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

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

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

multivariate quality control based on regression adjusted variables when performing quality control in a situation in which measures are made of several possibly related variables it is desirable to use methods that capitalize on the relationship between the variables to provide controls more sensitive than those that may be made on the variables individually the most common methods of multivariate quality control that assess the vector of variables as a whole are those based on the hotelling t 2 between the variables and the specification vector although t 2 is the optimal single test statistic for a general multivariate shift in the mean vector it is not optimal for more structured mean shifts for example shifts in only some of the variables measures based on quadratic forms like t 2 also confound mean shifts with variance shifts and require quite extensive analysis following a signal to determine the nature of the shift this article proposes shewhart and cumulative sum cusum controls based on the vector z of scaled residuals from the regression of each varia

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

an asymptotic result for laguerre sobolev orthogonal polynomials abstract let s n denote the sequence of polynomials orthogonal with respect to the sobolev inner product f g s 0 f x g x x e x d x 0 f x g x x e x d x where 1 0 and the leading coefficient of the s n is equal to the leading coefficient of the laguerre polynomial l n then if x c s 0 lim n s n x l n 1 x is a constant depending on

multivariate cusum quality control procedures it is a common practice to use simultaneously several one sided or two sided cusum procedures of the type proposed by page 1954 in this article this method of control is considered to be a single multivariate cusum mcusum procedure methods are given for approximating parameters of the distribution of the minimum of the run lengths of the univariate cusum charts using a new method of comparing multivariate control charts it is shown that an mcusum procedure is often preferable to hotelling s tz procedure for the case in which the quality characteristics are bivariate normal random variables

non normality and the variable parameters x control charts abstract recent studies has demonstrated the adaptive i e variable sample sizes sampling intervals and or action limit coefficients x charts are quicker than standard shewhart ss x control chart in detecting process mean shifts the usual assumption for designing a control chart is that the data or measurements are normally distributed however this assumption may not be true for some processes in this paper the performance of the adaptive x chart is evaluated under non normality based on the study it is shown that the variable parameters vp x chart is more effective than the other adaptive control charts in detecting small process mean shifts under non normality more importantly the risk of false alarm of the vp x chart can be substantially decreased

sequential change point detection when unknown parameters are present in the pre change distribution in the sequential change point detection literature most research specifies a required frequency of false alarms at a given pre change distribution f and tries to minimize the detection delay for every possible post change distribution g in this paper motivated by a number of practical examples we first consider the reverse question by specifying a required detection delay at a given post change distribution and trying to minimize the frequency of false alarms for every possible pre change distribution f we present asymptotically optimal procedures for one parameter exponential families next we develop a general theory for change point problems when both the pre change distribution f and the post change distribution g involve unknown parameters we also apply our approach to the special case of detecting shifts in the mean of independent normal observations

a new look at warning and action lines of surveillance schemes abstract some authors have suggested an efficient dynamic monitoring procedure for detection of a change in the drift of a brownian motion their procedure can be described as a sequence of extremely short sequential probability ratio tests sprt s done in zero time with infinitesimal time between consecutive sprt s the drawbacks of this procedure are that it can be described only as a limit of practical procedures and it does not take into account the cost of initiating a test in this article we suggest a procedure that takes both sampling and overhead costs into account and that can reasonably be carried out in practice in this procedure the process is monitored continuously with a constant sampling rate the accumulated data are analyzed by the standard cumulative sum cusum statistics whenever the cusum procedure raises an alarm data are accumulated as fast as possible until either the alarm is relaxed or the process is stopped

hotelling s t2 charts with variable sample size and control limit abstract the ideas of variable sampling interval vsi variable sample size vss variable sample size and sampling interval vssi and variable parameters vp in the univariate case have been successfully applied to the multivariate case to improve the efficiency of hotelling s t 2 chart with fixed sampling rate fsr in detecting small process shifts however the main disadvantage in using most of these control schemes is an increasing in the complexity due to the adaptive changes in sampling intervals in this paper retaining the lengths of sampling intervals constant a variable sample size and control limit vssc t 2 chart is proposed and described the statistical efficiency of the vssc t 2 chart in terms of the average time to signal a shift in process mean vector is compared with that of the vp vssi vss vsi and fsr t 2 charts from the results of comparison it shows that the vssc t 2 chart for a very small shift in the process mean vector gives a better performance than the vssi vss vsi and fsr t 2 charts meanwhile it presents a similar performance to the vp t 2 chart furthermore from the viewpoint of practicability it is more convenient for administrating the control chart than the vsi vssi and vp t 2 chart thus it may provide a good option for quick response to small shifts in a multivariate process

the state of statistical process control as we proceed into the 21st century 2000 the state of statistical process control as we proceed into the 21st century journal of the american statistical association vol 95 no 451 pp 992 998

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

computing moments of the exit time distribution for markov processes by linear programming we provide a new approach to the numerical computation of moments of the exit time distribution of markov processes the method relies on a linear programming formulation of a process exiting from a bounded domain the lp formulation characterizes the evolution of the process through the moments of the induced occupation measure and naturally provides upper and lower bounds for the exact values of the moments the conditions the moments have to satisfy are derived directly from the generator of the markov process and are not based on some approximation of the process excellent software is readily available because the computations involve finite dimensional linear programs

exact results for shewhart control charts with supplementary runs rules this article gives a simple and efficient method using markov chains to obtain the exact run length properties of shewhart control charts with supplementary runs rules average run length comparisons are made among the shewhart chart with supplementary runs rules the basic shewhart chart and the cumulative sum cusum chart

snakes active contour models a snake is an energy minimizing spline guided by external constraint forces and influenced by image forces that pull it toward features such as lines and edges snakes are active contour models they lock onto nearby edges localizing them accurately scale space continuation can be used to enlarge the capture region surrounding a feature snakes provide a unified account of a number of visual problems including detection of edges lines and subjective contours motion tracking and stereo matching we have used snakes successfully for interactive interpretation in which user imposed constraint forces guide the snake near features of interest

statistical process control for shifts in mean or variance using a changepoint formulation statistical process control spc involves ongoing checks to ensure that neither the mean nor the variability of the process readings has changed conventionally this is done by pairs of charts shewhart x and s or r charts cumulative sum charts for mean and for variance or exponentially weighted moving average charts for mean and variance the traditional methods of calculating the statistical properties of control charts are based on the assumption that the in control true mean and variance were known exactly and use these assumed true values to set center lines control limits and decision intervals the reality however is that true parameter values are seldom if ever known exactly rather they are commonly estimated from a phase i sample the random errors in the estimates lead to uncertain run length distribution of the resulting charts an attractive alternative to the traditional charting methods is a single chart using the unknown parameter likelihood ratio test for a change in mean and o

multivariate generalizations of cumulative sum quality control schemes this article presents the design procedures and average run lengths for two mulativariater cumulative sum cusum quality control procedures the first cusum procedure reduces each multivariate observation to a scalar and then forms a cusum of the scalars the second cusum procedure forms a cusum vector directly from the observations these two procedures are compared with each other and with the multivariate shewhart chart other multivariate quality control procedures are mentioned robustness the fast initial response feature for cusum schemes and combined shewhart cusum schemes are discussed

decision theoretic optimality of the cusum procedure suppose x 1 x 2 are independent random variables such that for some unknown each of x 1 x 1 is distributed according to f 0 while x x 1 are all distributed according to f 1 we prove a result of moustakides that claims that the cusum procedures are optimal in the sense of lorden we do that by proving that the procedures are bayes for some stochastic mechanism of generating

optimal average sample number of the sprt chart for monitoring fraction nonconforming abstract the sequential probability ratio test sprt control chart is a powerful tool for monitoring manufacturing processes it is highly suitable for the applications where testing is destructive or very expensive such as the automobile airbags test this article studies the effect of the average sample number asn i e the average sample size on the chart s performance a design algorithm is proposed to develop the optimal sprt chart for monitoring the fraction nonconforming p of bernoulli processes by optimizing the asn and other charting parameters the average detection speed of the sprt chart is almost doubled it is also found that the optimal sprt chart significantly outperforms the optimal np and binomial cusum charts in terms of average number of defectives and under different combinations of the design specifications it is observed that the sprt chart using a relatively smaller asn and a shorter sampling interval h has a higher overall detection effectiveness

on the markov chain approach to the two sided cusum procedure a markov chain representation is given for the two sided possibly asymmetric cumulative sum cusum procedure of ewan and kemp 1960 for integer valued random variables the approach taken by brook and evans 1972 for the one sided cusum procedure to determine exact and approximate expressions for the run length distribution its moments and its percentage points is extended to the two sided cusum procedure the number of states included in the markov chain is minimized in order to make the methods as efftcient as possible

monitoring general linear profiles using multivariate exponentially weighted moving average schemes we propose a statistical process control scheme that can be implemented in industrial practice in which the quality of a process can be characterized by a general linear profile we start by reviewing the general linear profile model and the existing monitoring methods based on this we propose a novel multivariate exponentially weighted moving average monitoring scheme for such a profile we introduce two other enhancement features the variable sampling interval and the parametric diagnostic approach to further improve the performance of the proposed scheme throughout the article we use a deep reactive ion etching example from semiconductor manufacturing which has a profile that fits a quadratic polynomial regression model well to illustrate the implementation of the proposed approach

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

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

a robust likelihood cumulative sum chart in practice the cumulative sum cusum control chart is often used to detect small shifts in the mean of a normally distributed process but it performs poorly for thick tailed processes and for large shifts this article provides a robust likelihood cumulative sum rlcusum chart that discounts outliers and yet has the ability to detect large shifts quickly the new chart is motivated by the likelihood underpinnings of the cusum it is based on the likelihood of a variate constructed to ensure robust performance of the resulting chart the new chart is compared with the conventional cusum in terms of average run length with the finding that the rlcusum is much better than the conventional cusum especially for large shifts for small shifts the two charts are essentially equivalent we study the properties of the conditional limiting distribution a final application of the rlcusum in assessing livestock disease shows that the method is applicable in process control

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

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

data efficient quickest change detection in minimax settings the classical problem of quickest change detection is studied with an additional constraint on the cost of observations used in the detection process the change point is modeled as an unknown constant and minimax formulations are proposed for the problem the objective in these formulations is to find a stopping time and an on off observation control policy for the observation sequence to minimize a version of the worst possible average delay subject to constraints on the false alarm rate and the fraction of time observations are taken before change an algorithm called de cusum is proposed and is shown to be asymptotically optimal for the proposed formulations as the false alarm rate goes to zero numerical results are used to show that the de cusum algorithm has good tradeoff curves and performs significantly better than the approach of fractional sampling in which the observations are skipped using the outcome of a sequence of coin tosses independent of the observation process this study is guided by the insights gained from an earlier study of a bayesian version of this problem

asymptotics of sobolev orthogonal polynomials for coherent pairs of laguerre type abstract let s n n denote a sequence of polynomials orthogonal with respect to the sobolev inner product f g s f x g x d 0 x f x g x d 1 x where 0 and d 0 d 1 is a so called coherent pair with at least one of the measures d 0 or d 1 a laguerre measure we investigate the asymptotic behaviour of sn x outside the supports of d 0 and d 1 and n

asymptotics of sobolev orthogonal polynomials for coherent pairs of jacobi type abstract let sn n denote a sequence of polynomials orthogonal with respect to the sobolev inner product f g s f x g x d 0 x f x g x d 1 x where 0 and d 0 d 1 is a so called coherent pair with at least one of the measures d 0 or d 1 a jacobi measure we investigate the asymptotic behaviour of sn x for n and x fixed x c 1 1 as well as x 1 1

an alternative approach to fuzzy control charts direct fuzzy approach the major contribution of fuzzy set theory lies in its capability of representing vague data fuzzy logic offers a systematic base to deal with situations which are ambiguous or not well defined in the literature there exist few papers on fuzzy control charts which use defuzziffication methods in the early steps of their algorithms the use of defuzziffication methods in the early steps of the algorithm makes it too similar to the classical analysis linguistic data in those works are transformed into numeric values before control limits are calculated thus both control limits as well as sample values become numeric in this paper some contributions to fuzzy control charts based on fuzzy transformation methods are made by the use of a cut to provide the ability of determining the tightness of the inspection the higher the value of a the tighter inspection a new alternative approach direct fuzzy approach dfa is also developed in this paper in contrast to the existing fuzzy control charts the proposed approach is quite different in the sense it does not require the use of the defuzziffication this prevents the loss of information included by the samples it directly compares the linguistic data in fuzzy space without making any transformation we use some numeric examples to illustrate the performance of the method and interpret its results

bounds for the distribution of the run length of one sided and two sided cusum quality control schemes upper and lower bounds are derived for the distribution of the run length n of both the one sided and two sided cusum schemes based upon a sequence of iterates pr n 0 pr n 1 bounds are constructed such that m n i pr n n pr n n i m n i pr n n holds for all n i 1 2 with constants 0 m n m n 1 suitably chosen the bounds converge monotonically in the sense that m n i 1pr n n m n 1 i pr n n 1 m n i 1pr n n m n 1 i pr n n 1 and under some mild and natural conditions as a by product bounds are presented for the percentage points of the distribution function of n for the average run length of the inspection scheme for the standard deviation of n and finally for the probability mass function of n some numerical results are displayed to demonstrate the effkiency of the method

should exponentially weighted moving average and cumulative sum charts be used with shewhart limits traditional shewhart control charts are usually considered effective for detecting large shifts in process parameters but ineffective for detecting small shifts for detecting small parameter shifts it is much better to use exponentially weighted moving average ewma control charts or cumulative sum cusum control charts but these charts are not considered as effective as shewhart charts for large parameter shifts it is frequently recommended that ewma or cusum charts be used in combination with a shewhart chart to gain the benefits of both types of charts so that both small and large shifts can be detected quickly here we consider the problem of process monitoring when a continuous process variable is being observed and the objective is to detect small or large shifts in either the process mean or the process standard deviation in this situation it is customary to use a combination of two control charts one chart designed to monitor and the other designed to monitor for this situation

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

orthogonal polynomials on sobolev spaces old and new directions abstract during the last years orthogonal polynomials on sobolev spaces have attracted considerable attention algebraic properties distribution of their zeros and fourier expansions as well as their relevance in the analysis of spectral methods for partial differential equations provide a very large field to explore and to compare with the standard case in this paper we present an introductory survey about the subject the origin of the problems and their development show the interest and the promising future of this field

using an autoregressive model to detect departures from steady states in unequally spaced tumour biomarker data a new method based on a continuous time autoregressive car 1 model of time series data is provided for detecting departures of tumour markers from steady states in breast cancer patients following surgery a kalman filter recursive algorithm is used to calculate the likelihood function arising from the car 1 model and to calculate recursive residuals which are monitored by a shewhart cusum scheme this approach can be used to monitor the serial marker data of large numbers of patients even when the series are short and the data are serially correlated and unequally spaced further the methodology can be used to recommend appropriate testing intervals

regression segmentation for m 3 spinal images clinical routine often requires to analyze spinal images of multiple anatomic structures in multiple anatomic planes from multiple imaging modalities m 3 unfortunately existing methods for segmenting spinal images are still limited to one specific structure in one specific plane or from one specific modality s 3 in this paper we propose a novel approach regression segmentation that is for the first time able to segment m 3 spinal images in one single unified framework this approach formulates the segmentation task innovatively as a boundary regression problem modeling a highly nonlinear mapping function from substantially diverse m 3 images directly to desired object boundaries leveraging the advancement of sparse kernel machines regression segmentation is fulfilled by a multi dimensional support vector regressor msvr which operates in an implicit high dimensional feature space where m 3 diversity and specificity can be systematically categorized extracted and handled the proposed regression segmentation approach was thoroughly tested on images from 113 clinical subjects including both disc and vertebral structures in both sagittal and axial planes and from both mri and ct modalities the overall result reaches a high dice similarity index dsi 0 912 and a low boundary distance bd 0 928 mm with our unified and expendable framework an efficient clinical tool for m 3 spinal image segmentation can be easily achieved and will substantially benefit the diagnosis and treatment of spinal diseases

factor screening for simulation with multiple responses sequential bifurcation the goal of factor screening is to find the really important inputs factors among the many inputs that may be changed in a realistic simulation experiment a specific method is sequential bifurcation sb which is a sequential method that changes groups of inputs simultaneously sb is most efficient and effective if the following assumptions are satisfied i second order polynomials are adequate approximations of the input output functions implied by the simulation model ii the signs of all first order effects are known and iii if two inputs have no important first order effects then they have no important second order effects either heredity property this paper examines sb for random simulation with multiple responses outputs called multi response sb msb this msb selects groups of inputs such that within a group all inputs have the same sign for a specific type of output so no cancellation of first order effects occurs to obtain enough replicates replications for correctly classifying a group effect or an individual effect as being important or unimportant msb applies wald s sequential probability ratio test sprt the initial number of replicates in this sprt is also selected efficiently by msb moreover msb includes a procedure to validate the three assumptions of msb the paper evaluates the performance of msb through extensive monte carlo experiments that satisfy all msb assumptions and through a case study representing a logistic system in china the results are very promising

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

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

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

a multivariate exponentially weighted moving average control chart a multivariate extension of the exponentially weighted moving average ewma control chart is presented and guidelines given for designing this easy to implement multivariate procedure a comparison shows that the average run length arl performance of this chart is similar to that of multivariate cumulative sum cusum control charts in detecting a shift in the mean vector of a multivariate normal distribution as with the hotelling s 2 and multivariate cusum charts the arl performance of the multivariate ewma chart depends on the underlying mean vector and covariance matrix only through the value of the noncentrality parameter worst case scenarios show that hotelling s 2 charts should always be used in conjunction with multivariate cusum and ewma charts to avoid potential inertia problems examples are given to illustrate the use of the proposed procedure

fast approximate energy minimization via graph cuts many tasks in computer vision involve assigning a label such as disparity to every pixel a common constraint is that the labels should vary smoothly almost everywhere while preserving sharp discontinuities that may exist e g at object boundaries these tasks are naturally stated in terms of energy minimization the authors consider a wide class of energies with various smoothness constraints global minimization of these energy functions is np hard even in the simplest discontinuity preserving case therefore our focus is on efficient approximation algorithms we present two algorithms based on graph cuts that efficiently find a local minimum with respect to two types of large moves namely expansion moves and swap moves these moves can simultaneously change the labels of arbitrarily large sets of pixels in contrast many standard algorithms including simulated annealing use small moves where only one pixel changes its label at a time our expansion algorithm finds a labeling within a known factor of the global minimum while our swap algorithm handles more general energy functions both of these algorithms allow important cases of discontinuity preserving energies we experimentally demonstrate the effectiveness of our approach for image restoration stereo and motion on real data with ground truth we achieve 98 percent accuracy

control charts for multivariate processes abstract this article uses the concept of data depth to introduce several new control charts for monitoring processes of multivariate quality measurements for any dimension of the measurements these charts are in the form of two dimensional graphs that can be visualized and interpreted just as easily as the well known univariate x x and cusum charts moreover they have several significant advantages first they can detect simultaneously the location shift and scale increase of the process unlike the existing methods which can detect only the location shift second their construction is completely nonparametric in particular it does not require the assumption of normality for the quality distribution which is needed in standard approaches such as the 2 and hotelling s t 2 charts thus these new charts generalize the principle of control charts to multivariate settings and apply to a much broader class of quality distributions

optimal detection of a change in distribution abstract document discusses a stopping rule that is a limit of bayes rules derived then an almost minimax rule is presented

surveillance strategies for detecting changepoint in incidence rate based on exponentially weighted moving average methods surveillance is a major issue in the today s world the need to develop adequate surveillance strategies is genuine in many spheres of human activity in this article we focus on a specific problem of surveillance and discuss some related statistical issues this specific problem deals with a possible change in the incidence rate of an event to a higher value when a system is studied at discrete time points we apply the exponentially weighted moving average methods for detecting an increased incidence rate per exposure unit of an event different measures of evaluation suitable in different types of applications such as the expected delay out of control average run length and probability of successful detection are studied analytical bounds are provided for those measures of evaluation results from intensive simulations indicate that the analytical bounds perform fairly well when the weight parameter is large

three triplet np control charts abstract an algorithm is presented for designing the np control charts on the basis of their statistical performance the algorithm gives the sample size and control limits for an np chart the 3 triplet np chart based on the specified values of a the in control fraction nonconforming value p 0 a downward shifted value p and an upward shifted value p b the corresponding design run lengths rl and c the corresponding probabilities w specifically whenever the process fraction nonconforming equals one of the three specified values the 3 triplet np chart will produce a signal in a predetermined run length with a predetermined probability this feature makes the operating characteristics of the np chart highly specifiable and provides the quality assurance engineers with better perception and more control in the design and operation of the np charts the 3 triplet np chart is designed by seeking an optimal combination of the sample size and the control limits

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

modeling the shape of the scene a holistic representation of the spatial envelope in this paper we propose a computational model of the recognition of real world scenes that bypasses the segmentation and the processing of individual objects or regions the procedure is based on a very low dimensional representation of the scene that we term the spatial envelope we propose a set of perceptual dimensions naturalness openness roughness expansion ruggedness that represent the dominant spatial structure of a scene then we show that these dimensions may be reliably estimated using spectral and coarsely localized information the model generates a multidimensional space in which scenes sharing membership in semantic categories e g streets highways coasts are projected closed together the performance of the spatial envelope model shows that specific information about object shape or identity is not a requirement for scene categorization and that modeling a holistic representation of the scene informs about its probable semantic category

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

adaptive sampling enhancement for hotelling s t2 charts abstract this paper makes a study of an adaptive sampling scheme useful to increase the power of the fixed sampling rate fsr t2 control chart in our study the three parameters of t2 control chart the sample size the sampling interval and the upper percentage factor that is used for determining the action limit vary between two values for a relaxed or tightened control depending on the most recent t2 value the average time to signal ats and adjusted average time to signal aats a shift in the process mean vector for the new chart are derived and regarded as an objective function respectively to optimize its design parameters with some minor changes the new chart can be reduced to the variable sampling interval vsi t2 chart the sample size vss t2 chart the variable sample size and sampling interval vssi t2 chart or the fsr t2 chart numerical comparisons among them are made and discussed furthermore the effects of the initial sample number use for estimating the in control process parameters upon the chart s performance and adaptive design parameters are presented

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

risk adjusted monitoring of time to event recently there has been interest in risk adjusted cumulative sum charts cusums to monitor the performance of e g hospitals taking into account the heterogeneity of patients even though many outcomes involve time only conventional regression models are commonly used in this article we investigate how time to event models may be used for monitoring purposes we consider monitoring using cusums based on the partial likelihood ratio between an out of control state and an in control state we consider both proportional and nonproportional alternatives as well as a head start against proportional alternatives we present an analytic method of computing the expected number of observed events before stopping or the probability of stopping before a given observed number of events in a stationary set up the former is roughly proportional to the average run length in calendar time adding a head start changes the threshold only slightly if the expected number of events until hitting is used as a criterion however it changes the threshold substantially if a false alarm probability is used in simulation studies charts based on survival analysis perform better than simpler monitoring schemes we present one example from retail finance and one medical application

ladder heights gaussian random walks and the riemann zeta function let s n n geq 0 be a random walk having normally distributed increments with mean theta and variance 1 and let tau be the time at which the random walk first takes a positive value so that s tau is the first ladder height then the expected value e theta s tau originally defined for positive theta maybe extended to be an analytic function of the complex variable theta throughout the entire complex plane with the exception of certain branch point sin gularities in particular the coefficients in a taylor expansion about theta 0 may be written explicitly as simple expressions involving the riemann zeta function previously only the first coefficient of the series developed here was known this term has been used extensively in developing approximations for boundary crossing problems for gaussian random walks knowledge of the complete series makes more refined results possible we apply it to derive asymptotics for boundary crossing probabilities and the limiting expected overshoot

svm multiregression for nonlinear channel estimation in multiple input multiple output systems this paper addresses the problem of multiple input multiple output mimo frequency nonselective channel estimation we develop a new method for multiple variable regression estimation based on support vector machines svms a state of the art technique within the machine learning community for regression estimation we show how this new method which we call m svr can be efficiently applied the proposed regression method is evaluated in a mimo system under a channel estimation scenario showing its benefits in comparison to previous proposals when nonlinearities are present in either the transmitter or the receiver sides of the mimo system

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

cusum charts with variable sampling intervals a standard cumulative sum cusum chart for controlling the process mean takes samples from the process at fixed length sampling intervals and uses a control statistic based on a cumulative sum of differences between the sample means and the target value this article proposes a modification of the standard cusum scheme that varies the time intervals between samples depending on the value of the cusum control statistic the variable sampling interval vsi cusum chart uses short sampling intervals if there is an indication that the process mean may have shifted and long sampling intervals if there is no indication of a change in the mean if the cusum statistic actually enters the signal region then the vsi cusum chart signals in the same manner as the standard cusum chart a markov chain approach is used to evaluate properties such as the average time to signal and the average number of samples to signal results show that the proposed vsi cusum chart is considerably more efficient than the standard cus

the distribution of the run length of one sided cusum procedures for continuous random variables a method is given for approximating the moments and percentage points of the run length distribution of one sided cusum procedures for continuous random variables the run length probabilities are calculated recursively using numerical quadrature until the ratio of successive probabilities stabilizes this ratio and the probabilities of low run length values are then used to approximate parameters of the run length distribution the accuracy of this method is compared with that of previous methods in examples involving normally distributed random variables

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

control charts and the efficient allocation of sampling resources control charts for monitoring the process mean and process standard deviation are often based on samples of n 1 observations but in many applications individual observations are used n 1 in this article we investigate the question of whether it is better from the perspective of statistical performance to use n 1 or n 1 we assume that the sampling rate in terms of the number of observations per unit time is fixed so using n 1 means that samples can be taken more frequently than when n 1 the best choice for n depends on the type of control chart being used so we consider shewhart exponentially weighted moving average ewma and cumulative sum cusum charts for each type of control chart we investigate a combination of two charts one chart designed to monitor and the other designed to monitor most control chart comparisons in the literature assume that a special cause produces a sustained shift in a process parameter that lasts until the shift is detected we also consider

optimal np control chart with curtailment this article presents an algorithm for the optimization design of the np control chart with curtailment the objective is to maximize the effectiveness of the np chart while holding the false alarm rate at a specified level and maintaining its simplicity for understanding and operation to a large degree the optimization algorithm can be applied to a 100 inspection as well as a general random sampling inspection the effectiveness of the chart is measured by the out of control average time to signal ats under the steady state mode this mode allows a shift in fraction nonconforming p to occur at any time during the inspection of a sample and therefore provides more realistic results than the zero state mode according to several performance studies and an illustrative example that are conducted in this research the optimal np chart with curtailment may reduce the out of control ats by nearly half on average compared to the conventional np charts

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

change point models in industrial applications in many industrial applications of statistics it is not reasonable to assume that the same model remains adequate as time progresses models in which the environment and related parameters undergo abrupt changes at unknown moments of time are found to be relevant in a much wider class of practical situations these models spawned a number of fundamental problems in the field of the change point theory such as the problems of detection of changes monitoring estimation of the current process parameters filtering identifying points of change and regimes segmentation and tests for data homogeneity these problems have been addressed to various extent in a large number of works including several recent books and review papers cf l 4 problems related to change point models are typically relevant in either hxed sample or sequential settings for example in the problem of on line detection of a change decisions to trigger an out of control signal are made sequentially based on some stopping variable some problems however can be formulated in both sequential and fixed sample settings for example in process capability analysis the problem of segmentation involves identifying all the regimes and change points present in a given data set however in speech analysis the problem of segmentation is typically relevant in a sequential setting with emphasis placed on identification of the most recent regime similarly the problem of estimating parameters at a given point in time can be formulated as a sequential filtering or a fixed sample smoothing settings in this article we focus on sequential methods with emphasis on the problems of detection and filtering

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

x charts with variable sampling intervals the usual practice in using a control chart to monitor a process is to take samples from the process with fixed sampling intervals this article considers the properties of the chart when the sampling interval between each pair of samples is not fixed but rather depends on what is observed in the first sample the idea is that the time interval until the next sample should be short if a sample shows some indication of a change in the process and long if there is no indication of a change the proposed variable sampling interval vsi chart uses a short sampling interval if is close to but not actually outside the control limits and a long sampling interval if is close to target if is actually outside the control limits then the chart signals in the same way as the standard fixed sampling interval fsi chart properties such as the average time to signal and the average number of samples to signal are evaluated comparisons between the fsi and the vsi charts indicate that the vsi chart is substantially

using autoregressive and random walk models to detect trends and shifts in unequally spaced tumour biomarker data continuous time autoregressive car 1 and random walk models of time series data are provided for detecting non random shifts and trends of tumour markers in breast cancer patients following resection for cure the continuous time random walk model with observation error is extended to the case of multiple patient time series these models can be used to monitor large numbers of patients with time series with few sampling events that are serially correlated and unequally spaced further the methodologies can be used to recommend appropriate testing intervals a kalman filter recursive algorithm is used to calculate the likelihood functions arising from the car 1 and random walk models and to calculate recursive residuals which are monitored by shewhart cusum schemes

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

comparisons of some exponentially weighted moving average control charts for monitoring the process mean and variance an exponentially weighted moving average ewma control chart for monitoring the process mean may be slow to detect large shifts in when the ewma tuning parameter is small an additional problem sometimes called the inertia problem is that the ewma statistic may be in a disadvantageous position on the wrong side of the target when a shift in occurs which may significantly delay detection of a shift in options for improving the performance of the ewma chart include using the ewma chart in combination with a shewhart chart or in combination with an ewma chart based on squared deviations from target the ewma chart based on squared deviations from target is designed to detect increases in the process standard deviation but it is also very effective for detecting large shifts in capizzi and masarotto recently proposed the option of an adaptive ewma control chart in which is a function of the data with the adaptive feature the ewma chart behaves like a standard ewma chart when the curren