The double sampling S2 chart with estimated process variance

This paper proposes useful exact bounds for the parameters of the double sampling S² chart with known process variance and it also investigates the properties of the double sampling S² chart with estimated process variance, in terms of the average run length, the standard deviation of the run length and the average sample size, providing a numerical comparison with the known process variance case. It also provides guidelines to systematically design the double sampling S² chart both with known and estimated process variance and proposes two optimal design procedures with estimated process variance, for (a) minimizing the out-of-control average run length and (b) minimizing the out-of-control average sample size.     

Performance of the zone control chart

Average run lengths of the zone control chart are presented, The performance of this chart is compared with that of several Shewhart charts with and without runs rules, It is shown that the standard zone control chart has performance similar to some even simpler charts and a much higher false alarm rate than the Shewhart chart with all of the common runs rules. It is also shown that a slightly modified zone control chart outperforms the Shewhart chart with the common runs rules.     

Application of copulas to multivariate control charts

The most popular multivariate control chart for monitoring the mean of a distribution is probably the Hotelling T² rule. Unfortunately, this rule relies on the assumption that the distribution under control is Gaussian, which is rarely true in practice. The objective of this paper is to propose a new approach for the non-normal multivariate case. It consists in the construction of a tolerance region obtained from a density level set estimation. The method follows a “plug-in” approach in which the density of the observations is previously estimated. This estimation is conducted using copulas modeling, an increasingly popular tool in multivariate modeling.     

Additional variables and adjusted estimates with arbitrary known variance-covariance structure

When additional variables are fitted in a linear model under arbitrary known variance-covariance struture, the extra sum of squares due to fitting the new variables and adjusted parameter estimates can be computed in an efficient manner without actually explicity fitting the entire augmented model. When the additional variables are specific dummy variables, downdating formulae are readily obtained, thus generatina methods which are well known for the linear model with variance-covariance structure σ²I. Two different methods to downdate a linear model are presented.     

不同模覆盖系的模倒数之和

构造性证明了当Z的不同模覆盖系最小模为2,3与4时,其模倒数之和可任意接近于1或2,并提出两个未解决问题.     

关于积分区间可加性定理的证明

指出数学分析现用教材中定积分性质定理６证明中的错误，并给出正确的证     

Development of a multiattribute synthetic-np chart

Over the last few decades, multiattribute control charts have been widely recommended in practice. They outperform the simultaneous uniattribute charts for monitoring multiattribute processes in many applications. Jolayemi [A statistical model for the design of multiattribute control charts. Indian J Stat. 1999;61:351–365] developed a statistical model for the design of a multiattribute np (Mnp) chart. Based on this model, a multiattribute synthetic (MSyn) chart is proposed in this article. Furthermore, the main features of the MSyn chart and Mnp chart are integrated to build a multiattribute Syn-np (MSyn-np) chart. The results of the comparative studies indicate that the new MSyn-np chart significantly outperforms the Mnp chart and MSyn chart by 83% and 27%, respectively, in terms of the average number of defectives over a wide range of process shifts under different circumstances.     

Shewhart x-charts with estimated process variance

Properties of the Shewhart X-chart for controlling the mean of a process with a normal distribution are investigated for the situation where the process variance Ó²must be estimated from initial sample data. The control limits of the X-chart depend on the estimate of Ó²and thus, unlike the case when Ó²is known, the X-chart is not equivalent to a sequence of independent tests. When Ó²is estimated the distribution of the run length is not geometric and cannot be characterized simply in terms of the probability of a signal at a given point. The average run length (ARL) for the X-chart is expressed in terms of an integral involving the normal cdf, and it is shown that the chart signals with

probability one, but the ARL may not be finite if the size of the 2 sample used to estimate Ó²is sufficiently small. In addition, certain bounds for the ARL are also derived. Numerical integration is use to show that the effect of using small sample sizes in estimating Ó²is to increase the ARL and the variance of the run length distribution     

创业企业品牌建设的选择模型研究

创业企业的品牌建设是创业机会观研究框架下创业机会开发领域的重要组成部分.本文给出了创业企业品牌建设活动应该遵循的一般性模式:以系统思维考察本企业PJ图的完整性以完成品牌建设内容的选择;以战略思维来指导品牌建设方法的选择.最后,在此基础上构建了创业企业品牌建设的选择模型.     

A Sequential Rank-Based Nonparametric Adaptive EWMA Control Chart

Nonparametric control chart is useful when the underlying distribution is unknown, or is not likely to be normal. In this article, we provide a sequential rank-based nonparametric adaptive EWMA (NAE) control chart for detecting the persistent shift in the location parameter. This NAE chart is a self-starting scheme and thus can be used to monitor processes at the start-up stages rather than waiting for the accumulation of sufficiently large calibration samples. Moreover, we do not require any prior knowledge of the underlying distribution, and to prespecify any tuning parameter either. A Markov chain model is suggested to calibrate the run-length distribution of NAE, which is shown to have approximate tail probability as a geometric distribution. A simulation study demonstrates that the proposed control chart not only performs robustly for different distributions, but also is efficient in detecting various magnitude of shifts. A real-data example from manufacturing shows that it performs quite well in practical applications.