CUSUM,GLR,GEWMA以及RFCuscore控制图监测稳定过程均值漂移的效果比较(英)

本文给出了累积和控制图(CUSUM)监测稳定过程均值漂移的平均运行长度(ARL)的区间估计,并采用数字模拟的方法对CUSUM,GLR,GEWMA以及RFCuscore四种控制图监测稳定过程均值漂移的效果进行比较,结果显示CUSUM效果最好.     

监测Lévy稳定过程均值变点的平均运行时间估计

平均运行长度(时间)(ARL)是判断一控制图监测变点效果好坏的一个重要工具.本文主要研究Lévy稳定过程的均值变点监测问题.我们给出了三个控制图,即EWMA,GEWMA和GLR的ARL估计,并通过数值模拟比较了4个控制图监测均值变点的效果和差异.     

监测L\'{e}vy稳定过程均值变点的平均运行时间估计

平均运行长度(时间) (ARL)是判断一控制图监测变点效果好坏的一个重要工具\bd 本文主要研究L\'{e}vy 稳定过程的均值变点监测问题\bd 我们给出了三个控制图, 即EWMA, GEWMA和GLR的ARL 估计, 并通过数值模拟比较了4个控制图监测均值变点的效果和差异.     

监测均值变动的多重控制图方法

本文证明了当受控平均运行长度充分大时, 多重控制图有两个优点: 一是相比较GLR (广义似然比) 和GEWMA (广义指数权重移动平均)控制图它可以大大降低运算的复杂性; 二是能够较快地监测均值变化的大小. 数值模拟也表明: 多重控制图不仅优于其构成的单个控制图, 而且在监测未知的均值变动方面也优于单个的CUSUM, EWMA, 多重EWMA和GLR控制图.     

Optimization designs and performance comparison of two CUSUM schemes for monitoring process shifts in mean and variance

In statistical process control (SPC), when dealing with a quality characteristic x that is a variable, it is usually necessary to monitor both the mean value and variability. This article proposes an optimization algorithm (called the holistic algorithm) to design the CUSUM charts for this purpose. It facilitates the determination of the charting parameters of the CUSUM charts and considerably or significantly increases their overall detection effectiveness. A single CUSUM chart (called the ABS CUSUM chart) has been developed by the holistic algorithm and fully investigated. This chart is able to detect two-sided mean shifts and increasing variance shifts by inspecting the absolute value of sample mean shift. The results of performance studies show that the overall performance of the ABS CUSUM chart is nearly as good as an optimal 3-CUSUM scheme (a scheme incorporating three individual CUSUM charts). However, since the ABS CUSUM chart is easier for implementation and design, it may be more suitable for many SPC applications in which both mean and variance of a variable have to be monitored.     

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In recent years, statistical process control (SPC) has been widely used to monitor the performance of clinical practitioners, such as surgeons and general practitioners. In this paper, two risk-adjusted geometric control charts namely cumulative sum (CUSUM) and weighted likelihood ratio test (WLRT) are proposed to monitor surgery performance in phase II. The performance of the proposed control charts is evaluated and compared by simulation experiments for different shift values in the parameters of a risk-adjusted logistic regression model in terms of the average run length (ARL) criterion. The results show that all methods work well in the sense that they can effectively detect shifts in the process parameters.     

关于累积和(CUSUM)检验的改进

对连续检验问题，常用的检测方法有三大类其一是众所周知的Shewhartt控制图，它是最常用的对生产过程进行连续监控的控制方法，不过，如果过程均值有小的漂移(即μ-μo小)时，Shewhart控制图的检验效果不是很好，除了Shewhart控制图外，另有二类常用的控制图法，其一是累积和控制图(CUSUM)，由Page^[1]基于似然比导出，其二是指数加权移动平均控制图(EWMA)，由Roberts^[2]给出，它们已被证明在检测小的漂移时效果不错。许多人对CUSUM与EWMA进行了比较，总的来说。最好的CUSUM与最好的EWMA在检测小的漂移方面难分优劣，但CUSUM是由似然比导出的，且其平均运行长度的计算相对来说要简便些，因此，CUSUM在与EWMA的比较中更具优势，应用更广．我们分析了CUSUM的导出过程和公式。指出CUSUM有二个可以进一步改进的方面在此基础上，我们给出了二个新的累积和检验统计量及其判断难则，它们分别是PCUSUM检验统计量Pn和DCUSUM检验统计量Sn．在连续检验问题中判断一个检验方法好坏的最重要的标难是其平均运行长度比较标难是在要求具有相同的受控状态下平均运行长度ARL0的条件下，比较其失控状态下的平均运行长度ARL1，ARL1越小越好我们对PCUSUM检验和DCUSUM检验都建立了其平均运行长度ARL的计算公式．通过对CUSUM，PCUSUM，DCUSUM的平均运行长度的比较我们发现我们提出的新的累积和控制方法确比原来的CUSUM有较大改进。     

CUSUM control charts based on likelihood ratio for preliminary analysis

To detect and estimate a shift in either the mean and the deviation or both for the preliminary analysis, the statistical process control (SPC) tool, the control chart based on the likelihood ratio test (LRT), is the most popular method. Sullivan and woodall pointed out the test statistic lrt(n1, n2) is approximately distributed as x2(2) as the sample size n,n1 and n2 are very large, and the value of n1 = 2,3,..., n - 2 and that of n2 = n - n1. So it is inevitable that n1 or n2 is not large. In this paper the limit distribution of lrt(n1, n2) for fixed n1 or n2 is figured out, and the exactly analytic formulae for evaluating the expectation and the variance of the limit distribution are also obtained. In addition, the properties of the standardized likelihood ratio statistic slr(n1, n) are discussed in this paper. Although slr(n1, n) contains the most important information, slr(i, n)(i≠n1) also contains lots of information. The cumulative sum (CUSUM) control chart can obtain more information in this condition. So we propose two CUSUM control charts based on the likelihood ratio statistics for the preliminary analysis on the individual observations. One focuses on detecting the shifts in location in the historical data and the other is more general in detecting a shift in either the location and the scale or both. Moreover, the simulated results show that the proposed two control charts are, respectively, superior to their competitors not only in the detection of the sustained shifts but also in the detection of some other out-of-control situations considered in this paper.     

控制过程方差的CUSUMQ图及其性质

崔恒建．控制过程方差的ＣＵＳＵＭＱ图及其性质．数理统计与管理，１９９８，１７（４），３３～３８．Ｑｕｓｅｎｂｅｒｒｙ（１９９５）基于样本方差的标准化变换Φ－１［Ｈｎ－１（（ｎ－１）Ｓ２／σ２０）］提出了控制过程方差的累积和（ＣＵＳＵＭ）Ｑ控制图。本文我们描述了在控制过程方差变化中这种ＣＵＳＵＭＱ控制图的性质，并将控制图的设计方法用到单边及双边的ＣＵＳＵＭＱ图，说明它几乎是最优的。而且我们发现在控制过程方差的微小变化时，设计的ＣＵＳＵＭＱ图的性能要优于基于ｌｏｇ（Ｓ２）的ＣＵＳＵＭ和ＥＷＭＡ图     

Chi-square Control Charts with Runs Rules

The Hotelling’s χ² control chart is one of the most widely used multivariate charting procedures for monitoring the vector of means of several quality characteristics. As a Shewhart-type control chart, it incorporates information pertaining to most recently inspected sample and subsequently it is relatively insensitive in quickly detecting small magnitude shifts in the process mean vector. A popular solution suggested to overcome this handicap was the use of runs and scans rules as criteria to declare a process out-of-control. During the last years, the examination of Hotelling’s χ² control charts supplemented with various runs rules has attracted continuous research interest. In the present article we study the performance of the Hotelling’s χ² control chart supplemented with a r-out-of-m runs rule. The new control chart demonstrates an improved performance over other competitive runs rules based control charts.     

MULTIVARIATE SURVIVAL DISTRIBUTIONS OF AGE AND RESIDUAL LIFETIME PROCESSES IN NONHOMOGENEOUS POISSON PROCESS

Let{N(t),t≥0} be the nonhomogeneous Poisson process with cumulative intensity parameter Λ(t),{δt,t≥0} the age process,and {yi,t≥0) the residual lifetime process.In the present paper the expressions of n-dimensional survival distribution functions of the processes{δi} and {yi}, and their Lebesgue decompositions are derived.     

Testing for changes in the mean or variance of long memory processes

In this paper, we study the asymptotic CUSUM tests for detecting changes in the mean or variance of a moving-average process with long memory. When there is no change over [O,T], the asymptotic distribution of the test statistic is derived, which allows us to find asymptotic critical values. When there is a change, the behavior of the test statistic is discussed. Conditions for the consistency of these tests are also discussed. Based on the asymptotic results, simulation studies of testing for changes in the mean show that the CUSUM test proposed performs well.     

On correct selection for a ranking problem

Givenk populations which belong to the exponential class, and having specified two positive constants (δ ^*,P ^*), an experimenter wishes to selectt populations which (a) exclude all those populations with a parameter value not greater than thetth largest parameter value minusδ ^*, and (b) include all those populations with a parameter value not smaller than the (t+1)th largest parameter value plusδ ^*. This paper shows that the probability of successfully making such a selection, called aδ ^*-correct selection, is at leastP ^* if the basic sequential procedure,P _B ^* , of Bechhofer, et al. [3] is used. This result includes the corresponding old result of their book (p. 129) as a particular case.     

Value distribution of Painlevé transcendents of the first and the second kind

We examine value distribution properties of the first and the second Painlevé transcendents. For every transcendental meromorphic solution ϕ(z) (resp. ψ(z)) of the first (resp. second) Painlevé equation, the deficiency δ(g,ϕ) (resp. δ(g, ψ)) of a small functiong(z) does not exceed 1/2. Furthermore, for ϕ(z), the ramification index satisfies ϑ(gφ)≤5/12.     

Generalizations of coatomic modules

For a ring R and a right R-module M, a submodule N of M is said to be δ-small in M if, whenever N+X=M with M/X singular, we have X=M. Let ℘ be the class of all singular simple modules. Then δ(M)=Σ{ L≤ M| L is a δ-small submodule of M} = Re _jm(℘)=∩{ N⊂ M: M/N∈℘. We call M δ-coatomic module whenever N≤ M and M/N=δ(M/N) then M/N=0. And R is called right (left) δ-coatomic ring if the right (left) R-module R _R(_RR) is δ-coatomic. In this note, we study δ-coatomic modules and ring. We prove M=⊕ _i=1 ⁿ M_i is δ-coatomic if and only if each M _i (i=1,…, n) is δ-coatomic.     

On fuzzy semi δ-<Emphasis Type="Italic">V</Emphasis> continuity in fuzzy δ-<Emphasis Type="Italic">V</Emphasis> topological space

New concepts of fuzzy semi δ-V and fuzzy semi δ-Λ sets were introduced in our work “On fuzzy semi δ-Λ sets and fuzzy semi δ-V sets V-6,” J. Trip. Math. Soc., 6, 81–88 (2004). It was shown that the family of all fuzzy semi δ-V sets forms a fuzzy supra topological space on X denoted by (X, FS ^δV ). The aim of this paper is to introduce the concept of fuzzy semi δ-V continuity in a fuzzy δ-V topological space. Finally, some properties, preservation theorems, etc., are studied. Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 5, pp. 712–717, May, 2008.     

Sopra le trasformazioni in sè della varietà di Jacobi relativa ad una curva di genere effettivo diverso dal genere virtuale,in ispecie nel caso di genere effettivo nullo

Sunto. Si precisa la natura del problema di determinare le trasformazioni in sè della varietà quasi abeliana diJacobi, relativa ad una curva di genere virtualeπ, ottenuta da una curva di genere effettivop considerando su questaδ ₁ coppie neutre a punti distinti eδ ₂ coppie neutre a punti coincidenti, in modo che siaπ=p+δ ₁+δ₂. Come nel coso abeliano (δ ₁=δ₂=0), tale problema ha un aspetto aritmetico, che si collega alla considerazione di relazioni, che generalizzano quelle note diHurwitz. Nel casop=0 si trovano tutte le trasformazioni in sè dellaV _π diJacobi, mostrando che queste costituiscono un gruppo formato sempre da infinite schiere ∞^π (tranne nel casoπ=δ ₁=1, δ₂=0), dipendenti da parametri in parte variabili in modo continuo ed in parte in modo discreto. Le trasformazioni sono tutte birazionali seδ ₁=0 oδ ₂=0, mentre seδ ₁ ≠ 0 eδ ₂ ≠ 0 si presentano anche trasformazioni trascendenti.     

Length and Stable Length

This paper establishes the existence of a gap for the stable length spectrum on a hyperbolic manifold. If M is a hyperbolic n-manifold, for every positive ϵ there is a positive δ depending only on n and on ϵ such that an element of π₁(M) with stable commutator length less than δ is represented by a geodesic with length less than ϵ. Moreover, for any such M, the first accumulation point for stable commutator length on conjugacy classes is at least 1/12. Conversely, “most” short geodesics in hyperbolic 3-manifolds have arbitrarily small stable commutator length. Thus stable commutator length is typically good at detecting the thick-thin decomposition of M, and 1/12 can be thought of as a kind of homological Margulis constant. Received: June 2006 Revision: May 2007 Accepted: June 2007     

(<Emphasis Type="Italic">δ</Emphasis>,<Emphasis Type="Italic">δ</Emphasis>′)-continuity on generalized topological spaces

We introduce the notion of (δ,δ′)-continuous functions on generalized topological spaces and investigate characterizations for such functions. We study the relationship between (δ,δ′)-continuity and several types of continuity on generalized topological spaces.     

The extrapolation of band-limited signals in L2 with sampling errors

In this paper we will provide a theory for an extrapolation algorithm of band-limited signals with sampling errors or low noises. The main result is as follows: Suppose thatf(t) is in L² and is a continuous Ω band-limited signal. Then for any positive numbers T, A(>T) and ε, there exists a δ>0 such that when the sampling errors (or noises) off(t) on [−T, T] is less than δ we can extrapolate the values off(t) on the interval [−A, A] such that the difference between the extrapolated value and the exact value off(t) does not exceed ε.