改进的SPC控制图在食品质量检测中的应用

统计过程控制中的控制图是从事统计过程管理常用的重要工具多年的发展与实践表明传统的控制图已得到广泛的应用可是运用多张控制图进行过程控制仍然存在许多不便和弊端.对此用综合主成分分析法对传统的控制图进行了整合,从而得到一张综合控制图并用这个改进的综合控制图对食品检验过程进行控制,给出了具体的应用步骤以及对结果进行了详细地分析.其结果表明综合控制图不仅结合了传统控制图的优点避免了运用多张控制图进行控制的不便同时又提升了警报的准确率降低了虚假警报的概率.     

推广的Q空间

Q空间(或Qp,或Qα空间)的研究受到许多研究者的关注.最近,Wu和Xie将Q空间推广到Qpα,q空间.本文对一般的Q空间进行研究.首先,表明某些实变量刻画和小波刻画的等价性,主要想法是用2n维小波分析属于n维空间Rn的Qpα,q中的元素.其次,也构造出了空间Qpα,q的预对偶空间Ppα,q,其中Ppα,q是由小波定义的原子生成.     

基于高质量过程的WMedian-EWMA控制图的统计设计及应用

针对事件间隔时间(Time Between Events,TBE)服从威布尔分布的高质量过程,设计WMedian-EWMA控制图监控过程的小偏移.首先,给出WMedian-EWMA控制图的设计方法及控制限参数的估计方法;其次,通过平均运行链长的均值AARL (Average of Average Run Length)和平均运行链长的标准差SDARL(Standard Deviation of Average Run Length)分析了参数估计对所设计的控制图性能的影响,结果表明当形状参数β≥1时,所设计的控制图受参数估计的影响小,对过程偏移有较好的探测能力;最后,通过算例说明所设计的控制图在实际中的使用.     

修正贝叶斯控制图与累积和控制图的比较分析

面向多品种、小批量制造过程的小波动检验是目前统计过程控制图发展和研究的方向.在对修正贝叶斯控制图与累积和控制图原理进行比较后,通过一组过程仿真数据对两种控制图进行了分析,指出了两种控制图的特性和应用前景.     

对称中心相同的正交平衡多小波的存在性及参数化

1 引 言 多小波因为可同时满足对称性、紧支撑性、高阶消失矩和正交性,所以在信号处理等应用方面比单小波更有优势,但是,基于多小波的信号处理需进行预滤波[1,2],而预滤波又会破坏所设计的多小波的正交性、对称性等特性,这阻碍了多小波的应用.     

混合正态分布下基于斜线截断的稳健似然比累积和控制图北大核心CSCD

累积和控制图主要用于对正态分布过程中均值的中小漂移的检测,但是对厚尾分布过程监测并不稳定.MacEachern等(2007)提出了用于监测厚尾分布过程的稳健似然比累积和(RLCUSUM)控制图.文章主要研究RLCUSUM控制图的性质,包括可控平均运行长度关于控制限的性质和过程失控时不同真实均值对平均运行长度的影响等,并提出了对于对数似然比函数进行斜线截断的方式,同时分析总结了不同污染程度的混合正态分布下各种截断方式得到的RLCUSUM控制图的适用情况.     

一种可用于检测过程尺度参数的非参数控制图

传统的控制图多数是在已知过程分布的假设下构建的,这种控制图被称为参数控制图。然而,在实际应用中,大多数过程因为其数据的复杂性导致他们的精确分布往往难以确定。当预先指定的参数分布无效时,参数控制图的结果将不再可靠。为了解决这个问题,通常考虑非参数控制图,因为非参数控制图比参数控制图更加稳健。近年来对非参数控制图的研究越来越多,但大多数现有的控制图主要是用于检测位置参数的变化。本文提出一个新的非参数Shewhart控制图(称为LOG图),可用来检测未知连续过程分布的尺度参数。文中依据运行长度分布的均值,方差和分位数,分析了LOG图在过程受控和失控时的性能表现,并与其他非参数控制图进行比较。模拟结果表明,LOG图在不同过程分布下对检测尺度参数的漂移都具有很好的性能。最后用一个实例来说明LOG图在实际中的应用。     

两阶段相关过程的VP均值-残差联合控制图

基于回归残差监控的思想研究了两阶段过程变参数控制图设计的问题.考虑样本容量、抽样区间和控制限全部可变的情况下,采用马尔可夫链的方法,构建了监控过程的可变参数(VP)Z_(?)-Z_(?)联合控制图。以修正的平均信号时间(AATS)为准则,首先利用汽车刹车系统的案例说明了VP Z_(?)-Z_(?)联合控制图的监控效果,然后通过仿真对不同过程参数情形下VP Z_(?)-Z_(?)联合控制图、固定参数Z_(?)-Z_(?)联合控制图和VSSI Z_(?)-Z_(?)联合控制图的监控效果进行了比较分析。结果表明,VP Z_(?)-Z_(?)联合控制图能够更为有效地实现对两阶段相关过程的质量控制.     

两阶段抽样中位值-极差联合控制图

在统计质量控制中,通常利用中位值图和极差图来控制生产过程的均值和方差.建立了两阶段中位值和极差联合控制图,在第一阶段抽取一个样本进行检测,如果过程处于控制,就停止抽样,否则进行第二阶段抽样检测.文中将其与其他类型的中位值-极差联合控制图做了比较.结果表明,两阶段抽样控制图能更有效地检测生产过程的波动变化.     

混合正态分布下基于斜线截断的稳健似然比累积和控制图

累积和控制图主要用于对正态分布过程中均值的中小漂移的检测,但是对厚尾分布过程监测并不稳定.MacEachern等(2007)提出了用于监测厚尾分布过程的稳健似然比累积和(RLCUSUM)控制图.文章主要研究RLCUSUM控制图的性质,包括可控平均运行长度关于控制限的性质和过程失控时不同真实均值对平均运行长度的影响等,并提出了对于对数似然比函数进行斜线截断的方式,同时分析总结了不同污染程度的混合正态分布下各种截断方式得到的RLCUSUM控制图的适用情况.     

Wavelets collocation methods for the numerical solution of elliptic BV problems

Based on collocation with Haar and Legendre wavelets, two efficient and new numerical methods are being proposed for the numerical solution of elliptic partial differential equations having oscillatory and non-oscillatory behavior. The present methods are developed in two stages. In the initial stage, they are developed for Haar wavelets. In order to obtain higher accuracy, Haar wavelets are replaced by Legendre wavelets at the second stage. A comparative analysis of the performance of Haar wavelets collocation method and Legendre wavelets collocation method is carried out. In addition to this, comparative studies of performance of Legendre wavelets collocation method and quadratic spline collocation method, and meshless methods and Sinc–Galerkin method are also done. The analysis indicates that there is a higher accuracy obtained by Legendre wavelets decomposition, which is in the form of a multi-resolution analysis of the function. The solution is first found on the coarse grid points, and then it is refined by obtaining higher accuracy with help of increasing the level of wavelets. The accurate implementation of the classical numerical methods on Neumann’s boundary conditions has been found to involve some difficulty. It has been shown here that the present methods can be easily implemented on Neumann’s boundary conditions and the results obtained are accurate; the present methods, thus, have a clear advantage over the classical numerical methods. A distinct feature of the proposed methods is their simple applicability for a variety of boundary conditions. Numerical order of convergence of the proposed methods is calculated. The results of numerical tests show better accuracy of the proposed method based on Legendre wavelets for a variety of benchmark problems.     

A numerical assessment of parabolic partial differential equations using Haar and Legendre wavelets

In this paper we present two new numerically stable methods based on Haar and Legendre wavelets for one- and two-dimensional parabolic partial differential equations (PPDEs). This work is the extension of the earlier work ,  and  from one- and two-dimensional boundary-value problems to one- and two- dimensional PPDEs. Two generic numerical algorithms are derived in two phases. In the first stage a numerical algorithm is derived by using Haar wavelets and then in the second stage Haar wavelets are replaced by Legendre wavelets in quest for better accuracy. In the proposed methods the time derivative is approximated by first order forward difference operator and space derivatives are approximated using Haar (Legendre) wavelets. Improved accuracy is obtained in the form of wavelets decomposition. The solution in this process is first obtained on a coarse grid and then refined towards higher accuracy in the high resolution space. Accuracy wise performance of the Legendre wavelets collocation method (LWCM) is better than the Haar wavelets collocation method (HWCM) for problems having smooth initial data or having no shock phenomena in the solution space. If sharp transitions exists in the solution space or if there is a discontinuity between initial and boundary conditions, LWCM loses its accuracy in such cases, whereas HWCM produces a stable solution in such cases as well. Contrary to the existing methods, the accuracy of both HWCM and LWCM do not degrade in case of Neumann’s boundary conditions. A distinctive feature of the proposed methods is its simple applicability for a variety of boundary conditions. Performances of both HWCM and LWCM are compared with the most recent methods reported in the literature. Numerical tests affirm better accuracy of the proposed methods for a range of benchmark problems.     

向量值正交小波的构造与向量值小波包的特征

The notion of vector-valued multiresolution analysis is introduced and the concept of orthogonal vector-valued wavelets with 3-scale is proposed.A necessary and sufficient condition on the existence of orthogonal vector-valued wavelets is given by means of paraunitary vector filter bank theory.An algorithm for constructing a class of compactly supported orthogonal vector-valued wavelets is presented.Their characteristics is discussed by virtue of operator theory,time-frequency method.Moreover,it is shown how to design various orthonormal bases of space L2(R,Cn) from these wavelet packets.     

小波级数的一些讨论

本文针对小波变换数学中,学员对于小波变换多分辨率分析概念理解困难的问题,提出了小波级数教学方法,通过分析小波多分辨分析概念的本质,建立起与傅立叶级数之间的比较和联系,清楚地描述了小波多分辨分析的本质,从而对加深对小波多分辨分析的理解有明显的效果,最终提高了整个小波课程教学效果。     

Subspace Design of Compactly Supported Orthonormal Wavelets

We derive a new matrix parameterization of compactly supported orthonormal wavelets where the coefficients of the wavelet filter are the solution of a linear system of equations that is parameterized by an arbitrary vector. The parameterization shows that the vector of the wavelet filter coefficients is the kernel of a subspace of the condition matrix row-space. This property is exploited to develop a new design procedure for orthonormal wavelets of compact support. The proposed parameterization also describes the class of two-channel orthogonal filter banks where in this case we have two extra degrees of freedom in the design. The effectiveness of the proposed procedure is illustrated by design examples of common orthonormal wavelets.     

A fast numerical algorithm based on the Taylor wavelets for solving the fractional integro‐differential equations with weakly singular kernels

In this paper, a fast numerical algorithm based on the Taylor wavelets is proposed for finding the numerical solutions of the fractional integro‐differential equations with weakly singular kernels. The properties of Taylor wavelets are given, and the operational matrix of fractional integration is constructed. These wavelets are utilized to reduce the solution of the given fractional integro‐differential equation to the solution of a linear system of algebraic equations. Also, convergence of the proposed method is studied. Illustrative examples are included to demonstrate the validity and applicability of the technique.     

State Analysis and Optimal Control of Time-Varying Discrete Systems via Haar Wavelets

The state analysis and optimal control of time-varying discrete systems via Haar wavelets are the main tasks of this paper. First, we introduce the definition of discrete Haar wavelets. Then, a comparison between Haar wavelets and other orthogonal functions is given. Based upon some useful properties of the Haar wavelets, a special product matrix and a related coefficient matrix are proposed; also, a shift matrix and a summation matrix are derived. These matrices are very effective in solving our problems. The local property of the Haar wavelets is applied to shorten the calculation procedures.     

一类紧支撑矩阵值正交小波的构造

In this paper,we introduce matrix-valued multiresolution analysis and orthogonal matrix-valued wavelets.We obtain a necessary and sufficient condition on the existence of orthogonal matrix-valued wavelets by means of paraunitary vector filter bank theory.A method for constructing a class of compactly supported orthogonal matrix-valued wavelets is proposed by using multiresolution analysis method and matrix theory.     

Wavelets from the Loop Scheme

Anewwavelet-based geometric mesh compression algorithm was developed recently in the area of computer graphics by Khodakovsky, Schröder, and Sweldens in their interesting article [23]. The new wavelets used in [23] were designed from the Loop scheme by using ideas and methods of [26, 27], where orthogonal wavelets with exponential decay and pre-wavelets with compact support were constructed. The wavelets have the same smoothness order as that of the basis function of the Loop scheme around the regular vertices which has a continuous second derivative; the wavelets also have smaller supports than those wavelets obtained by constructions in [26, 27] or any other compactly supported biorthogonal wavelets derived from the Loop scheme (e.g., [11, 12]). Hence, the wavelets used in [23] have a good time frequency localization. This leads to a very efficient geometric mesh compression algorithm as proposed in [23]. As a result, the algorithm in [23] outperforms several available geometric mesh compression schemes used in the area of computer graphics. However, it remains open whether the shifts and dilations of the wavelets form a Riesz basis of L₂(?²). Riesz property plays an important role in any wavelet-based compression algorithm and is critical for the stability of any wavelet-based numerical algorithms. We confirm here that the shifts and dilations of the wavelets used in [23] for the regular mesh, as expected, do indeed form a Riesz basis of L₂(?²) by applying the more general theory established in this article.     

Construction and decomposition of biorthogonal vector-valued wavelets with compact support

In this article, we introduce vector-valued multiresolution analysis and the biorthogonal vector-valued wavelets with four-scale. The existence of a class of biorthogonal vector-valued wavelets with compact support associated with a pair of biorthogonal vector-valued scaling functions with compact support is discussed. A method for designing a class of biorthogonal compactly supported vector-valued wavelets with four-scale is proposed by virtue of multiresolution analysis and matrix theory. The biorthogonality properties concerning vector-valued wavelet packets are characterized with the aid of time–frequency analysis method and operator theory. Three biorthogonality formulas regarding them are presented.