Better approximate confidence intervals for a binomial parameter

This paper discusses five methods for constructing approximate confidence intervals for the binomial parameter Θ, based on Y successes in n Bernoulli trials. In a recent paper, Chen (1990) discusses various approximate methods and suggests a new method based on a Bayes argument, which we call method I here. Methods II and III are based on the normal approximation without and with continuity correction. Method IV uses the Poisson approximation of the binomial distribution and then exploits the fact that the exact confidence limits for the parameter of the Poisson distribution can be found through the x² distribution. The confidence limits of method IV are then provided by the Wilson-Hilferty approximation of the x². Similarly, the exact confidence limits for the binomial parameter can be expressed through the F distribution. Method V approximates these limits through a suitable version of the Wilson-Hilferty approximation. We undertake a comparison of the five methods in respect to coverage probability and expected length. The results indicate that method V has an advantage over Chen's Bayes method as well as over the other three methods.     

基于加权似然比检验的监控线性曲线的控制图

文章提出了一种基于加权似然比检验的阶段二监控线性曲线的控制图,称为WLRT图,并通过平均运行长度来衡量控制图的性能表现。模拟结果表明,WLRT图对于线性曲线的截距、斜率、标准差的变化及截距和斜率同时变化都具有很好的检测能力。通过与其他几种控制图的性能比较,得出WLRT图能较快地发现过程变化,而且设计简单、操作方便。     

新型叶丝限长设备

为大幅降低叶丝长丝率,改善烟丝结构,设计了一种叶丝限长设备。该设备的部件通过键联方式连接,并可通过 调整打辊的间隙套的厚度和改变方刀之间的间隙,获得所需烟丝限长效果,具有操作简单、拆装方便、成本较低、适应性 强的特点。实际应用效果表明：应用前后叶丝的长丝率降低约7%和叶丝的中丝率提高约4%,可见,这种设计能够有效 改善烟丝分布的均匀度,减少卷烟燃烧端掉落现象的发生。     

BMAP/G/1 Queue Under D-Policy: Queue Length Analysis

ABSTRACT

We study the queue length distribution of a queueing system with BMAP arrivals under D-policy. The idle server begins to serve the customers only when the sum of the service times of all waiting customers exceeds some fixed threshold D. We derive the vector generating functions of the queue lengths both at a departure and at an arbitrary point of time. Mean queue lengths are derived and a numerical example is presented.     

A geometrically motivated parametric model in manifold estimation

The general aim of manifold estimation is reconstructing, by statistical methods, an m-dimensional compact manifold S on ^d (with m≤d) or estimating some relevant quantities related to the geometric properties of S. Focussing on the cases d=2 and d=3, with m=d or m=d?1, we will assume that the data are given by the distances to S from points randomly chosen on a band surrounding S. The aim of this paper is to show that, if S belongs to a wide class of compact sets (which we call sets with polynomial volume), the proposed statistical model leads to a relatively simple parametric formulation. In this setup, standard methodologies (method of moments, maximum likelihood) can be used to estimate some interesting geometric parameters, including curvatures and Euler characteristic. We will particularly focus on the estimation of the (d?1)-dimensional boundary measure (in Minkowski's sense) of S. It turns out, however, that the estimation problem is not straightforward since the standard estimators show a remarkably pathological behaviour: while they are consistent and asymptotically normal, their expectations are infinite. The theoretical and practical consequences of this fact are discussed in some detail.     

Optimal One-Way Random Effects Designs for the Intraclass Correlation Based on Confidence Intervals

ABSTRACT

Confidence intervals for the intraclass correlation coefficient (ρ) are used to determine the optimal allocation of experimental material in one-way random effects models. Designs that produce narrow intervals are preferred since they provide greater precision to estimate ρ. Assuming the total cost and the relative cost of the two stages of sampling are fixed, the authors investigate the number of classes and the number of individuals per class required to minimize the expected length of confidence intervals. We obtain results using asymptotic theory and compare these results to those obtained using exact calculations. The best design depends on the unknown value of ρ. Minimizing the maximum expected length of confidence intervals guards against worst-case scenarios. A good overall recommendation based on asymptotic results is to choose a design having classes of size 2 + √4 + 3r, where r is the relative cost of sampling at the class-level compared to the individual-level. If r = 0, then the overall cost is the sample size and the recommendation reduces to a design having classes of size 4.     

A Multivariate Synthetic Control Chart for Monitoring Process Mean Vector

In this article, a multivariate synthetic control chart is developed for monitoring the mean vector of a normally distributed process. The proposed chart is a combination of the Hotelling's T ² chart and Conforming Run Length chart. The operation, design, and performance of the chart are described. Average run length comparisons between some other existing control charts and the synthetic T ² chart are presented. They indicate that the synthetic T ² chart outperforms Hotelling's T ² chart and T ² chart with supplementary runs rules.     

Estimation of Traffic Intensity Based on Queue Length in a Single M/M/1 Queue

In this article, maximum likelihood estimator (MLE) as well as Bayes estimator of traffic intensity (ρ) in an M/M/1/∞ queueing model in equilibrium based on number of customers present in the queue at successive departure epochs have been worked out. Estimates of some functions of ρ which provide measures of effectiveness of the queue have also been derived. A comprehensive simulation study starting with the transition probability matrix has been carried out in the last section.     

An adaptive multivariate CUSUM control chart for signaling a range of location shifts

ABSTRACT

In this work, we proposed an adaptive multivariate cumulative sum (CUSUM) statistical process control chart for signaling a range of location shifts. This method was based on the multivariate CUSUM control chart proposed by Pignatiello and Runger (1990 Pignatiello, J.J., Runger, G.C. (1990). Comparisons of multivariate CUSUM charts. J. Qual. Technol. 22(3):173–186.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), but we adopted the adaptive approach similar to that discussed by Dai et al. (2011 Dai, Y., Luo, Y., Li, Z., Wang, Z. (2011). A new adaptive CUSUM control chart for detecting the multivariate process mean. Qual. Reliab. Eng. Int. 27(7):877–884.[Crossref], [Web of Science ®] , [Google Scholar]), which was based on a different CUSUM method introduced by Crosier (1988 Crosier, R.B. (1988). Multivariate generalizations of cumulative sum quality-control schemes. Technometrics 30(3):291–303.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]). The reference value in this proposed procedure was changed adaptively in each run, with the current mean shift estimated by exponentially weighted moving average (EWMA) statistic. By specifying the minimal magnitude of the mean shift, our proposed control chart achieved a good overall performance for detecting a range of shifts rather than a single value. We compared our adaptive multivariate CUSUM method with that of Dai et al. (2001 Dai, Y., Luo, Y., Li, Z., Wang, Z. (2011). A new adaptive CUSUM control chart for detecting the multivariate process mean. Qual. Reliab. Eng. Int. 27(7):877–884.[Crossref], [Web of Science ®] , [Google Scholar]) and the non adaptive versions of these two methods, by evaluating both the steady state and zero state average run length (ARL) values. The detection efficiency of our method showed improvements over the comparative methods when the location shift is unknown but falls within an expected range.     

A New GWMA Control Chart for Monitoring Process Mean and Variability

In this article, we extend a single exponentially weighted moving average semicircle (EWMA-SC) chart to a single generally weighted moving average (GWMA) chart. This new control chart can effectively combine the features of the SC chart with GWMA techniques, and can easily indicate the source and direction of a change. We perform simulations to evaluate the average run length, standard deviation of the run length, and diagnostic abilities of the GWMA-SC and EWMA-SC charts. An extensive comparison shows that the GWMA-SC control chart is more sensitive than the EWMA-SC chart for detecting small shifts in the process mean and/or variability.