MR) chart are investigated as well as several types of exponentially weighted moving average (EWMA) charts and combinations of control charts involving these EWMA charts. It is shown that the combination of the X and MR charts will not detect small and moderate parameter shifts as fast as combinations involving the EWMA charts, and that the performana of the X and MR charts is very sensitive to the normality assumption. It is also shown that certain combinations of EWMA charts can be designed to be robust to non-normality and very effective at detecting small and moderate shifts in the process mean and/or variance. Although autocorrelation can have a significant effect on the in-control performances of these combinations of EWMA charts, their relative out-of-control performances under independence are generally maintained for low to moderate levels of autocorrelation.     

Bayesian Estimation and Model Choice in Item Response Models

Item response models are essential tools for analyzing results from many educational and psychological tests. Such models are used to quantify the probability of correct response as a function of unobserved examinee ability and other parameters explaining the difficulty and the discriminatory power of the questions in the test. Some of these models also incorporate a threshold parameter for the probability of the correct response to account for the effect of guessing the correct answer in multiple choice type tests. In this article we consider fitting of such models using the Gibbs sampler. A data augmentation method to analyze a normal-ogive model incorporating a threshold guessing parameter is introduced and compared with a Metropolis-Hastings sampling method. The proposed method is an order of magnitude more efficient than the existing method. Another objective of this paper is to develop Bayesian model choice techniques for model discrimination. A predictive approach based on a variant of the Bayes factor is used and compared with another decision theoretic method which minimizes an expected loss function on the predictive space. A classical model choice technique based on a modified likelihood ratio test statistic is shown as one component of the second criterion. As a consequence the Bayesian methods proposed in this paper are contrasted with the classical approach based on the likelihood ratio test. Several examples are given to illustrate the methods.     

学习迁移的系统理论:PPEE理论模型的建构和意义

学习是人类社会永恒的主题。为了更好地利用过去的经验，增强学习效果，个人和组织进行学习迁移具有重要意义。学习迁移是指将在以往通过学习或解决问题所获得的经验，用于解决之后所遇到的问题。本文力图建立系统的学习迁移理论，研究人、问题、环境的因素对于学习迁移的影响。本文采用理论推导的研究方法，在前人研究的基础上，提出相应的理论模型。本文运用系统的观点，构建了学习迁移的PPEE理论模型，认为人的因素、问题的因素、人和问题的交互作用、以及环境的调节作用，会共同影响学习迁移的效果。本理论主要从五个方面论述学习迁移的机制。首先，将人的因素按照不同层面划分为后端基本能力、中端心理过程、前端知识结构，讨论了其各自对学习迁移效果的直接影响。其次，将问题的因素划分为形象相似性和抽象相似性，并根据这两个维度构建了四种问题间关系类型，并探究了其与学习迁移效果之间的关系。第三，同时考虑人的因素和问题的因素，研究了二者之间的互动对于学习迁移效果的影响。第四，将环境因素划分为时间紧迫性和空间重要性两个维度，探讨了人和环境，以及问题和环境之间的互动对学习迁移效果的影响。第五，基于系统整体的方面，研究人、问题、环境三者之间的互动对学习迁移效果的交互影响。本文还认为，该模型不仅适用于个人，也同样适用于团队、组织、地区、甚至国家和社会等各个层面，影响各个层面主体的学习迁移。本文最后总结了研究的理论和实践贡献，并提出了未来研究课题。本文对丰富学习理论、特别是学习迁移理论，以及推动教育和管理实践的发展进步具有重要的意义。     

Economic and economic statistical designs for three-level control charts

In some situations, an appropriate quality measure uses three or more discrete levels to classify a product characteristic. For these situations, some control charts have been developed based on statistical criteria regardless of economic considerations. In this paper, we develop economic and economic statistical designs (ESD) for 3-level control charts. We apply the cost model proposed by Costa and Rahim.[Economic design of X charts with variable parameters: the Markov chain approach, J Appl Stat 28 (2001), 875–885] Furthermore, we assume that the length of time that the process remains in control is exponentially distributed which allows us to apply the Markov chain approach for developing the cost model. We apply a genetic algorithm to determine the optimal values of model parameters by minimizing the cost function. A numerical example is provided to illustrate the performance of the proposed models and to compare the cost of the pure economic and ESD for three-level control charts. A sensitivity analysis is also conducted in this numerical example.     

The star-shaped Λ-coalescent and Fleming–Viot process

The star-shaped Λ-coalescent and corresponding Λ-Fleming–Viot process, where the Λ measure has a single atom at unity, are studied in this article. The transition functions and stationary distribution of the Λ-Fleming–Viot process are derived in a two-type model with mutation. The distribution of the number of non-mutant lines back in time in the star-shaped Λ-coalescent is found. Extensions are made to a model with d types, either with parent-independent mutation or general Markov mutation, and an infinitely-many-types model, when d → ∞. An eigenfunction expansion for the transition functions is found, which has polynomial right eigenfunctions and left eigenfunctions described by hyperfunctions. A further star-shaped model with general frequency-dependent change is considered and the stationary distribution in the Fleming–Viot process derived. This model includes a star-shaped Λ-Fleming–Viot process with mutation and selection. In a general Λ-coalescent explicit formulae for the transition functions and stationary distribution, when there is mutation, are unknown. However, in this article, explicit formulae are derived in the star-shaped coalescent.     

荷兰战后移民及其影响

战后非殖民化运动导致印度尼西亚和苏里南大量人口移居荷兰;20世纪50年代中期开始到70年代初,荷兰从地中海沿岸国家输入大量劳工,随后劳工移民带来大量家庭移民;80年代中期以后,难民以及寻求庇护者纷纷进入荷兰,成为荷兰移民的重要部分。随着类型多样、来源广泛的移民不断进入,荷兰的人口结构发生重大改变,大量外来移民的存在,尤其大量穆斯林人口的存在,成为荷兰社会面临的重要问题。     

A Hellinger distance approach to MCMC diagnostics

Bayesian analysis often requires the researcher to employ Markov Chain Monte Carlo (MCMC) techniques to draw samples from a posterior distribution which in turn is used to make inferences. Currently, several approaches to determine convergence of the chain as well as sensitivities of the resulting inferences have been developed. This work develops a Hellinger distance approach to MCMC diagnostics. An approximation to the Hellinger distance between two distributions f and g based on sampling is introduced. This approximation is studied via simulation to determine the accuracy. A criterion for using this Hellinger distance for determining chain convergence is proposed as well as a criterion for sensitivity studies. These criteria are illustrated using a dataset concerning the Anguilla australis, an eel native to New Zealand.     

An Additive–Multiplicative Restricted Mean Residual Life Model

The mean residual life measures the expected remaining life of a subject who has survived up to a particular time. When survival time distribution is highly skewed or heavy tailed, the restricted mean residual life must be considered. In this paper, we propose an additive–multiplicative restricted mean residual life model to study the association between the restricted mean residual life function and potential regression covariates in the presence of right censoring. This model extends the proportional mean residual life model using an additive model as its covariate dependent baseline. For the suggested model, some covariate effects are allowed to be time‐varying. To estimate the model parameters, martingale estimating equations are developed, and the large sample properties of the resulting estimators are established. In addition, to assess the adequacy of the model, we investigate a goodness of fit test that is asymptotically justified. The proposed methodology is evaluated via simulation studies and further applied to a kidney cancer data set collected from a clinical trial.     

Tactical production and distribution planning with dependency issues on the production process

Tactical production-distribution planning models have attracted a great deal of attention in the past decades. In these models, production and distribution decisions are considered simultaneously such that the combined plans are more advantageous than the plans resolved in a hierarchical planning process. We consider a two-stage production process, where in the first stage raw materials are transformed into continuous resources that feed the discrete production of end products in the second stage. Moreover, the setup times and costs of resources depend on the sequence in which they are processed in the first stage. The minimum scheduling unit is the product family which consists of products sharing common resources and manufacturing processes. Based on different mathematical modelling approaches to the production in the first stage, we develop a sequence-oriented formulation and a product-oriented formulation, and propose decomposition-based heuristics to solve this problem efficiently. By considering these dependencies arising in practical production processes, our model can be applied to various industrial cases, such as the beverage industry or the steel industry. Computation tests on instances from an industrial application are provided at the end of the paper.