An economic statistical design of the Poisson EWMA control charts for monitoring nonconformities

An economic statistical model of the exponentially weighted moving average (EWMA) control chart for the average number of nonconformities in the sample is proposed. The statistical and economic performance of proposed design are evaluated using the average run length (ARL) and the hourly expected cost, respectively. A Markov chain approach is applied to derive expressions for ARL. The cost model is established based on the general cost function given in Lorenzen and Vance [The economic design of control charts: a unified approach. Technometrics. 1986;28:3–11]. An example is provided to illustrate the application of the proposed model. A sensitivity analysis is also carried out to investigate the effects of model parameters on the solution of the economic statistical design by using the design of experiments (DOE) technique.     

On the estimation of homogeneous population size from a complex dual-record system

ABSTRACT

A dual-record system (DRS) (equivalently two sample capture–recapture experiments) model, with time and behavioural response variation, has attracted much attention specifically in the domain of official statistics and epidemiology, as the assumption of list independence often fails. The relevant model suffers from parameter identifiability problem, and suitable Bayesian methodologies could be helpful. In this article, we formulate population size estimation in DRS as a missing data problem and two empirical Bayes approaches are proposed along with the discussion of an existing Bayes treatment. Some features and associated posterior convergence for these methods are mentioned. Investigation through an extensive simulation study finds that our proposed approaches compare favourably with the existing Bayes approach for this complex model depending upon the availability of directional nature of underlying behavioural response effect. A real-data example is given to illustrate these methods.     

An optimality criterion for supersaturated designs with quantitative factors

A supersaturated design (SSD) is a factorial design in which the degrees of freedom for all its main effects exceed the total number of distinct factorial level-combinations (runs) of the design. Designs with quantitative factors, in which level permutation within one or more factors could result in different geometrical structures, are very different from designs with nominal ones which have been treated as traditional designs. In this paper, a new criterion is proposed for SSDs with quantitative factors. Comparison and analysis for this new criterion are made. It is shown that the proposed criterion has a high efficiency in discriminating geometrically nonisomorphic designs and an advantage in computation.     

Gender and Mathematics Achievement in China and the United States

This study examines the relationship between gender and mathematics achievement among students in China and the United States, with an emphasis on the gender gap among mathematically talented students. The results show that in neither the US nor China are there gender differences in eighth grade math-achievement test scores. In China, there are no gender differences in mean college entrance examination math scores among high-school seniors, while in America, the mean SAT-Math score among male high-school seniors has been consistently higher than those of their female counterparts. In both the US and China, there are gender differences among the top math performers on college entrance examinations; boys are over-represented. The Chinese national mathematics curriculum, well-trained teachers, beliefs by students and their parents that academic achievement is more a product of effort than of natural ability, a gender-neutral parental expectation for children’s education, and generous family spending on the education of girls are suggested as possible factors underlying the comparable performance of the Chinese female and male students. The sorting system at Chinese secondary school level and a cultural stereotype favoring boys in mathematics are suggested as possible contributors to the math-achievement gender gap found among the top Chinese high school seniors.

The Effect of Mixing Events on the Dynamics of pH1N1 Outbreaks at Small Residential Colleges

Abstract

Objective: The authors examine the dynamics and the impact of all-campus events on pH1N1 spread at Bates College in fall 2009, with comparisons to 3 other campuses. Participants: Students (N = 285) presented or called in to the Bates Health Center with symptoms consistent with influenza-like illness. Methods: Health Center staff at Bates collected data on the outbreak; data from other colleges are from Web sites and journal articles. Data were analyzed using a mathematical model for influenza. Results: Bates held 2 vaccine clinics mid-outbreak. The data are consistent with the hypothesis that the vaccine clinics may have altered routine student interactions, facilitating transmission of pH1N1 among students who otherwise might not have encountered each other. Conclusion: The vaccine clinics, held when vaccine became available, were too late to halt transmission. The disruptions to campus rhythms due to the vaccine clinics may instead have contributed to pH1N1 spread.     

浅谈函数f(x)=x k/x(k>0)的单调性的应用

利用函数f(x) =x kx(k>0 )的单调性 ,可以求解某些复杂三角函数方程的极值、求解某些复杂分式的极值 ,这对于训练高中学生灵活处理难题具有一定的意义