The MLE of Geometric Parameter for a Geometric Process

In this article, we provide the MLE of the ratio parameter of a geometric process and discuss its consistency and asymptotic normality.     

Distribution of busy period in stochastic fluid models

We consider the busy period in a stochastic fluid flow model with infinite buffer where the input and output rates are controlled by a finite homogeneous Markov process. We derive an explicit expression for the distribution of the busy period and we obtain an algorithm to compute it which exhibits nice numerical properties.

     

The performance of multivariate CUSUM control charts with estimated parameters

In this paper, we study the effect of estimating the vector of means and the variance–covariance matrix on the performance of two of the most widely used multivariate cumulative sum (CUSUM) control charts, the MCUSUM chart proposed by Crosier [Multivariate generalizations of cumulative sum quality-control schemes, Technometrics 30 (1988), pp. 291–303] and the MC1 chart proposed by Pignatiello and Runger [Comparisons of multivariate CUSUM charts, J. Qual. Technol. 22 (1990), pp. 173–186]. Using simulation, we investigate and compare the in-control and out-of-control performances of the competing charts in terms of the average run length measure. The in-control and out-of-control performances of the competing charts deteriorate significantly if the estimated parameters are used with control limits intended for known parameters, especially when only a few Phase I samples are used to estimate the parameters. We recommend the use of the MC1 chart over that of the MCUSUM chart if the parameters are estimated from a small number of Phase I samples.     

Developing a variables repetitive group sampling plan based on process capability index C pk with unknown mean and variance

In this paper, variables repetitive group sampling plans are developed based on the process capability index C _pk when the quality characteristic follows a normal distribution with unknown mean and variance. The sampling plan parameters such as the sample size and the acceptance constant are determined to minimize the average sample number. Symmetric and asymmetric cases, in percent defectives due to two specification limits, are dealt with for specified combinations of acceptable quality level and limiting quality level. Tables are provided and examples are given to use proposed plans in practice.     

环境规制、R&D资本存量与绿色技术创新

科技创新是一个国家经济发展的内生动力。技术创新能力的提升需要持续的R&D投入,而R&D资本存量正是衡量持续研发投入水平的最佳指标。本文基于BEA原理,合理测算出中国大陆30个省区市（西藏除外）的R&D资本存量,并采用省际面板数据,构建空间计量模型,探讨环境规制下R&D资本存量对绿色技术创新的影响机制。研究表明：环境规制与R&D资本存量对绿色技术创新均具有促进作用,但一定强度的环境规制会挤占R&D投入资源,与R&D资本存量的累积发生“负挤出效应”,进而影响绿色技术创新;同时,R&D资本存量、环境规制对中国东部、中部与西部地区的绿色技术创新的影响呈现显著的区域异质性。因此,本文提出了制定差异化的R&D投资和环境规制策略。     

Exceedance probabilities for parametric control charts

Common control charts assume normality and known parameters. Quite often, these assumptions are not valid and large relative errors result in the usual performance characteristics such as the false alarm rate or the average run length. A fully nonparametric approach can form an attractive alternative but requires more Phase I observations than usually available. Sufficiently general parametric families then provide realistic intermediate models. In this article, the performance of charts based on such families is considered. Exceedance probabilities of the resulting stochastic performance characteristics during in-control are studied. Corrections are derived to ensure that such probabilities stay within prescribed bounds. Attention is also devoted to the impact of the corrections for an out-of-control process. Simulations are presented both to illustrate and to demonstrate that the approximations obtained are sufficiently accurate for practical usage.     

Formulas for stationary planar fibre processes III – intersections with fibre systems

In this paper we investigate the distribution of the periodogram, respectively, the periodogram matrix for stationary random sequences. These .distributions are consid¬ered in the case of a fixed frequency as well as in the case of a finite number of frequencies for Gaussian sequences and for sequences of independent random variables. The exact distribution is obtained in the case of a fixed frequence for one-dimensional GAUSsian sequences. Asymptotic expansions, respectively, the rate of convergence to the asymptotic distribution are given in the case mentioned above