addendum to estimates of the determinant of a perturbed identity matrix linear algebra appl 558 2018 101 107 abstract many bounds for the determinant det i e of a perturbed identity matrix are known mostly the upper bound is inferior to the classical hadamard bound in this note we give simple and efficiently computable relative bounds differing by e f 3 where the upper bound is usually better than hadamard s bound

perron frobenius theorem for matrices with some negative entries abstract we extend the classical perron frobenius theorem to matrices with some negative entries we study the cone of matrices that has the matrix of 1 s ee t as the central ray and such that any matrix inside the cone possesses a perron frobenius eigenpair we also find the maximum angle of any matrix with ee t that guarantees this property

some omnibus exponentially weighted moving average statistical process monitoring schemes exponentially weighted moving average ewma quality monitoring schemes capahlc of detecting changes in both location and spread referred to as omnibus ewma s are proposed omnibus ewma s are based on the exponentiation of the absolute value of the standardized sample mean of the observations the process target mean and standard deviation are used for standardizing design procedures and considerations including a fast initial response feature are discussed average run lengths for exponents of 5 and 2 and various values of the weighting constant are presented the proposed schemes are compared with each other and with a number of selected well known omnibus schemes and a proposed omnibus cumulative sum scheme schemes with different sample sizes are used and off target models include both static and dynamic alternatives comparisons are based on average number of observations to detection and expected loss due to poor quality one of the omnibus ewma schemes is shown to be best with regard to exp

ray solvable linear systems and ray s2ns matrices abstract ray solvable linear systems and ray s 2 ns matrices are complex generalizations of the sign solvable linear systems and s 2 ns matrices we use the determinantal ray unique matrices instead of ray nonsingular matrices as a generalization of sns matrices to generalize some fundamental results of s 2 ns matrices from the real case to complex case such as the graph theoretical characterization the inverse ray patterns and the upper bound of the number of nonzero entries of s 2 ns matrices the well known characterization of the sign solvable linear systems in terms of the l matrices and s matrices is also generalized to ray solvable linear systems and the relationships between the ray s matrices and real s matrices are investigated some examples are also given to illustrate that some results such as the characterization of the sign inconsistent linear systems do not carry over to the complex case

dynamic sampling plan in shiryayev roberts procedure for detecting a change in the drift of brownian motion in this paper a dynamic sampling plan in the shiryayev roberts procedure is considered it is shown that a two rate dynamic sampling plan is optimal in the sense that it minimizes the stationary average delay time sadt analytical results as well as numerical comparisons show that it is significantly superior to the fixed sampling plan the comparison also shows that it is as powerful as the dynamic sampling procedure of assaf and ritov the generalizations to the fast initial response and to the cusum procedure are also briefly discussed

verified bounds for the determinant of real or complex point or interval matrices abstract we discuss several methods to compute a verified inclusion of the determinant of a real or complex point or interval matrix for point matrices large condition number 1 0 15 and large dimension n 1000 still highly accurate inclusions are computed for real interval matrices we show that any vertex may be a unique extreme point for wide radii we show that preconditioning may widen an inclusion significantly and hadamard s bound may be much better

joint monitoring of process mean and variance using exponentially weighted moving average control charts the performances of control charting schemes for thejoint monitoring of a process mean and a variance are evaluated and compared certain schemes are shown to be inadequate for this purpose and the potential risk of using these schemes alone is discussed a combined scheme consisting of a two sided exponentially weighted moving average ewma mean chart and a two sided ewma variance chart is found to perform well under several types of out of control situations a simple method is provided for approximating the average run length and the percentage points of a run length distribution of a combined ewma scheme a simple procedure is also proposed for the design of a combined ewma scheme

hierarchical poisson regression modeling abstract the poisson model and analyses here feature nonexchangeable gamma distributions although exchangeable following a scale transformation for individual parameters with standard deviations proportional to means a relatively uninformative prior distribution for the shrinkage values eliminates the ill behavior of maximum likelihood estimators of the variance components when tested in simulation studies the resulting procedure provides better coverage probabilities and smaller risk than several other published rules and thus works well from bayesian and frequentist perspectives alike the computations provide fast accurate density approximations to individual parameters and to structural regression coefficients the computer program is publicly available through statlib

the performance of exponentially weighted moving average charts with estimated parameters the exponentially weighted moving average ewma control chart is typically designed assuming that standards are given for the process parameters in practice the parameters are rarely known and control charts are constructed using estimates in place of the parameters this practice can affect the control chart s run length performance in both in and out of control situations specifically estimation can lead to substantially more frequent false alarms and yet reduce the sensitivity of the chart to detecting process changes in this article the run length distribution of the ewma chart with estimated parameters is derived the effect of estimation on the performance of the chart is discussed in a variety of practical scenarios

higher order derivatives and perturbation bounds for determinants the first derivative of the determinant function is given by the well known jacobi s formula we obtain three different expressions for all higher order derivatives norms of these derivatives are then evaluated exactly

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

accurate floating point summation part i faithful rounding given a vector of floating point numbers with exact sum s we present an algorithm for calculating a faithful rounding of s i e the result is one of the immediate floating point neighbors of s if the sum s is a floating point number we prove that this is the result of our algorithm the algorithm adapts to the condition number of the sum i e it is fast for mildly conditioned sums with slowly increasing computing time proportional to the logarithm of the condition number all statements are also true in the presence of underflow the algorithm does not depend on the exponent range our algorithm is fast in terms of measured computing time because it allows good instruction level parallelism it neither requires special operations such as access to mantissa or exponent it contains no branch in the inner loop nor does it require some extra precision the only operations used are standard floating point addition subtraction and multiplication in one working precision for example double precision certain constants used in the algorithm are proved to be optimal

design and performance analysis of the exponentially weighted moving average mean estimate for processes subject to random step changes the exponentially weighted moving average ewma is a well known and popular statistic used for smoothing and forecasting time series and as a process mean estimator due to its simplicity and ability to capture nonstationarity the ewma statistic has been shown to be an optimal mean estimator for a certain disturbance process and an effective estimator for various other processes in this article we focus on a practical disturbance process relatively small random step changes that are difficult to distinguish from white noise and usually overlooked by practitioners we propose an optimal ewma parameter for step change disturbance processes as well as methodologies to identify and estimate the process models the ewma estimator s performance is then evaluated analytically we demonstrate that a well designed ewma control scheme can effectively reduce the process variation even for processes subject to infrequent small step changes a semiconductor process example illustrates the design and analysis

accurate sum and dot product algorithms for summation and dot product of floating point numbers are presented which are fast in terms of measured computing time we show that the computed results are as accurate as if computed in twice or k fold working precision k ge 3 for twice the working precision our algorithms for summation and dot product are some 40 faster than the corresponding xblas routines while sharing similar error estimates our algorithms are widely applicable because they require only addition subtraction and multiplication of floating point numbers in the same working precision as the given data higher precision is unnecessary algorithms are straight loops without branch and no access to mantissa or exponent is necessary

multivariate statistical process control using lasso this article develops a new multivariate statistical process control spc methodology based on adapting the lasso variable selection method to the spc problem the lasso method has the sparsity property of being able to select exactly the set of nonzero regression coefficients in multivariate regression modeling which is especially useful in cases where the number of nonzero coefficients is small in multivariate spc applications process mean vectors often shift in a small number of components our primary goals are to detect such a shift as soon as it occurs and to identify the shifted mean components using this connection between the two problems we propose a lasso based multivariate test statistic and then integrate this statistic into the multivariate ewma charting scheme for phase ii multivariate process monitoring we show that this approach balances protection against various shift levels and shift directions and thus provides an effective tool for multivariate spc applications this article

optimal stopping times for detecting changes in distributions it is shown that page s stopping time is optimal for the detection of changes in distributions in a well defined sense this work is a generalization of an existing result where it was shown that page s stopping time is optimal asymptotically

monitoring profiles based on nonparametric regression methods the use statistical process control spc in monitoring and diagnosis of process and product quality profiles remains an important problem in various manufacturing industries the spc problem with a nonlinear profile is particularly challenging this article proposes a novel scheme to monitor changes in both the regression relationship and the variation of the profile online it integrates the multivariate exponentially weighted moving average procedure with the generalized likelihood ratio test based on nonparametric regression the proposed scheme not only provides an effective spc solution to handle nonlinear profiles which are common in industrial practice but it also resolves the latent problem in popular parametric monitoring methods of being unable to detect certain types of changes due to a misspecified out of control model our simulation results demonstrate the effectiveness and efficiency of the proposed monitoring scheme in addition a systematic diagnostic approach is provided to locate t

the inertial properties of quality control charts many types of control charts have an ability to detect process changes that can weaken over time depending on the past data observed this is often referred to as the inertia problem we propose a new measure of inertia the signal resistance to be the largest standardized deviation from target not leading to an immediate out of control signal we calculate the signal resistance values for several types of univariate and multivariate charts our conclusions support the recommendation that shewhart limits should be used with exponentially weighted moving average charts especially when the smoothing parameter is small

adaptive thresholds monitoring streams of network counts this article describes a fast statistically principled method for monitoring streams of network counts which have long term trends rough cyclical patterns outliers and missing data the key step is to build a reference predictive model for the counts that captures their complex salient features but has just a few parameters that can be kept up to date as the counts flow by without requiring access to past data this article justifies using a negative binomial reference distribution with parameters that capture trends and patterns and method of moment estimators that can be computed quickly enough to keep up with the data flow the reference distribution may be of interest in its own right for traffic engineering and load balancing but a more challenging task is to use it to identify degraded network performance as quickly as possible here we detect changes in network performance not by monitoring quantiles of the predictive distribution directly but by applying control chart methodology to normal scores of the p values of the counts using p values adjusts for the lack of stationarity from one count to the next compared with thresholding isolated counts control charting reduces the false alarm rate increases the chance of detecting ongoing low level events and reduces the time to detection of long events this adaptive count thresholding procedure is shown to perform well on both real and simulated data

a diffusion process and its applications to detecting a change in the drift of brownian motion abstract the purpose of the present paper is to make a quantitative comparison of the shiryayev roberts and page procedures we do this in the context of continuous time in order to use the machinery of diffusion processes to perform explicitly certain calculations which seem impossible in discrete time although the continuous time results are not especially good approximations to the corresponding quantities in discrete time they provide very useful comparative information on which to base selection of a stopping rule this paper is organized as follows the shiryayev roberts process is defined and shown to be a novel diffusion process with some surprising properties we also specify more precisely the basis for our comparison of the two procedures and give the results of some elementary calculations these developments contain an asymptotic evaluation we define a modification of our basic procedure and give an asymptotic evaluation of its average run length numerical comparisons and a discussion of their significance are contained next our conclusions are roughly these in simple situations where the two procedures can be directly compared neither seems dramatically superior to the other however the shiryayev roberts procedure is more easily adapted to complex circumstances and consequently warrants additional study

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

sequential detection of a change in a normal mean when the initial value is unknown three stopping rules are proposed to detect a change in a normal mean when the initial value of the mean is unknown but an estimate obtained from a training sample is available asymptotic approximations are given for the average run length when there is no change under certain hypotheses about the length of time before the change occurs and the magnitude of the change we obtain asymptotic approximations for the expected delay in detection in terms of the corresponding expected delay in the much simpler case of a known initial value the results of a monte carlo experiment supplement our asymptotic theory to yield some general conclusions about the relative merits of the three stopping rules and guidelines for choosing the size of the training sample

joint statistical design of double sampling x and s charts abstract in statistical quality control usually the mean and variance of a manufacturing process are monitored jointly by two statistical control charts e g a x chart and a r chart because of the efficiency of double sampling ds x charts in detecting shifts in process mean and ds s charts in process standard deviation it seems reasonable to investigate the joint ds x and s charts for statistical quality control in this paper a joint ds x and s chart scheme is proposed the statistical design of the joint ds x and s charts is defined and formulated as an optimization problem and solved using a genetic algorithm the performance of the joint ds x and s charts is also investigated the results of the investigation indicate that the joint ds x and s charts offer a better statistical efficiency in terms of average run length arl than combined ewma and cusum schemes omnibus ewma scheme over certain shift ranges when all schemes are optimized to detect certain shifts in comparison with the joint standard two stage samplings and variable sampling size x and r charts the joint ds charts offer a better statistical efficiency for all ranges of the shifts

systems of linear interval equations this paper presents theory and methods for computing the exact bounds on the solution of a system of n linear equations in n variables whose coefficients and right hand sides vary in some real intervals finite and iterative methods are given based on results from linear complementarity theory also regularity conditions regularity testing and computing the exact inverse of an interval matrix are dealt with

ray pattern matrices requiring perron frobenius properties abstract a ray pattern matrix is a matrix whose nonzero entries are all unimodular an n n ray pattern matrix a is said to require the weak perron frobenius property if for any n n entrywise positive matrix k the spectral radius k a is one of the eigenvalues of k a to require the strong perron frobenius property if k a is an algebraically simple eigenvalue of k a and the left and right eigenvectors associated to k a are strictly nonzero in this paper necessary and sufficient conditions for ray pattern matrices requiring the weak strong perron frobenius property are given

sequential changepoint detection in quality control and dynamical systems after a brief survey of a large variety of sequential detection procedures that are widely scattered in statistical references on quality control and engineering references on fault detection and signal processing we study some open problems concerning these procedures and introduce a unified theory of sequential changepoint detection this theory leads to a class of sequential detection rules which are not too demanding in computational and memory requirements for on line implementation and yet are nearly optimal under several performance criteria

accurate floating point product and exponentiation several different techniques and softwares intend to improve the accuracy of results computed in a fixed finite precision here we focus on a method to improve the accuracy of the product of floating point numbers we show that the computed result is as accurate as if computed in twice the working precision the algorithm is simple since it only requires addition subtraction and multiplication of floating point numbers in the same working precision as the given data such an algorithm can be useful for example to compute the determinant of a triangular matrix and to evaluate a polynomial when represented by the root product form it can also be used to compute the integer power of a floating point number

a rank based multivariate cusum procedure we consider statistical process control when measurements are multivariate a cumulative sum cusum procedure is suggested in detecting a shift in the mean vector of the measurements which is based on the cross sectional antiranks of the measurements at each time point the measurements are ordered and their antiranks which are the indices of the order statistics are recorded when the process is in control and the joint distribution of the multivariate measurements satisfies some regularity conditions the antirank vector at each time point has a given distribution this distribution changes to some other distribution when the process is out of control and the components of the shift in the mean vector of the process are not all the same this cusum can therefore detect shifts in all directions except the one in which the components of the shift in the mean vector are all the same but not 0 the shift with equal components however can be easily detected by another univariate cusum the former cusu

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 profile monitoring by mixed effects modeling in some applications the quality of a process is characterized by the functional relationship between a response variable and one or more explanatory variables profile monitoring is for checking the stability of this relationship over time control charts for monitoring nonparametric profiles are useful when the relationship is too complicated to be described parametrically most existing control charts in the literature are for monitoring parametric profiles they require the assumption that within profile measurements are independent of each other which is often invalid in practice this article focuses on nonparametric profile monitoring when within profile data are correlated a novel control chart is suggested which incorporates local linear kernel smoothing into the exponentially weighted moving average ewma control scheme in this method within profile correlation is described by a nonparametric mixed effects model our proposed control chart is fast to compute and convenient to use numeric

optimal design of second order linear filters for control charting in many common control charting situations the statistic to be charted can be viewed as the output of a linear filter applied to the sequence of process measurement data in recent work that has generalized this concept the charted statistic is the output of a general linear filter in impulse response form and the filter is designed by selecting its impulse response coefficients to optimize its average run length performance in this work we restrict attention to the class of all second order linear filters applied to the residuals of a time series model of the process data we present an algorithm for optimizing the design of the second order filter that is more computationally efficient and robust than the algorithm for optimizing the general linear filter we demonstrate that the optimal second order filter performs almost as well as the optimal general linear filter in many situations both methods share a number of interesting characteristics and are tuned to detect any distinct features of the p

using invariants to change detection in dynamical system with chaos abstract change detection is the crucial subject in dynamical systems there are suitable methods for detecting changes for linear systems and some methods for nonlinear systems but there is a lack of methods concerning chaotic systems this paper presents change detection techniques for dynamical systems with chaos we consider the dynamical system described by the time series which originated from ordinary differential equation and real world phenomena we assume that the change parameters are unknown and the change could be either slight or drastic the process of change detection is based on characteristic dynamical system invariants changes in the invariants values of the dynamical systems are the indicators of change we propose a method of change detection based on the fractal dimension and recurrence plot the automatic detection is provided by control charts methods were checked by using small data sets and stream data

bounds for determinants of perturbed m matrices abstract a sharp upper bound for the relative error of the determinant of an m matrix in terms of the relative errors of the matrix entries is given it improves and completes a bound derived by jungong and jiang

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

joint economic design of ewma control charts for mean and variance abstract control charts with exponentially weighted moving average ewma statistics mean and variance are used to jointly monitor the mean and variance of a process an ewma cost minimization model is presented to design the joint control scheme based on pure economic or both economic and statistical performance criteria the pure economic model is extended to the economic statistical design by adding constraints associated with in control and out of control average run lengths the quality related production costs are calculated using taguchi s quadratic loss function the optimal values of smoothing constants sampling interval sample size and control chart limits are determined by using a numerical search method the average run length of the control scheme is computed by using the markov chain approach computational study indicates that optimal sample sizes decrease as the magnitudes of shifts in mean and or variance increase and higher values of quality loss coefficient lead to shorter sampling intervals the sensitivity analysis results regarding the effects of various inputs on the chart parameters provide useful guidelines for designing an ewma based process control scheme when there exists an assignable cause generating concurrent changes in process mean and variance

a generalized ewma control chart and its comparison with the optimal ewma cusum and glr schemes it is known that both the optimal exponentially weighted moving average ewma and cumulative sum cusum control charts are based on a given reference value delta which for the cusum chart is the magnitude of a shift in the mean to be detected quickly in this paper a generalized ewma control chart gewma which does not depend on delta is proposed for detecting the mean shift we compare theoretically the gewma control chart with the optimal ewma cusum and the generalized likelihood ratio glr control charts the results of the comparison in which the in control average run length approaches infinity show that the gewma control chart is better than the optimal ewma control chart in detecting a mean shift of any size and is also better than the cusum control chart in detecting the mean shift which is not in the interval 0 7842 delta 1 3798 delta moreover the glr control chart has the best performance in detecting mean shift among the four control charts except when detecting a particular mean shift delta when the in control average run length approaches infinity

a markov chain model for the multivariate exponentially weighted moving averages control chart abstract a markov chain approximation is used to determine the run length performance of a multivariate statistical process control chart the markov chain approach is widely used in the analysis of univariate control charts we extend the advantages of this type of analysis to a multivariate exponentially weighted moving averages control chart the analysis can be applied whenever the multivariate control statistic can be modeled as a markov chain and the run length performance depends on the off target mean only through the noncentrality parameter

a least angle regression control chart for multidimensional data in multidimensional applications it is very rare that all variables shift at the same time a statistical process control procedure would have superior efficiency when limited to the subset of variables likely responsible for the out of control conditions the key idea of this article consists of combining a variable selection method with a multivariate control chart to detect changes in both the mean and variability of a multidimensional process with gaussian errors in particular we develop a control chart for phase ii monitoring which integrates the least angle regression algorithm with a multivariate exponentially weighted moving average comparisons with related multivariate control schemes demonstrate the efficiency of the proposed control chart in a wide range of practical applications including profile and multistage process monitoring further the proposed scheme may also provide valuable diagnostic information for fault isolation supplemental materials including an r package are available

average run lengths of an optimal method of detecting a change in distribution abstract suppose one accumulates independent observations from a certain process initially the process is at state 0 at some unknown point in time something occurs e g a breakdown which puts the process in state 1 and consequently the stochastic behavior of the observations changes it is of interest to declare that a change took place to raise an alarm as soon as possible after its occurrence subject to a restriction on the rate of false detections it is assumed that the aforementioned observations are the only information one has about the process and the problem is to construct a good detection scheme practical examples of this problem arise in areas such as health quality control ecological monitoring etc for instance consider surveillance for congenital malformations in newborn infants under normal circumstances the percentage of babies born with a certain type of malformation has a known value should something occur such as an environmental change the introduction of a new drug to the market etc the percentage may increase one would want to raise an alarm as quickly as possible after a change would have taken place subject to an acceptable rate of false alarms

a new two sided cumulative sum quality control scheme a new two sided cumulative sum quality control scheme is proposed the new scheme was developed specifically to be generalized to a multivariate cumulative sum quality control scheme the multivariate version will be examined in a subsequent paper this article evaluates the univariate version a comparison of the conventional two sided cumulative sum scheme and the proposed scheme indicates that the new scheme has slightly better properties ratio of on aim to off aim average run lengths than the conventional scheme steady state average run lengths are discussed the new scheme and the conventional two sided cumulative sum scheme have equivalent steady state average run lengths methods for implementing the fast initial response feature for the new cumulative sum scheme are given a comparison of average run lengths for the conventional and proposed schemes with fast initial response features is also favorable to the new scheme a markov chain approximation is used to calculate the average run lengths

multivariate exponentially weighted moving covariance matrix multivariate exponentially weighted moving average mewma charts are among the best control charts for detecting small changes in any direction the well known mewma is directed at changes in the mean vector but changes can occur in either the location or the variability of the correlated multivariate quality characteristics calling for parallel methodologies for detecting changes in the covariance matrix this article discusses an exponentially weighted moving covariance matrix for monitoring the stability of the covariance matrix of a process used together with the location mewma this chart provides a way to satisfy shewhart s dictum that proper process control monitor both mean and variability we show that the chart is competitive generally outperforming current control charts for the covariance matrix

on perron frobenius property of matrices having some negative entries we extend the theory of nonnegative matrices to the matrices that have some negative entries we present and prove some properties which give us information when a matrix possesses a perron frobenius eigenpair we apply also this theory by proposing the perron frobenius splitting for the solution of the linear system ax b by classical iterative methods perron frobenius splittings constitute an extension of the well known regular splittings weak regular splittings and nonnegative splittings convergence and comparison properties are given and proved

change point detection in multinomial data with a large number of categories we consider a sequence of multinomial data for which the probabilities associated with the categories are subject to abrupt changes of unknown magnitudes at unknown locations when the number of categories is comparable to or even larger than the number of subjects allocated to these categories conventional methods such as the classical pearson s chi squared test and the deviance test may not work well motivated by high dimensional homogeneity tests we propose a novel change point detection procedure that allows the number of categories to tend to infinity the null distribution of our test statistic is asymptotically normal and the test performs well with finite samples the number of change points is determined by minimizing a penalized objective function based on segmentation and the locations of the change points are estimated by minimizing the objective function with the dynamic programming algorithm under some mild conditions the consistency of the estimators of multiple change points is established simulation studies show that the proposed method performs satisfactorily for identifying change points in terms of power and estimation accuracy and it is illustrated with an analysis of a real data set

an adaptive exponentially weighted moving average control chart lucas and saccucci showed that exponentially weighted moving average ewma control charts can be designed to quickly detect either small or large shifts in the mean of a sequence of independent observations but a single ewma chart cannot perform well for small and large shifts simultaneously furthermore in the worst case situation this scheme requires a few observations to overcome its initial inertia the main goal of this article is to suggest an adaptive ewma aewma chart that weights the past observations of the monitored process using a suitable function of the current error the resulting scheme can be viewed as a smooth combination of a shewhart chart and an ewma chart a design procedure for the new control schemes is suggested comparisons of the standard and worst case average run length profiles of the new scheme with those of different control charts show that aewma schemes offer a more balanced protection against shifts of different sizes

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

a multivariate sign ewma control chart nonparametric control charts are useful in statistical process control spc when there is a lack of or limited knowledge about the underlying process distribution especially when the process measurement is multivariate this article develops a new multivariate spc methodology for monitoring location parameters it is based on adapting a powerful multivariate sign test to online sequential monitoring the weighted version of the sign test is used to formulate the charting statistic by incorporating the exponentially weighted moving average control ewma scheme which results in a nonparametric counterpart of the classical multivariate ewma mewma it is affine invariant and has a strictly distribution free property over a broad class of population models that is the in control ic run length distribution can attain or is always very close to the nominal one when using the same control limit designed for a multivariate normal distribution moreover when the process distribution comes from the elli

comparison of ewma cusum and shiryayev roberts procedures for detecting a shift in the mean pollak and siegmund compared the shiryayev roberts procedure with the cusum procedure for detecting a change in the drift of a brownian motion based on the conditional average delay time in this paper the exponentially weighted moving average ewma procedure proposed by roberts is compared with the shiryayev roberts and cusum procedures the comparison is based on the stationary average delay time as advocated by shiryayev the optimal design for the ewma procedure and its asymptotic properties are studied when the average in control run length is large the results show that the ewma procedure is less efficient than the other two procedures

proportional integral derivative charts for process monitoring we introduce a new class of monitoring procedures based on the relationship between a proportional integral derivative pid feedback control scheme and the corresponding prediction scheme the charts are obtained by applying the pid predictor to the autocorrelated data to get residuals and then monitoring the residuals this class of procedures includes as special cases several charts that have been recently proposed in the literature and thus provides a unifying framework the pid charts have three parameters that can be suitably tuned to achieve good average run length arl performance for large or small mean shifts methods for determining chart parameters to obtain good arl performance are discussed simulation studies for autoregressive moving average 1 1 models show that pid charts are competitive with the special cause charts of alwan and roberts for detecting large shifts and perform better in detecting small to moderate shifts the effects of model parameter misspecification and bias in esti

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