线性无量纲化方法比较研究

根据线性无量纲化方法函数构成所使用的中心点值和值域指标以及其斜率和截距的表达式,对8种线性无量纲化方法进行分析,从不同的角度再次论证不同线性无量纲化方法所满足的性质定理,并进行了理论论证。同时,通过对线性无量纲化方法的分类比较,结合相关性质定理提出了多种线性无量纲化方法,并说明了其相关性质,具有一定的科学性。同时还分析了在对多指标数据进行综合评价的过程中只采用一种线性无量纲化方法的不足,提出了采用多种无量纲化方法的设想的理论可行性,并用案例进行了实证分析,表明其存在一定的合理性。     

单发线性结构突变对DF单位根检验的影响分析—“Perron现象”的进一步研究

 “Perron现象”是指当真实的数据生成过程为带有结构突变的（趋势）平稳过程时，传统的DF单位根检验易将其误判为单位根过程。本文考虑了水平突变、截距突变、斜率突变以及截距与斜率双突变等四种突变情形下DF统计量的检验功效，推导了前两种突变情形下DF统计量的渐近分布，并对四种突变情形下DF统计量的有限样本性质进行了探讨。本研究是对“Perron现象”的进一步深入分析，也是对DF单位根检验的进一步补充和完善。     

统计分组与虚拟变量在线性模型中的比较应用

一、统计分组的应用及其在线性模型拟合中的优缺点统计分组是根据事物内在的特点和统计研究的目的,将特定的总体按某种划分标准区分为若干个不同的组成部分的一种统计方法。统计分组的应用相当广泛。对数据按一定的标准分组后,可以发现数据内的潜在的规律性,呈现出不同组别之间的联系与差异,便于找出深藏于表面现象之下的内在本质,比如列联表分析。统计分组也可以应用于模型的建立中。在拟合样本数据进行建立模型时,常常会有一些质的因素(比如职业、性别、战争、季节等等)影响被解释变量,这些质的因素可能会使回归模型中的参数发生变化。在这种情况下,如果对样本数据笼统地用一个模型来拟合就会产生很大的误差。相反,如果将样本数据按引起线性模型的截距或斜率变化的标志分组,再针对每一组分别拟合模型,则可以得到拟合程度更高的模型。     

我国经济增长与就业问题

本文采用学术界普遍认同的柯布--道格拉斯函数为基础,引入虚拟变量建立截距斜率变动模型,对我国从1978～2003年这26年的经济增长进行分析,探讨劳动力投入、资本投入与经济增长之间的关系.     

角度平均方向-合向量长度(θ)-R控制图模拟

文章以计角值控制图的性能分析为研究出发点,充分借鉴常规控制图性能分析的研究思路,结合圆上闭域的特点,从质量特性值服从VonMises分布这一角度展开分析,运用统计过程控制工具平均链长对计角值控制图中角度平均方向-合向量长度控制图进行模拟,分析该控制图在发生参数偏移的情况下平均链长的变化。分析结果显示当n取5时平均方向控制图的控制效果最好。     

自相关对MEWMA控制图影响的模拟研究

为了分析样本协方差不同时自相关结构对常规多元控制图监测偏移能力的影响,针对传统样本协方差矩阵S_1和基于相邻向量差数据构建的协方差矩阵S_2的两种不同取值,通过Monte Carlo模拟对比忽略自相关的原始数据和考虑自相关时基于多变量时间序列模型VAR(1)构建的残差数据的两种情况,以平均运行链长比较了不同均值偏移大小及不同自相关结构下多元控制图的性能。对比结果发现:基于VAR(1)模型的残差MEWMA控制图整体表现更佳,可以更快地捕捉到均值的变化,且该控制图在均值偏移大于一个标准偏差时监测效果更明显;当S_2作为总体协方差估计值时,基于残差数据构建的MEWMA控制图受控平均运行链长ARL_0较低,但该方法能更快地检测到均值的偏移。最后通过一个案例验证了结论的准确性。     

通用型指数加权移动平均控制图的设计

为提高质量控制图监测微小到中等过程偏移的灵敏度,文章提出一种新的用于过程均值监控的通用型指数加权移动平均(UEWMA)控制图,该控制图是EWMA控制图的一般性推广,根据数据特征,自定义选取平滑系数λ₁,λ₂,…,λ_s,使控制效果达到最优;给出UEWMA控制图的均值与控制限的求取方法,并推导出平均运行长度(ARL)和运行长度标准偏差(SDRL);最后,研究平滑系数对该控制图性能的影响,并将其与现有控制图监测微小到中等过程偏移的灵敏度进行比较。研究结果表明,UEWMA控制图通过数据特征设计平滑系数,具有灵活性好、灵敏度高、扩展性强和控制效果好的特点。     

我国宏观经济调控的区域差异性分析

文章根据通胀—产出缺口模型,提出了一种基于总供给曲线(AS)的宏观经济调控差异测度方法。根据1996~2009年间数据运用HP滤波计算出潜在产出以及通胀率,并结合虚拟变量回归模型得出2003年前后两段的AS曲线斜率;最后使用面板数据模型对我国东中西三个地区的AS斜率进行测算,得出相应结果和建议。     

从通胀预期角度看国内通胀的成因

预期因素被理论界认为是引起通货膨胀的主要因素之一.为了控制通货膨胀,人们必须掌握通货膨胀的内在成因.因此,文章以企业家信心指数和消费者预期指数两个调查数据代替通胀预期指标.建立截距和斜率同时变动的虚拟变量模型,分别研究紧缩和扩张时期通货膨胀的成因.模型估计结果显示.企业家的预期对通货膨胀的影响显著,我国的通货膨胀主要是成本推动型通货膨胀,而房价、医疗费用等重要生活支出在消费者价格指数中所占的比重较低,不能很好的衡量通货膨胀.     

基于自相关过程的控制图的性能评价

文章以AR（2）过程为例,对控制图监测自相关过程失效的原因进行了探讨,以平均运行长度（ARL）为评价指标,通过仿真分析验证了自相关性对控制图性能的影响。     

Profile Monitoring Using Nonparametric Bootstrap T 2 Control Chart

In certain statistical process control applications, performance of a product or process can be monitored effectively using a linear profile or a linear relationship between a response variable and one or more explanatory variables. In this article, we design a nonparametric bootstrap control chart for monitoring simple linear profiles based on T ² statistic. We evaluate the performance of the proposed method in phase II. The average and standard deviation of the run length under different shifts in the intercept, slope, and standard deviation are considered as the performance measures. Simulation results show that the performance of the proposed bootstrap control chart improves as the size of the available data increases.     

A weighted likelihood ratio test-based chart for monitoring process mean and variability

In this paper, a new single exponentially weighted moving average (EWMA) control chart based on the weighted likelihood ratio test, referred to as the WLRT chart, is proposed for the problem of monitoring the mean and variance of a normally distributed process variable. It is easy to design, fast to compute, and quite effective for diverse cases including the detection of the decrease in variability and individual observation case. The optimal parameters that can be used as a design aid in selecting specific parameter values based on the average run length (ARL) and the sample size are provided. The in-control (IC) and out-of-control (OC) performance properties of the new chart are compared with some other existing EWMA-type charts. Our simulation results show that the IC run length distribution of the proposed chart is similar to that of a geometric distribution, and it provides quite a robust and satisfactory overall performance for detecting a wide range of shifts in the process mean and/or variability.     

The monitoring of simple linear regression profiles with two observations per sample

We evaluate and compare the performance of Phase II simple linear regression profile approaches when only two observations are used to establish each profile. We propose an EWMA control chart based on average squared deviations from the in-control line, to be used in conjunction with two EWMA control charts based on the slope and Y-intercept estimators, to monitor changes in the three regression model parameters, i.e., the slope, intercept and variance. Simulations establish that the performance of the proposed technique is generally better than that of other approaches in detecting parameter shifts.     

Phase I Analysis of Multiple Linear Regression Profiles

This article considers the Phase I analysis of data when the quality of a process or product is characterized by a multiple linear regression model. This is usually referred to as the analysis of linear profiles in the statistical quality control literature. The literature includes several approaches for the analysis of simple linear regression profiles. Little work, however, has been done in the analysis of multiple linear regression profiles. This article proposes a new approach for the analysis of Phase I multiple linear regression profiles. Using this approach, regardless of the number of explanatory variables used to describe it, the profile response is monitored using only three parameters, an intercept, a slope, and a variance. Using simulation, the performance of the proposed method is compared to that of the existing methods for monitoring multiple linear profiles data in terms of the probability of a signal. The advantage of the proposed method over the existing methods is greatly improved detection of changes in the process parameters of linear profiles with high-dimensional space. The article also proposes useful diagnostic aids based on F-statistics to help in identifying the source of profile variation and the locations of out-of-control samples. Finally, the use of multiple linear profile methods is illustrated by a data set from a calibration application at National Aeronautics and Space Administration (NASA) Langley Research Center.     

Short run spc based upon the second order dynamic linear model for trend detection

Recently, several new applications of control chart procedures for short production runs have been introduced. Bothe (1989) and Burr (1989) proposed the use of control chart statistics which are obtained by scaling the quality characteristic by target values or process estimates of a location and scale parameter. The performance of these control charts can be significantly affected by the use of incorrect scaling parameters, resulting in either an excessive "false alarm rate," or insensitivity to the detection of moderate shifts in the process. To correct for these deficiencies, Quesenberry (1990, 1991) has developed the Q-Chart which is formed from running process estimates of the sample mean and variance. For the case where both the process mean and variance are unknown, the Q-chaxt statistic is formed from the standard inverse Z-transformation of a t-statistic. Q-charts do not perform correctly, however, in the presence of special cause disturbances at process startup. This has recently been supported by results published by Del Castillo and Montgomery (1992), who recommend the use of an alternative control chart procedure which is based upon a first-order adaptive Kalman filter model Consistent with the recommendations by Castillo and Montgomery, we propose an alternative short run control chart procedure which is based upon the second order dynamic linear model (DLM). The control chart is shown to be useful for the early detection of unwanted process trends. Model and control chart parameters are updated sequentially in a Bayesian estimation framework, providing the greatest degree of flexibility in the level of prior information which is incorporated into the model. The result is a weighted moving average control chart statistic which can be used to provide running estimates of process capability. The average run length performance of the control chart is compared to the optimal performance of the exponentially weighted moving average (EWMA) chart, as reported by Gan (1991). Using a simulation approach, the second order DLM control chart is shown to provide better overall performance than the EWMA for short production run applications     

A non parametric approach to monitor simple linear profiles in phases I and II

In this paper, a non parametric approach is first proposed to monitor simple linear profiles with non normal error terms in Phase I and Phase II. In this approach, two control charts based on a transformation technique and decision on beliefs are designed in order to monitor the intercept and the slope, simultaneously. Then, some simulation experiments are performed in order to evaluate the performance of the proposed control charts in Phase II under both step and drift shifts in terms of out-of-control average run length (ARL₁). Besides, the performance of the proposed control charts is compared to the ones of seven other existing schemes in the literature. Simulation results show that the proposed control charts outperform the other control charts in detecting both the small step and small drift shifts of intercept. However, they have a weaker performance compared to other control charts in detecting both small step and small drift shifts of the slope. At the end, a real example from an electronic industry is used to illustrate the implementation of the proposed method.     

Optimal Statistical Design of a Multivariate EWMA Chart Based on ARL and MRL

Statistical design is applied to a multivariate exponentially weighted moving average (MEWMA) control chart. The chart parameters are control limit H and smoothing constant r. The choices of the parameters depend on the number of variables p and the size of the process mean shift δ. The MEWMA statistic is modeled as a Markov chain and the Markov chain approach is used to determine the properties of the chart. Although average run length has become a traditional measure of the performance of control schemes, some authors have suggested other measures, such as median and other percentiles of the run length distribution to explain run length properties of a control scheme. This will allow a thorough study of the performance of the control scheme. Consequently, conclusions based on these measures would provide a better and comprehensive understanding of a scheme. In this article, we present the performance of the MEWMA control chart as measured by the average run length and median run length. Graphs are given so that the chart parameters of an optimal MEWMA chart can be determined easily.     

Economic and economic–statistical designs of VSI Bayesian control chart using Monte Carlo method and ABC algorithm

The usual practice in using a Bayesian control chart to monitor a process is done by taking samples from the process with fixed sampling intervals. Recent studies on traditional control charts have shown that variable sampling interval (VSI) scheme compared to classical scheme (fixed ratio sampling, FRS) helps practitioners to detect process shifts more quickly. In this paper, the effectiveness of VSI scheme on performance of Bayesian control chart has been studied, based on economic (ED) and economic–statistical designs (ESD). Monte Carlo method and artificial bee colony algorithm have been utilized to obtain optimal design parameters of Bayesian control chart (sample size, sampling intervals, warning limit and control limit) since the statistic of this approach does not have any specified distribution. Finally, VSI Bayesian control chart has been compared to FRS Bayesian and VSI X-bar approaches based on ED and ESD, separately. According to the results, it has been found that the performance of VSI Bayesian scheme is better than FRS Bayesian and VSI X-bar approaches.     

Sample size calculation for method validation using linear regression

In this article, we present a method for sample size calculation for studies involving both the intercept and slope parameters of a simple linear regression model. Some methods have been proposed in the literature to determine the adequate sample size. However, they are usually based on the line slope only. We propose a method based on the F statistic that involves both the intercept and the slope parameters of the model. The validation process is conducted by fitting a simple linear regression model and by testing a zero intercept and unity slope hypothesis. Compared to a traditional method and using Monte Carlo simulations, encouraging results attest for the clear superiority of the proposed method. The article ends with a real-life example showing the value of the new method in practice.     

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.