a reference free cuscore chart for dynamic mean change detection and a unified framework for charting performance comparison to detect and estimate nonconstant time varying mean shifts statistical process control spc tools such as the cumulative score cuscore and generalized likelihood ratio test glrt charts have recently been proposed however their efficiency is based on previous and exact knowledge of a reference pattern in this article a reference free cuscore rfcuscore chart is proposed that can trace and detect dynamic mean changes quickly without knowing the reference pattern in addition a unified framework that contains most of the control charts is presented and applied for a theoretical comparison of the rfcuscore cuscore glrt and cusum charts in detecting dynamic mean changes moreover numerical simulations and a real example are used to illustrate and verify the results both theoretical analysis and numerical results show that the rfcuscore chart performs not only robustly but also quickly in detecting both small and large dynamic mean changes

minimal structure in the block decoupling problem with stability abstract in this paper we consider the block decoupling problem with stability we characterize the minimal mcmillan degree achievable for the block decoupled system for this we introduce a new list of integers which are feedback invariant these integers are related in a simple way to the minimal number of unstable and infinite zeros of the block decoupled system

grassmannian central projection and output feedback pole assignment of linear systems a sufficient rank condition for arbitrary pole assignability by static output feedback of m input p output linear systems of mcmillan degree n mp is given this condition is easy to check and is satisfied by the generic system an effective computational method to compute the feedback laws assigning any self conjugate set of closed loop poles is also given

design of exponentially weighted moving average control charts for autocorrelated processes with model uncertainty residual based control charts are popular methods for statistical process control of autocorrelated processes to implement these methods a time series model of the process is required the model must be estimated from data in practice and model estimation errors can cause the actual in control average run length to differ substantially from the desired value this article develops a method for designing residual based exponentially weighted moving average ewma charts under consideration of the uncertainty in the estimated model parameters the resulting ewma control limits are widened by an amount that depends on a number of factors including the level of model uncertainty

gaussian measures of dilatations of convex symmetric sets we prove that the inequality 1 ta t 1 a holds for any centered gaussian measure on a separable banach space f any convex closed symmetric set a f and t 1 where x 1 x x 2 1 2 x x exp y 2 2 dy as an application the best constants in comparison of moments of gaussian vectors are calculated

saturating constructions for normed spaces ii we prove several results of the following type given finite dimensional normed space v there exists another space x with log dim x o log dim v and such that every subspace or quotient of x whose dimension is not too small contains a further subspace isometric to v this sheds new light on the structure of such large subspaces or quotients resp large sections or projections of convex bodies and allows us to solve several problems stated in the 1980s by v milman

a transfer matrix approach to feedback invariants of linear systems application to decoupling abstract the transfer matrix approach allows one to exhibit fairly easily fundamental invariants of multivariable systems under the action of transformation groups these transformation groups include the classical state feedback state and input changes of coordinates then the solvability of numerous classical control problems e g decouplability disturbance rejection model following can be expressed directly in terms of these invariants in this expository paper we present in a unified way three lists of feedback invariants related to the infinite behavior of linear systems these invariants turn out to be crucial in studying feedback decoupling problems the main tools for this study are factorization of transfer matrices over the p i d of proper rational functions when dealing with stability we factor transfer matrices over the p i d of proper rational stable functions we illustrate the use of these invariants by studying some decoupling problems

input output and state space representations of finite dimensional linear time invariant systems in this paper we develop various representations for systems described by aset of high order differential equations of the form r0w r1w rsw s 0 with r0 r1 rs not necessarily square matrices the variables w are the external variables particular attention is paid to the problem of obtaining minimal state space realizations and input output or input state output representations of such systems

gaussian processes and almost spherical sections of convex bodies on presente une preuve simple avec des estimations pointues du theoreme de dvoretzky sur l existence des sections presque spheriques ayant une grande dimension dans des corps convexes arbitraires dans r n

a statistical control chart for stationary process data in the statistical process control environment a primary method to deal with autocorrelated data is the use of a residual chart although this methodology has the advantage that it can be applied to any autocorrelated data it needs some modeling effort in practice in addition the detection capability of the residual chart is not always great this article proposes a statistical control chart for stationary process data it is simple to implement and no modeling effort is required comparisons are made among the proposed chart the residual chart and other charts when the process autocorrelation is not very strong and the mean changes are not large the new chart performs better than the residual chart and the other charts

bounds for projection constants and 1 summing norms it is shown that projection constants k xn of dimensional normed spaces xn satisfy l xn 0 is a numer ical constant similarly the 1 summing norms of the identity of xn can be estimated by ttx xn fn c fn these estimates are the best possi ble for prime n translation invariant dimensional spaces xn such that k xn sfh 2l jn and itx xn 3v d xn lf fn 1 introduction and results the main results of the paper complete the investigation of an upper bound for the projection constants of arbitrary finite dimensional banach spaces which had started with the kadec snobar kas estimate k xn yfn for any n dimensional space xn this estimate was further studied in several papers koll ko kol lew2 in particular it has recently been shown by lewis lew2 that k xf yfh n 5 our main theorem gives an essential strengthening stated in the abstract upper bounds for projection constants are intimately connected to lower bounds for the 1 summing norm of the identity operator for spaces with enough symmetries these bounds follow from each other by a simple formal argument in general it turns out that similar but somewhat simpler calcula tions than for the projection constants lead to the lower bound for nx xn both upper and lower bounds are the best possible up to terms of higher order the approach used by konig in ko based on some number theoretic results gives the relevant constructions the same approach leads to a con struction of a finite dimensional space with large gordon lewis constant this provides the first deterministic example of such a space our notation essentially follows tj for completeness let us recall the main

monitoring processes that wander using integrated moving average models often the least appropriate assumption in traditional control charting technology is that process data constitute a random sample in reality most process data are correlated either temporally spatially or due to nested sources of variation one approach to monitoring temporally correlated data uses a control chart on the forecast errors from a time series model of the process with possibly a transfer function term to model compensatory adjustments if the time series term is an integrated moving average then a sudden level shift in the process results in a patterned shift in the mean of forecast errors initially the mean shifts by the same amount as the process level but then it decays geometrically back to 0 corresponding to the ability of the forecast to recover from the upset we study four monitoring schemes umulative sums cusum s exponentially weighted moving averages shewhart individuals charts and a likelihood ratio scheme comparisons of signaling probabilities and average run lengt

designing x charts for known autocorrelations and unknown marginal distribution abstract in the design of the x control chart both the sample size m of x and the control limit factor k the number of standard deviations from the center line must be determined we address this problem under the assumption that the quality characteristic follows an autocorrelated process with known covariance structure but unknown marginal distribution shape we propose two methods for determining m and k chosen to minimize the out of control arl average run length while maintaining the in control arl at a specified value method 1 calculates the arl values as if the sample means were independent normal random variables method 2 calculates the arl values as if the sample means were an ar 1 process method 2 outperforms method 1 when the correlation and mean shift are both high we also modify methods 1 and 2 with a minimum sample size of 30 the modification moves the in control arl closer to the specified value our numerical results show that the modified method 2 performs better than two previous design procedures especially when the correlation is high

the minimal delay decoupling problem feedback implementation with stability in this paper we solve the minimal delay decoupling problem of linear multivariable systems we look for feedback implementable solutions which moreover guarantee closed loop stability we prove that dynamic state feedback decoupling with stability is achievable if the number of independent inputs is large enough to compensate the intrinsic nondecouplability of the system we introduce new feedback invariants characterizing the minimal number of infinite and unstable zeros of the decoupled system

run length distributions of special cause control charts for correlated processes we derive run length distributions of the special cause control chart proposed by alwan and roberts for correlated observations given that the assignable cause to be detected is a shift in the process mean both recursive and closed form solutions are derived for the run length distribution average run length arl and standard deviation of the run length srl for any ar p process and approximate solutions are derived for the more general arma p q processes the expressions derived do not depend on the type of shift in the process mean numerical results are illustrated for the arl and srl of the arma l l model given that the shift in the mean is a step shift these results show that the arl and srl of the specialcause control chart are relatively smaller when the process is negatively rather than positively autocorrelated regardless of the sign of the autocorrelation the shape of the probability mass function of the run length reveals that the probability of detecting shifts very early is subs

on the structure at infinity of linear square decoupled systems the purpose of this note is to demonstrate that a square invertible linear system c a b is decouplable by static state feedback if and only if its infinite zero orders are respectively equal to the infinite zero orders of the subsystems c i a b where c i denotes the i th row of c until now only the necessity of this condition has been established 1

linear feedback decoupling transfer function analysis the problem of linear system decoupling is examined based on recent results on linear feedback new insight is obtained through which resolution of the decoupliug problem is accomplished by calculations performed directly on the given transfer matrix computation of the decoupling compensators follows by easy constructions the problem of feedback block decoupling with internal stability is also formulated and resolved

feedback block decoupling and infinite structure of linear systems abstract using factorizations at infinity of the transfer matrix two interesting necessary and sufficient conditions arc obtained for the block decoupling problem of linear systems by state feedback and a constant non singular input transformation these conditions are expressed in a very simple way in terms of integers which are feedback invariants for the system under consideration these feedback invariants are related either to the system infinite structure or to the reachability indices of the feedback reduced system

invariant spaces at infinity of linear systems application to block decoupling the dynamic state feedback block decoupling problem in the general case i e with singular or nonsingular input transformations is solved it is proven that the problem is solvable if the number of inputs is large enough the main tools for this study are some invariant spaces associated with the columns infinite behavior of a rational matrix it turns out that when the problem is solvable it is also solvable with stability

block decoupling by precompensation revisited the block decoupling problem by admissible dynamic precompensation for lti systems is considered admissibility refers to the preservation of the class of controlled output trajectories i e functional output controllability is concerned which is more demanding than just pointwise output controllability this problem has been solved by hautus and heyman within a transfer function matrix approach different new equivalent solvability conditions in terms of controllability subspaces transfer function matrices or matrix pencils are given one of these conditions expressed in the input space is at the origin of new necessary and sufficient conditions for block decoupling by general precompensation possibly non admissible and nonsquare in the wider sense of basile and marro

control chart tests based on geometric moving averages a geometrical moving average gives the most recent observation the greatest weight and all previous observations weights decreasing in geometric progression from the most recent back to the first a graphical procedure for generating geometric moving averages is described in which the most recent observation is assigned a weight r the properties of control chart tests based on geometric moving averages are compared to tests based on ordinary moving averages

nonparametric dynamic curve monitoring rapid sequential comparison between the longitudinal pattern of a given subject and a target pattern has become increasingly important in modern scientific research for detecting abnormal activitie

smith mcmillan factorizations at infinity of rational matrix functions and their control interpretation in this paper the smith mcmillan factorizations at infinity of a transfer function are studied the non uniqueness of these factorizations is characterized via a multiplicative group of bicausal isomorphisms control interpretations are given in terms of system equivalence under some groups of transformations a characterization of the stabilizer of morse group at a b c is given for irreducible systems

causal factorization and linear feedback an algebraic framework for the investigation of linear dynamic output feedback is introduced pivotal in the present theory is the problem of causal factorization i e the problem of factoring two systems over each other through a causal factor the basic issues are resolved with the aid of the new concept of latency kernels

spectral analysis in quality control a control chart based on the periodogram variations in manufacturing processes are expected to fluctuate around a constant level called the process mean this article is concerned with the development of a control chart that detects cycles in the process mean the new control chart the spectral control chart is based on the periodogram the value plotted at each point in time is the ratio of the largest periodogram ordinate to the average of all ordinates when an observation falls above the prescribed control limit an out of control signal is given the spectral control chart is compared with the shewhart and geometric moving average charts data obtained from monte carlo simulations show that the spectral control chart is superior for detecting cyclic variations but that it is not effective for detecting shifts in the process mean thus the spectral control chart should be used along with existing control charts so that both shifts and cycles in the process mean can be detected

multivariable nyquist criteria root loci and pole placement a geometric viewpoint classical control theory is concerned with the topics in our title in the context of single input single output systems there is now a large and growing literature on the extension of these ideas to the multiinput multioutput case this development has posed certain difficulties some due to the intrinsic nature of the problem and some we would argue due to an inadequate reflection on what the multivariable problem calls for in this paper we describe what seems to us to be the natural multivariable analogs of these concepts from classical control theory a rather satisfactory generalization of the nyquist criterion will be described and a clear analog of the asymptotic properties of the root locus will be obtained in the multiparameter case however an example is given which illustrates the quite surprising fact that the root locus map is not always continuous at infinite gains this calls for a new ingredient a compactification of the space of gains and perhaps the most interesting new feature in this circle of ideas comes in the area of pole placement this problem is difficult in the multivariable case but by establishing a correspondence with a classical set of problems in geometry we are able to understand its main aspects and to derive results on pole placement by output feedback over the real field

exponentially weighted moving average control schemes properties and enhancements roberts 1959 first introduced the exponentially weighted moving average ewma control scheme using simulation to evaluate its properties he showed that the ewma is useful for detecting small shifts in the mean of a process the recognition that an ewma control scheme can be represented as a markov chain allows its properties to be evaluated more easily and completely than has previously been done in this article we evaluate the properties of an ewma control scheme used to monitor the mean of a normally distributed process that may experience shifts away from the target value a design procedure for ewma control schemes is given parameter values not commonly used in the literature are shown to be useful for detecting small shifts in a process in addition several enhancements to ewma control schemes are considered these include a fast initial response feature that makes the ewma control scheme more sensitive to start up problems a combined shewhart ewma that provides protection against both larg

cascade equivalence of linear systems abstract this paper concerns the characterization of a linear system with respect to output feedback as well as to slightly more general transformations called cascade transformations with a transfer function t s we associate a finite tuplee of numbers that is invariant under cascade transformation

on the linear static output feedback problem the annihilating polynomial approach abstract one of the fundamental open problems in control theory is that of the stabilization of a linear time invariant dynamical system through static output feedback we are given a linear dynamical system defined through w a w b u y c w the problem is to find if it exists a feedback u k y such that the matrix a b k c has all its eigenvalues in the complex left half plane and if such a feedback does not exist to prove that it does not substantial progress has not been made on the computational aspect of the solution to this problem in this paper we consider instead which annihilating polynomials can a matrix of the form a b k c possess we give a simple solution to this problem when the system has either a single input or a single output for the multi input multi output case we use these ideas to characterize the annihilating polynomials when k has rank one and suggest possible computational solutions for general k we also present some numerical evidence for the plausibility of this approach for the general case as well as for the problem of shifting the eigenvalues of the system

control charts for detecting cyclical behavior one way that a process can be out of statistical control is that the process mean can follow a cyclical pattern over time this out of control condition leads to increased variability in the variable of interest over any production interval recently a control chart based on a common time series technique the periodogram was proposed as a means of detecting cyclical behavior of the process mean we show that this control chart is not able to detect certain periodicities and that it does not make use of all available information when multiple observations are taken at each sampling time using a multiple regression approach we present modifications of the periodogram approach that produce control charts sensitive to a wider range of periodicities and use all available information we compare the average run lengths of the procedures

a simple method for studying run length distribution of exponentially weighted moving average charts a numerical procedure using integral equations is presented for the tabulation of moments of run lengths of exponentially weighted moving average ewma charts both average run lengths arl s and standard deviations of run lengths sdrl s are presented for the twosided ewma chart assuming normal observations along with an example illustrating how to design such a chart the procedure given extends easily to many nonnormal cases and to one sided versions of the ewma chart