quickest detection of a random pulse in white gaussian noise a class of stochastic processes characterized by rapid transitions in their structure is considered and the quickest detection of such transitions is studied in a bayesian framework the emphasis is on stochastic processes consisting of a randomly arrived causal pulse possibly with a set of random parameters such as amplitude and duration and an additive white gaussian noise in this model the pulse shape and the prior joint density of the arrival time and other random parameters are assumed known the task of quickest detection in this paper is described mathematically by minimizing the expected detection error the detection error is represented by a nonlinear function of the distance between the actual transition time and its associated detection time the assumptions on this function are fairly mild and allow to flexibly design its shape for a desired trade off between the detection delay and the false alarm rate two special cases of such design are well known error measures mean squared and mean absolute error the quickest detection problem a subclass of optimal stopping time problems is formulated as a stochastic optimal control problem and is resolved using dynamic programming the optimal detection rule is determined in terms of the solution of an integral equation that cannot be directly solved due to its complexity this equation is later used to develop a class of suboptimal detection rules and a lower bound on the minimum error using this lower bound it is shown for a numerical example that the suboptimal detector is nearly optimal

on the geometry of the term structure of interest rates we present recently developed geometric methods for the analysis of finite dimensional term structure models of the interest rates this includes an extension of the frobenius theorem for fr echet spaces in particular this approach puts new light on many of the classical models such as the hull white extended vasicek and cox ingersoll ross short rate models the notion of a finite dimensional realization fdr is central for this analysis we motivate it classify all generic fdrs and provide some new results for the corresponding factor processes such as hypoellipticity of its generators and the existence of smooth densities furthermore we include finite dimensional external factors thus admitting a stochastic volatility structure

a robust surveillance scheme for stochastically ordered alternatives we sequentially observe independent observations x 1 x 2 such that initially they have distribution g 0 at some unknown time v they become stochastically larger having distribution g 1 neither g 0 nor g 1 is fully specified we wish to detect that a change has taken place as soon as possible after its occurrence subject to a constraint on the rate of false alarms we derive a family of nonparametric sequential procedures based on ranks with noncontiguous alternatives in mind large sample approximations to the operating characteristics are obtained analytically the proposed procedures all possess robustness of validity because they are based on ranks near optimal sensitivity can be obtained for specific alternatives by choosing an appropriate procedure for example when observations are normally distributed with one standard deviation shift in mean postchange an appropriate nonparametric surveillance scheme yields 97 asymptotic relative efficiency as compared to the optimal procedure when all distributional parameters are known our procedures are computationally feasible monte carlo experiments confirm the applicability of the asymptotic calculations including high levels of efficiency for sample sizes met in practice

wiener disorder problem with observations at fixed discrete time epochs suppose that a wiener process gains a known drift rate at some unobservable disorder time with some zero modified exponential distribution the process is observed only at known fixed discrete time epochs which may not always be spaced in equal distances the problem is to detect the disorder time as quickly as possible by means of an alarm that depends only on the observations of wiener process at those discrete time epochs we show that bayes optimal alarm times which minimize expected total cost of frequent false alarms and detection delay time always exist optimal alarms may in general sound between observation times and when the space time process of the odds that disorder happened in the past hits a set with a nontrivial boundary the optimal stopping boundary is piecewise continuous and explodes as time approaches from left to each observation time on each observation interval if the boundary is not strictly increasing everywhere then it first decreases and then increases it is strictly monotone wherever it does not vanish its decreasing portion always coincides with some explicit function we develop numerical algorithms to calculate nearly optimal detection algorithms and their bayes risks and we illustrate their use on numerical examples the solution of wiener disorder problem with discretely spaced observation times will help reduce risks and costs associated with disease outbreak and production quality control where the observations are often collected and or inspected periodically

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

quickest sequential multiband spectrum sensing with mixed observations spectrum sensing is a key technology enabling the cognitive radio system in this paper the problem of how to quickly and accurately find an unoccupied channel from a large amount of potential channels is considered the cognitive radio system under consideration is equipped with a narrow band sensor hence it can only sense those potential channels in a sequential manner in this scenario we propose a novel two stage mixed observation sensing strategy in the first stage which is named as scanning stage the sensor observes a linear combination of the signals from a pair of channels the purpose of the scanning stage is to quickly identify a pair of channels such that at least one of them is highly likely to be unoccupied in the second stage which is called refinement stage the sensor only observers the signal from one of those two channels identified from the first stage and selects one of them as the unoccupied channel the problem under this setup is an ordered two concatenated markov stopping time problem the optimal solution is solved using the tools from the multiple stopping time theory it turns out that the optimal solution has a rather complex structure hence a low complexity algorithm is proposed to facilitate the implementation in the proposed low complexity algorithm the cumulative sum test is adopted in the scanning stage and the sequential probability ratio test is adopted in the refinement stage the performance of this low complexity algorithm is analyzed when the presence of unoccupied channels is rare numerical simulation results show that the proposed sensing strategy can significantly reduce the sensing time when the majority of potential channels are occupied

quadratic tests for detection of abrupt changes in multivariate signals this article considers the problem of detecting abrupt changes in the mean of a multivariate gaussian random signal a fixed sample size spl chi sup 2 test is compared against the optimum sequential tests spl chi sup 2 cusum and spl chi sup 2 glr

quickest detection of parameter changes in stochastic regression nonparametric cusum we consider the problem of detecting abrupt parameter changes in a stochastic regression with unknown noise distribution the process changes at some unknown point of time under general conditions on the regression function and unknown distributions of observations before and after the disruption the paper develops a nonparametric cumulative sum procedure cusum unlike likelihood based cusum algorithms constructed mostly on log likelihood ratio statistics we use a special system of basic statistics in page s procedure by applying a sequential sampling scheme which measures time in terms of accumulated kullback leibler k l divergence we come to a system of statistics with the martingale properties close to those of the log likelihood ratios the proposed approach suggests also an alternative performance criterion in the analysis of the procedure by replacing the expected detection delay by the corresponding k l divergence we show that under the false alarm probability constraint the nonparametric cusum rule is optimal in the sense that it ensures the logarithmic asymptotic for the detection delay

information bounds and quick detection of parameter changes in stochastic systems by using information theoretic bounds and sequential hypothesis testing theory this paper provides a new approach to optimal detection of abrupt changes in stochastic systems this approach not only generalizes previous work in the literature on optimal detection far beyond the relatively simple models treated but also suggests alternative performance criteria which are more tractable and more appropriate for general stochastic systems in addition it leads to detection rules which have manageable computational complexity for on line implementation and yet are nearly optimal under the different performance criteria considered

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

densities for rough differential equations under hormander s condition we consider stochastic differential equations dy v y dx driven by a multidimensional gaussian process x in the rough path sense t lyons rev mat iberoamericana 14 1998 215 310 using malliavin calculus we show that y t admits a density for t 0 t provided i the vector fields v v 1 v d satisfy hormander s condition and ii the gaussian driving signal x satisfies certain conditions examples of driving signals include fractional brownian motion with hurst parameter h 1 4 the brownian bridge returning to zero after time t and the ornstein uhlenbeck process

quickest change detection and kullback leibler divergence for two state hidden markov models in this paper the quickest change detection problem is studied in two state hidden markov models hmm where the vector parameter theta of the hmm changes from theta 0 to theta 1 at some unknown time and one wants to detect the true change as quickly as possible while controlling the false alarm rate it turns out that the generalized likelihood ratio glr scheme while theoretically straightforward is generally computationally infeasible for the hmm to develop efficient but computationally simple schemes for the hmm we first discuss a subtlety in the recursive form of the generalized likelihood ratio glr scheme for the hmm then we show that the recursive cusum scheme proposed in fuh ann statist 2003 can be regarded as a quasi glr scheme for pseudo post change hypotheses with certain dependence structure between pre and postchange observations next we extend the quasi glr idea to propose recursive score schemes in the scenario when the postchange parameter theta 1 of the hmm involves a real valued nuisance parameter finally the kullback leibler kl divergence plays an essential role in the quickest change detection problem and many other fields however it is rather challenging to numerically compute it in hmms here we develop a non monte carlo method that computes the kl divergence of two state hmms via the underlying invariant probability measure which is characterized by the fredholm integral equation numerical study demonstrates an unusual property of the kl divergence for hmm that implies the severe effects of misspecifying the postchange parameter for the hmm

nonparametric sequential change point detection by a vertically trimmed box method this paper examines a new method for sequential detection of a sudden and unobservable change in a sequence of independent observations with completely unspecified distribution functions a nonparametric detection rule is proposed which relies on the concept of a moving vertically trimmed box as such it will be coined as the vertical box control chart v box chart its implementation requires merely to count the number of data points which fall into the box attached to the last available observation no a priori knowledge of data distributions is required and proper tuning of the box size provides a quick detection technique this is supported by establishing statistical properties of the method which explain the role of the tuning parameters used in the v box chart these theoretical results are verified by simulation studies which indicate that the v box chart may provide quick detection with zero delay for jumps of moderate sizes its averaged run length to detection is more favorable than the one for the classical ewma method by comparison with the classical shewhart chart which was optimized for normal errors our method provides comparable or better performance

efficient scalable schemes for monitoring a large number of data streams the sequential changepoint detection problem is studied in the context of global online monitoring of a large number of independent data streams we are interested in detecting an occurring event as soon as possible but we do not know when the event will occur nor do we know which subset of data streams will be affected by the event a family of scalable schemes is proposed based on the sum of the local cumulative sum cusum statistics from each individual data stream and is shown to asymptotically minimize the detection delays for each and every possible combination of affected data streams subject to the global false alarm constraint the usefulness and limitations of our asymptotic optimality results are illustrated by numerical simulations and heuristic arguments the appendices contain a probabilistic result on the first epoch to simultaneous record values for multiple independent random walks

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

existence of affine realizations for levy term structure models we investigate the existence of affine realizations for term structure models driven by levy processes it turns out that we obtain more severe restrictions on the volatility than in the classical diffusion case without jumps as special cases we study constant direction volatilities and the existence of short rate realizations

a note on ritov s bayes approach to the minimax property of the cusum procedure 1 introduction page 1954 proposed the cusum procedures as a solu tion to the problem of sequential detection of a change in distribution lorden 1971 introduced a notion of minimax optimality for change point models andshowed that the cusum procedures are asymptotically optimal in his sense moustakides 1986 then showed the minimax optimality of the cusum pro cedures when the initial and nal distribution are both known ritov 1990 used a bayes approach and gave an interesting argument for moustakides result similar to that of lehmann 1959 on the optimality of the sequentialprobability ratio test we transfer his approach to a continuous time modeland discuss the structure of the bayes risk let be an arbitrary but known constant we will consider a process wwithw

a likelihood ratio approach to sequential change point detection for a general class of parameters in this article we propose a new approach for sequential monitoring of a general class of parameters of a d dimensional time series which can be estimated by approximately linear functionals of t

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

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

non restarting cumulative sum charts and control of the false discovery rate cumulative sum or cusum charts are typically used to detect a change in the distribution of a sequence of observations e g shifts in the mean usually after signalling the chart is restarted by setting it to some value below the signalling threshold we propose a non restarting cusum chart which is able to detect periods during which the stream is out of control further we advocate an upper boundary to prevent the cusum chart rising too high which helps to detect a change back into control we present an algorithm to control the false discovery rate when considering cusum charts based on multiple streams of data we consider two definitions of a false discovery signalling out of control when the observations have been in control since the start and signalling out of control when the observations have been in control since the last time the chart was at zero we prove that the false discovery rate is controlled under both these definitions simultaneously simulations reveal the difference in false discovery rate control when using these and other desirable definitions of a false discovery copyright 2013 oxford university press

optimality of the cusum procedure in continuous time the optimality of cusum under a lorden type criterion setting is considered we demonstrate the optimality of the cusum test for ito processes in a sense similar to lorden s but with a criterion that replaces expected delays by the corresponding kullback leibler divergence

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

quantization effect on the log likelihood ratio and its application to decentralized sequential detection it is well known that quantization cannot increase the kullback leibler divergence which can be thought of as the expected value or first moment of the log likelihood ratio in this paper we investigate the quantization effects on the second moment of the log likelihood ratio it is shown via the convex domination technique that quantization may result in an increase in the case of the second moment but the increase is bounded above by 2 e the result is then applied to decentralized sequential detection problems not only to provide simpler sufficient conditions for asymptotic optimality theories in the simplest models but also to shed new light on more complicated models in addition some brief remarks on other higher order moments of the log likelihood ratio are also provided

follow the bouncing ball global results on tracking and state estimation with impacts in this paper we formulate tracking and state estimation problems of a translating mass in a polyhedral billiard as a stabilization problem for a suitable set due to the discontinuous trajectories arising from the impacts we use hybrid systems stability analysis tools to establish the results using a novel concept of mirrored images of the target mass we prove that 1 a tracking control algorithm and 2 an observer algorithm guarantee global exponential stability results for specific classes of polyhedral billiards including rectangles moreover we combine these two algorithms within dynamic controllers that guarantee global output feedback tracking the results are illustrated via simulations

detecting a suddenly arriving dynamic profile of finite duration this paper addresses the detection of a suddenly arriving dynamic profile of a finite duration often called a transient change in contrast to the traditional abrupt change detection where the post change period is assumed to be infinitely long the detection of a suddenly arriving transient change should be done before it disappears the detection of transient changes after their disappearance is considered as missed hence the traditional quickest change detection criterion minimizing the average detection delays provided a prescribed false alarm rate is compromised the proposed optimality criterion minimizes the worst case probability of missed detection provided that the worst case probability of false alarm during a certain period is upper bounded a suboptimal cusum type transient change detection algorithm based on a subclass of truncated sequential probability ratio tests is proposed the optimization of the proposed algorithm in this subclass leads to a specially designed finite moving average test the proposed method is analyzed theoretically and by simulation a special attention is paid to the case of gaussian observations with a dynamic profile

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

existence of affine realizations for stochastic partial differential equations driven by levy processes the goal of this paper is to clarify when a semilinear stochastic partial differential equation driven by levy processes admits an affine realization our results are accompanied by several examples arising in natural sciences and economics

finite dimensional markovian realizations for stochastic volatility forward rate models we consider forward rate models of heath jarrow morton type as well as more general infinite dimensional stochastic differential equations where the volatility diffusion term is stochastic in the sense of being driven by a separate hidden markov process within this framework we use the previously developed hilbert space realization theory in order to provide general necessary and sufficient conditions for the existence of a finite dimensional markovian realization for the stochastic volatility models we illustrate the theory by analysing a number of concrete examples

monitoring structural change contemporary tests for structural change deal with detections of the one shot type given an historical data set of fixed size these tests are designed to detect a structural break within the data set due to the law of the iterated logarithm one shot tests cannot be applied to monitor out of sample stability each time new data arrive without signalling a nonexistent break with probability one we propose and analyze two real time monitoring procedures with controlled size asymptotically the fluctuation and cusum monitoring procedures we extend an invariance principle in the sequential testing literature to obtain our results simulation results show that the proposed monitoring procedures indeed have controlled asymptotic size detection timing depends on the magnitude of parameter change the signal to noise ratio and the location of the out of sample break point

sprt and cusum in hidden markov models in this paper we study the problems of sequential probability ratio tests for parameterized hidden markov models we investigate in some detail the performance of the tests and derive corrected brownian approximations for error probabilities and expected sample sizes asymptotic optimality of the sequential probability ratio test for testing simple hypotheses based on hidden markov chain data is established next we consider the cumulative sum cusum procedure for change point detection in this model based on the renewal property of the stopping rule cusum can be regarded as a repeated one sided sequential probability ratio test asymptotic optimality of the cusum procedure is proved in the sense of lorden 1971 motivated by the sequential analysis in hidden markov models wald s likelihood ratio identity and wald s equation for products of markov random matrices are also given we apply these results to several types of hidden markov models i i d hidden markov models switch gaussian regression and switch gaussian autoregression which are commonly used in digital communications speech recognition bioinformatics and economics

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

optimality of cusum rule approximations in change point detection problems application to nonlinear state space systems the well known cumulative sum cusum sequential rule for abrupt model change detection in stochastic dynamic systems relies on the knowledge of the probability density functions of the system output variables conditional on their past values and on the system functioning mode at each time step this paper shows how to build an asymptotically optimal detection rule under the common average run length arl constraint when these densities are not available but can be consistently estimated this is the case for nonlinear state space systems observed through output variables for such systems a new class of particle filters based on convolution kernels allows to get consistent estimates of the conditional densities leading to an optimal cusum like filter detection rule fdr

a detection optimal min max test for transient signals page s 1954 test is optimal for detecting a permanent change in distribution in the sense that it minimizes the worst case average delay to detection given an average distance between false alarms when used to detect transient signals however it in fact becomes the generalized likelihood ratio test glrt since a glrt is in almost all cases ad hoc page s test used as such cannot be said to be optimal in any explicit sense this article discusses the development of the min max test via the new ideas of baygun and hero see ibid vol 41 p 688 703 1995 for the detection of a transient

asymptotic operating characteristics of an optimal change point detection in hidden markov models let 0 1 1 be observations from the hidden markov model with probability distribution p 0 and let 1 be observations from the hidden markov model with probability distribution p 1 the parameters 0 and 1 are given while the change point is unknown the problem is to raise an alarm as soon as possible after the distribution changes from p 0 to p 1 but to avoid false alarms specifically we seek a stopping rule n which allows us to observe the s sequentially such that e n is large and subject to this constraint sup k e k n k n k is as small as possible here e k denotes expectation under the change point k and e denotes expectation under the hypothesis of no change whatever in this paper we investigate the performance of the shiryayev roberts pollak srp rule for change point detection in the dynamic system of hidden markov models by making use of markov chain representation for the likelihood function the structure of asymptotically minimax policy and of the bayes rule and sequential hypothesis testing theory for markov random walks we show that the srp procedure is asymptotically minimax in the sense of pollak ann statist 13 1985 206 227 next we present a second order asymptotic approximation for the expected stopping time of such a stopping scheme when w 1 motivated by the sequential analysis in hidden markov models a nonlinear renewal theory for markov random walks is also given

existence of invariant manifolds for stochastic equations in infinite dimension we provide a frobenius type existence result for finite dimensional invariant submanifolds for stochastic equations in infinite dimension in the spirit of da prato and zabczyk 5 we recapture and make use of the convenient calculus on frechet spaces as developed by kriegl and michor 16 our main result is a weak version of the frobenius theorem on frechet spaces as an application we characterize all finite dimensional realizations for a stochastic equation which describes the evolution of the term structure of interest rates

malliavin calculus with time dependent coefficients and application to nonlinear filtering in this paper we prove using malliavin calculus that under a local hormander condition the solution of a stochastic differential equation with time depending coefficients admits ac density with respect to lebesgue measure an application of this result to nonlinear filtering is developed in this paper to prove the existence of ac density for the filter associated with a correlated system whose observation is one dimensional with unbounded coefficients

average run length to false alarm for surveillance schemes designed with partially specified pre change distribution observations are taken independently and sequentially detection of a change in distribution is studied when the problem has an invariance structure the prechange distribution is assumed to be a member of a specified family and is assumed known up to a nuisance parameter we provide a general method of constructing surveillance schemes in the presence of a nuisance parameter and give sufficient conditions for approximating their average run lengths to false alarm applications include detecting a change in scale of i i d gamma variates with unknown initial scale detecting a change in location of i i d normal variates with unknown initial mean and a non parametric scheme based on ranks for detecting a change to a stochastically larger distribution

a comparison of weighted cusum procedures that account for monotone changes in population size the cusum procedure has been popularly used for detecting a shift in the incidence rate of a rare health event many cusum methods are developed based on a poisson model with a constant mean number of events in practice the expected number of events is likely to vary over time as the population size at risk is not constant but often grows over time an increase in the baseline incidence rate tends to be masked by the population growth to efficiently detect an increase in the baseline incidence rate it is appealing to assign more weight to recent observations and less weight to older observations this paper compares weighted cusum wcusum and conventional cusum procedures in the presence of monotone changes in population size the simulation results show that the wcusum method may be more efficient than the conventional cusum methods in detecting increases in the incidence rate especially for small shifts an example based on mortality data from new mexico is used to illustrate the implementation of the wcusum method copyright 2010 john wiley sons ltd

invariant manifolds for weak solutions to stochastic equations viability and invariance problems related to a stochastic equation in a hilbert space h are studied finite dimensional invariant c2 submanifolds of h are characterized we derive nagumo type conditions and prove a regularity result any weak solution which is viable in a finite dimensional c2 submanifold is a strong solution these results are related to finding finite dimensional realizations for stochastic equations there has recently been increased interest in connection with a model for the stochastic evolution of forward rate curves

surveillance of a simple linear regression this article considers an important aspect of the general sequential analysis problem where a process is in control up to some unknown point i 1 after which the distribution from which the observations are generated changes an extensive sequential analytic literature assumes that the change in distribution is abrupt for example from n 0 1 to n 1 there is also an extensive literature that deals with a gradual change in the case where the decision whether or not a change has occurred is based on a fixed set of observations rather than an ongoing process of decision making every time a new observation is obtained however there is virtually no literature on the practical case of sequentially detecting a gradual change in distribution visualize a machine deteriorating gradually this article considers solutions to this problem as a first approximation the gradual change problem can be modeled as a change from a fixed distribution to a model of simple linear regression with respect to ti

information bounds and quickest change detection in decentralized decision systems the quickest change detection problem is studied in decentralized decision systems where a set of sensors receive independent observations and send summary messages to the fusion center which makes a final decision in the system where the sensors do not have access to their past observations the previously conjectured asymptotic optimality of a procedure with a monotone likelihood ratio quantizer mlrq is proved in the case of additive gaussian sensor noise if the signal to noise ratios snr at some sensors are sufficiently high this procedure can perform as well as the optimal centralized procedure that has access to all the sensor observations even if all snrs are low its detection delay will be at most pi 2 1ap 57 larger than that of the optimal centralized procedure next in the system where the sensors have full access to their past observations the first asymptotically optimal procedure in the literature is developed surprisingly the procedure has the same asymptotic performance as the optimal centralized procedure although it may perform poorly in some practical situations because of slow asymptotic convergence finally it is shown that neither past message information nor the feedback from the fusion center improves the asymptotic performance in the simplest model

minimax robust quickest change detection the popular criteria of optimality for quickest change detection procedures are the lorden criterion the pollak criterion and the bayesian criterion in this paper a robust version of these quickest change detection problems is considered when the pre change and post change distributions are not known exactly but belong to known uncertainty classes of distributions for uncertainty classes that satisfy a specific condition it is shown that one can identify least favorable distributions lfds from the uncertainty classes such that the detection rule designed for the lfds is optimal for the robust problem in a minimax sense the condition is similar to that required for the identification of lfds for the robust hypothesis testing problem originally studied by huber an upper bound on the delay incurred by the robust test is also obtained in the asymptotic setting under the lorden criterion of optimality this bound quantifies the delay penalty incurred to guarantee robustness when the lfds can be identified the proposed test is easier to implement than the cusum test based on the generalized likelihood ratio glr statistic which is a popular approach for such robust change detection problems the proposed test is also shown to give better performance than the glr test in simulations for some parameter values

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

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

performance analysis of sequential tests between poisson processes the problem of performance computation for sequential tests between poisson processes is considered the average sample numbers and error probabilities of the sequential probability ratio test sprt between two homogeneous poisson processes are known to solve certain delay differential equations ddes exact numerically stable solutions to these ddes are developed here and their asymptotic properties are explored these solutions are seen to be superior to earlier solutions of dvoretsky kiefer and wolfowitz 1953 which suffer from severe numerical instability in some ranges of parameters of interest in applications the application of these results is illustrated in the problem of performance approximation for the cumulative sum cusum quickest detection procedure

weighted cumulative sum technique a class of weighted control schemes that generalizes the basic cumulative sum cusum technique is introduced the schemes of the first type in which the weights represent information concomitant with the data prove to be especially useful when handling charts corresponding to samples of varying sizes the schemes of the second type are based on giving greater weight to more recent information representatives of this class are shown to have better run length characteristics with respect to drift in the level of a controlled process than does the classical cusum while maintaining good sensitivity with respect to shifts analogous to the classical cusum scheme they admit a dual graphical representation that is the scheme can be applied by means of a one or two sided decision interval or via a v mask a special case of this type of scheme designated the geometric cusum is considered in detail it can be viewed as a cusum type counterpart of the exponentially weighted moving average

second order asymptotic optimality in multisensor sequential change detection a generalized multisensor sequential change detection problem is considered in which a number of possibly correlated sensors monitor an environment in real time the joint distribution of their observations is determined by a global parameter vector and at some unknown time there is a change in an unknown subset of components of this parameter vector the goal is to detect the change as soon as possible while controlling the rate of false alarms we establish the second order asymptotic optimality with respect to lorden s criterion of various generalizations of the cusum rule that is we show that their additional expected worst case detection delay relative to the one that could be achieved if the affected subset was known remains bounded as the rate of false alarm goes to 0 for any possible subset of affected components this general framework incorporates the traditional multisensor setup in which only an unknown subset of sensors is affected by the change the latter problem has a special structure which we exploit in order to obtain feasible representations of the proposed schemes we present the results of a simulation study where we compare the proposed schemes with scalable detection rules that are only first order asymptotically optimal finally in the special case that the change affects exactly one sensor we consider the scheme that runs in parallel the local cusum rules and study the problem of specifying the local thresholds

a generalized change detection problem the purpose of this paper is to give a new statistical approach to the change diagnosis detection isolation problem the change detection problem has received extensive research attention however the change isolation problem has for the most part been ignored we consider a stochastic dynamical system with abrupt changes and investigate the multiple hypotheses extension of lorden s 1971 results we introduce a joint criterion of optimality for the detection isolation problem and then design a change detection isolation algorithm we also investigate the statistical properties of this algorithm we prove a lower bound for the criterion in a class of sequential change detection isolation algorithms it is shown that the proposed algorithm is asymptotically optimal in this class the theoretical results are applied to the case of additive changes in linear stochastic models

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

quickest detection of abrupt changes for a class of random processes we consider the problem of quickest detection of abrupt changes for processes that are not necessarily independent and identically distributed i i d before and after the change by making a very simple observation that applies to most well known optimum stopping times developed for this problem in particular cusum and shiryayev roberts 1963 stopping rule we show that their optimality can be easily extended to more general processes than the usual i i d case

tracking stopping times through noisy observations a novel quickest detection setting is proposed generalizing the well known bayesian change point detection model suppose xi yi i ges 1 is a sequence of pairs of random variables and that s is a stopping time with respect to xi i ges 1 the problem is to find a stopping time t with respect to yi i ges 1 that optimally tracks s in the sense that t minimizes the expected reaction delay bbe t s while keeping the false alarm probability p t s e t s below a given threshold alpha isin 0 1 this problem formulation applies in several areas such as in communication detection forecasting and quality control

detecting a change in regression first order optimality observations are generated according to a regression with normal error as a function of time when the process is in control the process potentially changes at some unknown point of time and then the ensuing observations are normal with the same mean function plus an arbitrary function under suitable regularity conditions the problem is to obtain a stopping rule that is optimal in the sense that the rule minimizes the expected delay in detecting a change subject to a constraint on the average run length to a false alarm a bound on the expected delay is first obtained it is then shown that the cusum and shiryayev roberts procedures achieve this bound to first order

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

quickest detection for changes in maximal knn coherence of random matrices this paper addresses the problem of quickest detection of a change in the maximal coherence between columns of an n times p random matrix based on a sequence of matrix observations having a single unknown change point the random matrix is assumed to have identically distributed rows and the maximal coherence is defined as the largest of the p atopwithdelims 2 correlation coefficients associated with any row likewise the k nearest neighbor knn coherence is defined as the k th largest of these correlation coefficients the forms of the pre and postchange distributions of the observed matrices are assumed to belong to the family of elliptically contoured densities with sparse dispersion matrices but are otherwise unknown a nonparametric stopping rule is proposed that is based on the maximal knn sample coherence between columns of each observed random matrix this is a summary statistic that is related to a test of existence of a hub vertex in a sample correlation graph having degree at least k performance bounds on the delay and false alarm performance of the proposed stopping rule are obtained in the purely high dimensional regime where p rightarrow infty and n is fixed when the prechange dispersion matrix is diagonal it is shown that among all functions of the proposed summary statistic the proposed stopping rule is asymptotically optimal under a minimax quickest change detection model as the stopping threshold approaches infinity the theory developed also applies to sequential hypothesis testing and fixed sample size tests

two strategies in the problem of change detection and isolation the comparison between optimal sequential and nonsequential fixed size sample strategies in the problem of abrupt change detection and isolation is discussed in particular we show that sometimes a simple fixed size sample algorithm is almost as efficient as an optimal sequential algorithm which leads to a burdensome number of arithmetical operations

quickest change detection of a markov process across a sensor array recent attention in quickest change detection in the multisensor setting has been on the case where the densities of the observations change at the same instant at all the sensors due to the disruption in this work a more general scenario is considered where the change propagates across the sensors and its propagation can be modeled as a markov process a centralized bayesian version of this problem is considered with a fusion center that has perfect information about the observations and a priori knowledge of the statistics of the change process the problem of minimizing the average detection delay subject to false alarm constraints is formulated in a dynamic programming framework insights into the structure of the optimal stopping rule are presented in the limiting case of rare disruptions it is shown that the structure of the optimal test reduces to thresholding the a posteriori probability of the hypothesis that no change has happened under a certain condition on the kullback leibler k l divergence between the post and the pre change densities it is established that the threshold test is asymptotically optimal in the vanishing false alarm probability regime it is shown via numerical studies that this low complexity threshold test results in a substantial improvement in performance over naive tests such as a single sensor test or a test that incorrectly assumes that the change propagates instantaneously

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

asymptotically optimal prediction for time varying data generating processes we develop a methodology referred to as kinetic prediction for predicting time series undergoing unknown changes in their data generating distributions based on kolmogorov tikhomirov s varepsilon entropy we propose a concept called varepsilon predictability that quantifies the size of a model class which can be parametric or nonparametric and the maximal number of abrupt structural changes that guarantee the achievability of asymptotically optimal prediction moreover for parametric distribution families we extend the aforementioned kinetic prediction with discretized function spaces to its counterpart with continuous function spaces and propose a sequential monte carlo based implementation we also extend our methodology for predicting smoothly varying data generating distributions under reasonable assumptions we prove that the average predictive performance converges almost surely to the oracle bound which corresponds to the case that the data generating distributions are known in advance the results also shed some light on the so called prediction inference dilemma various examples and numerical results are provided to demonstrate the wide applicability of our methodology

regularity of finite dimensional realizations for evolution equations we show that a continuous local semiflow of ck maps on a finite dimensional ck manifoldm can be embedded into a local ck flow on m under some weak necessary assumptions this result is applied to an open problem in 2 we prove that finite dimensional realizations for interest rate models are highly regular objects namely given by submanifolds m of d a where a is the generator of a strongly continuous semigroup

optimal sequential detection in multi stream data consider a large number of detectors each generating a data stream the task is to detect online distribution changes in a small fraction of the data streams previous approaches to this problem include the use of mixture likelihood ratios and sum of cusums we provide here extensions and modifications of these approaches that are optimal in detecting normal mean shifts we show how the optimal detection delay depends on the fraction of data streams undergoing distribution changes as the number of detectors goes to infinity there are three detection domains in the first domain for moderately large fractions immediate detection is possible in the second domain for smaller fractions the detection delay grows logarithmically with the number of detectors with an asymptotic constant extending those in sparse normal mixture detection in the third domain for even smaller fractions the detection delay lies in the framework of the classical detection delay formula of lorden we show that the optimal detection delay is achieved by the sum of detectability score transformations of either the partial scores or cusum scores of the data streams

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

asymptotic minimax robust quickest change detection for dependent stochastic processes with parametric uncertainty in this paper we consider the problem of quickly detecting an unknown change in the conditional densities of a dependent stochastic process in contrast to the existing quickest change detection approaches for dependent stochastic processes we propose minimax robust versions of the popular lorden pollak and bayesian criteria for when there is uncertainty about the parameter of the post change conditional densities under an information theoretic pythagorean inequality condition on the uncertainty set of possible post change parameters we identify asymptotic minimax robust solutions to our lorden pollak and bayesian problems finally through simulation examples we illustrate that asymptotically minimax robust rules can provide detection performance comparable to the popular but more computationally expensive generalized likelihood ratio rule

a mathematical framework for new fault detection schemes in nonlinear stochastic continuous time dynamical systems in this work a mathematical unifying framework for designing new fault detection schemes in nonlinear stochastic continuous time dynamical systems is developed these schemes are based on a stochastic process called the residual which reflects the system behavior and whose changes are to be detected a quickest detection scheme for the residual is proposed which is based on the computed likelihood ratios for time varying statistical changes in the ornstein uhlenbeck process several expressions are provided depending on a priori knowledge of the fault which can be employed in a proposed cusum type approximated scheme this general setting gathers different existing fault detection schemes within a unifying framework and allows for the definition of new ones a comparative simulation example illustrates the behavior of the proposed schemes

quickest detection in multiple on off processes we consider the quickest detection of idle periods in multiple on off processes at each time only one process can be observed and the observations are random realizations drawn from two different distributions depending on the current state on or off of the chosen process the objective is to catch an idle period in any of the on off processes as quickly as possible subject to a reliability constraint we show that this problem presents a fresh twist to the classic problem of quickest change detection that considers only one stochastic process a bayesian formulation of the problem is developed for both infinite and finite number of processes based on the theory of partially observable markov decision process pomdp while a general pomdp is pspace hard we show that the optimal decision rule has a simple threshold structure for the infinite case for the finite case basic properties of the optimal decision rule are established and a low complexity threshold policy is proposed which converges to the optimal decision rule for the infinite case as the number of processes increases this problem finds applications in spectrum sensing in cognitive radio networks where a secondary user searches for idle channels in the spectrum

asymptotic optimality of mixture rules for detecting changes in general stochastic models the paper addresses a sequential changepoint detection problem for a general stochastic model assuming that the observed data may be non i i d i e dependent and non identically distributed and prior distribution of the change point is arbitrary tartakovsky and veeravalli 2005 baron and tartakovsky 2006 and more recently tartakovsky 2017 developed a general asymptotic theory of changepoint detection for non i i d stochastic models assuming certain stability of the log likelihood ratio process in the case of simple hypotheses when both pre change and post change models are completely specified however in most applications the post change distribution is not completely known in the present paper we generalize previous results to the case of parametric uncertainty assuming that the parameter of the post change distribution is unknown we introduce two detection rules based on mixtures the mixture shiryaev rule and the mixture shiryaev roberts rule and study their asymptotic properties in the bayesian context in particular we provide sufficient conditions under which these rules are first order asymptotically optimal minimizing moments of the delay to detection as the probability of false alarm approaches zero

quickest search over multiple sequences the problem of sequentially finding an independent and identically distributed sequence that is drawn from a probability distribution q1 by searching over multiple sequences some of which are drawn from q1 and the others of which are drawn from a different distribution q0 is considered in the problem considered the number of sequences with distribution q1 is assumed to be a random variable whose value is unknown within a bayesian formulation a sequential decision rule is derived that optimizes a trade off between the probability of false alarm and the number of samples needed for the decision in the case in which one can observe one sequence at a time it is shown that the cumulative sum cusum test which is well known to be optimal for a non bayesian statistical change point detection formulation is optimal for the problem under study specifically the cusum test is run on the first sequence if a reset event occurs in the cusum test then the sequence under examination is abandoned and the rule switches to the next sequence if the cusum test stops then the rule declares that the sequence under examination when the test stops is generated by q1 the result is derived by assuming that there are infinitely many sequences so that a sequence that has been examined once is not retested if there are finitely many sequences the result is also valid under a memorylessness condition expressions for the performance of the optimal sequential decision rule are also developed the general case in which multiple sequences can be examined simultaneously is considered the optimal solution for this general scenario is derived

a suboptimal quadratic change detection scheme we address the problem of detecting changes in multivariate gaussian random signals with an unknown mean after the change the window limited generalized likelihood ratio glr scheme is a well known approach to solve this problem however this algorithm involves at least log spl gamma spl rho likelihood ratio computations at each stage where spl gamma spl gamma spl rarr spl infin is the mean time before a false alarm and spl rho is the kullback leibler information we establish a new suboptimal recursive approach which is based on a collection of l parallel recursive spl chi sup 2 tests instead of the window limited glr scheme this new approach involves only a fixed number l of likelihood ratio computations at each stage for any combinations of spl gamma and spl rho by choosing an acceptable value of nonoptimality the designer can easily find a tradeoff between the complexity of the quadratic change detection algorithm and its efficiency

bayesian sequential detection with phase distributed change time and nonlinear penalty a pomdp lattice programming approach we show that the optimal decision policy for several types of bayesian sequential detection problems has a threshold switching curve structure on the space of posterior distributions this is established by using lattice programming and stochastic orders in a partially observed markov decision process pomdp framework a stochastic gradient algorithm is presented to estimate the optimal linear approximation to this threshold curve we illustrate these results by first considering quickest time detection with phase type distributed change time and a variance stopping penalty then it is proved that the threshold switching curve also arises in several other bayesian decision problems such as quickest transient detection exponential delay risk sensitive penalties stopping time problems in social learning and multi agent scheduling in a changing world using blackwell dominance it is shown that for dynamic decision making problems the optimal decision policy is lower bounded by a myopic policy finally it is shown how the achievable cost of the optimal decision policy varies with change time distribution by imposing a partial order on transition matrices

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

misspecified and asymptotically minimax robust quickest change detection we investigate the quickest detection of an unknown change in the distribution of a stochastic process generating independent and identically distributed observations we develop new bounds on the performance of misspecified cumulative sum cusum rules and pose minimax robust versions of the popular lorden and pollak criteria with polynomial or higher order moment detection delay penalties by exploiting our results for misspecified cusum rules we identify solutions to our robust quickest change detection problems in the asymptotic regime of few false alarms in contrast to previous robust quickest change detection treatments our asymptotic results hold under relaxed conditions on the uncertainty sets of possible prechange and postchange distributions we illustrate our results in simulations and apply them to the problem of detecting target manoeuvres in low signal to noise ratio settings i e dim target manoeuvre detection

monitoring paired binary surgical outcomes using cumulative sum charts correlated binary data are encountered in many areas of medical research system reliability and quality control for monitoring failures rates in such situations simultaneous bivariate cumulative sum cusum charts with the addition of secondary control limits are proposed using an approach based on a markov chain model the run length properties of such a monitoring scheme can be determined for sudden or gradual changes in the failure rates the proposed control charts are easy to implement and are shown to be very effective at detecting small changes in the rate of undesirable outcomes especially when the changes are gradual this procedure is illustrated using bivariate outcome data arising from a series of paediatric surgeries the methodology is sufficiently general that it may be adapted for multivariate normal binomial or poisson responses

detection of stochastic processes this paper reviews two streams of development from the 1940 s to the present in signal detection theory the structure of the likelihood ratio for detecting signals in noise and the role of dynamic optimization in detection problems involving either very large signal sets or the joint optimization of observation time and performance this treatment deals exclusively with basic results developed for the situation in which the observations are modeled as continuous time stochastic processes the mathematics and intuition behind such developments as the matched filter the rake receiver the estimator correlator maximum likelihood sequence detectors multiuser detectors sequential probability ratio tests and cumulative sum quickest detectors are described

quickest detection with exponential penalty for delay the problem of detecting a change in the probability distribution of a random sequence is considered stopping times are derived that optimize the tradeoff between detection delay and false alarms within two criteria in both cases the detection delay is penalized exponentially rather than linearly as has been the case in previous formulations of this problem the first of these two criteria is to minimize a worst case measure of the exponential detection delay within a lower bound constraint on the mean time between false alarms expressions for the performance of the optimal detection rule are also developed for this case it is seen for example that the classical page cusum test can be arbitrarily unfavorable relative to the optimal test under exponential delay penalty the second criterion considered is a bayesian one in which the unknown change point is assumed to obey a geometric prior distribution in this case the optimal stopping time effects an optimal trade off between the expected exponential detection delay and the probability of false alarm finally generalizations of these results to problems in which the penalties for delay may be path dependent are also considered

input design for detection of abrupt changes in dynamical systems the detection and diagnosis of changes in stationary dynamical systems via statistical methods and using input design to improve detection performance are discussed a cumulative sum test to detect a change towards one of several hypotheses is obtained by exploiting connections with the sequential probability ratio test for input design the objectives are taken to be to decrease the detection time and at the same time to ensure a tolerable false alarm rate both off line auxiliary inputs and on line generation of the input signal by a linear output feedback are considered the problem is first introduced for the two hypotheses case and then the design techniques are extended to the general multiple hypotheses case

sequential detection and identification of a change in the distribution of a markov modulated random sequence the problem of detection and identification of an unobservable change in the distribution of a random sequence is studied via a hidden markov model hmm approach the formulation is bayesian on line discrete time allowing both single and multiple disorder cases dealing with both independent and identically distributed i i d and dependent observations scenarios allowing for statistical dependencies between the change time and change type in both the observation sequence and the risk structure and allowing for general discrete time disorder distributions several of these factors provide useful new generalizations of the sequential analysis theory for change detection and or hypothesis testing taken individually in this paper a unifying framework is provided that handles each of these considerations not only individually but also concurrently optimality results and optimal decision characterizations are given as well as detailed examples that illustrate the myriad of sequential change detection and identification problems that fall within this new framework

grouped data sequential probability ratio tests and cumulative sum control charts methodology is proposed for the design of sequential methods when data are obtained by gauging articles into groups exact expressions are obtained for the operating characteristics and average sampling number of wald sequential probability ratio tests and for the average run length of cumulative sum cusum schemes based on grouped data step by step design algorithms are provided to assist the practitioner the methodology is illustrated assuming a normal process with known standard deviation in which we wish to detect shifts in the mean an example from a progressive die operation is presented the methods proposed are simple to implement and are an economical alternative to variables data based sequential sampling plans and cusum control charts

an efficient sequential nonparametric scheme for detecting a change of distribution ble and remarkably efficient the method is based on the sequential vectors of signs and ranks of the observations the methodology is one of likelihood ratio a sequence of likelihood ratios for these vectors is computed and the shiryayev roberts approach to changepoint detection is then applied to yield a class of statistics and associated stopping rules inequalities and asymptotic approximations for the operating characteristics of these rules are developed these are found to be valid also for small average run lengths and early changepoints as well the relative efficiency of these schemes with respect to a normal parametric shift detection policy is very high making them a robust alternative to parametric methof s