Exponentially Weighted Moving Average Schemes Research Articles

Midpoint-radii principal component analysis -based EWMA and application to air quality monitoring network

Monitoring air quality is crucial for the safety of humans and the environment. Moreover, real world data collected from air quality network is often affected by different types of errors as measurement noise and variability of pollutant concentrations. The uncertainty in the data, which is strictly connected to the above errors, may be treated by considering interval-valued data analysis. In practical cases of measured data, the true value cannot be measured and the collected data on a process are only approximations given by sensors, and are thus imprecise. This is due mainly to the uncertainties induced by measurement errors or determined by specific experimental conditions. Thus, the main aim of this paper is to develop an enhanced monitoring of air quality network by taking into account the uncertainties on the data. To do that, we develop a new monitoring technique that merges the advantages of Midpoint-radii PCA (MRPCA) method with exponentially weighted moving average (EWMA) chart, in order to enhance sensor fault detection technique of air quality monitoring process. MRPCA is the most popular interval multivariate statistical method, able to tackle the issue of uncertainties on the models and one way to improve the fault detection abilities. On the other hand, the EWMA statistic allows an exponential weighted average to successive observations and able to detect small and moderate faults. The developed MRPCA-based EWMA method relies on using MRPCA as a modeling framework for fault detection and EWMA as a detection chart. The proposed MRPCA-based EWMA scheme is illustrated using a simulation example and applied for sensor fault detection of an air quality monitoring network. The monitoring performances of the developed technique are compared to the classical monitoring techniques. MRPCA model performances are compared with the interval PCA models: complete-information principal component analysis (CIPCA) and Centers PCA (CPCA). The MRPCA-based EWMA monitoring performances are compared to MRPCA-based Shewhart, generalized likelihood ratio test (GLRT) and squared prediction error (SPE) techniques.

Monitoring road traffic congestion using a macroscopic traffic model and a statistical monitoring scheme

Monitoring vehicle traffic flow plays a central role in enhancing traffic management, transportation safety and cost savings. In this paper, we propose an innovative approach for detection of traffic congestion. Specifically, we combine the flexibility and simplicity of a piecewise switched linear (PWSL) macroscopic traffic model and the greater capacity of the exponentially-weighted moving average (EWMA) monitoring chart. Macroscopic models, which have few, easily calibrated parameters, are employed to describe a free traffic flow at the macroscopic level. Then, we apply the EWMA monitoring chart to the uncorrelated residuals obtained from the constructed PWSL model to detect congested situations. In this strategy, wavelet-based multiscale filtering of data has been used before the application of the EWMA scheme to improve further the robustness of this method to measurement noise and reduce the false alarms due to modeling errors. The performance of the PWSL-EWMA approach is successfully tested on traffic data from the three lane highway portion of the Interstate 210 (I-210) highway of the west of California and the four lane highway portion of the State Route 60 (SR60) highway from the east of California, provided by the Caltrans Performance Measurement System (PeMS). Results show the ability of the PWSL-EWMA approach to monitor vehicle traffic, confirming the promising application of this statistical tool to the supervision of traffic flow congestion.

An adaptive exponentially weighted moving average chart for the mean with variable sampling intervals

AbstractThe AEWMA control chart is an adaptive EWMA (exponentially weighted moving average) type chart that combines the Shewhart and the classical EWMA schemes in a smooth way. To improve the detection performance of the FSI (fixed sampling interval) AEWMA control chart in terms of the ATS(average time to signal), this paper proposes a new VSI (variable sampling interval) AEWMA control chart. A Markov chain approach is used to calculate the ATS values of the new VSI AEWMA control chart, and comparative results show that the proposed control chart performs better than the standard FSI AEWMA control chart and than other VSI control charts over a wide range of shifts.

A Study on EWMA charts with runs rules—the Markov chain approach

ABSTRACTRuns rules are usually used with Shewhart-type charts to enhance the charts' sensitivities toward small and moderate shifts. Abbas et al. in 2011 took it a step further by proposing two runs rules schemes, applied to the exponentially weighted moving average (EWMA) chart and evaluated their average run length (ARL) performances using simulation. They showed that the proposed schemes are superior to the classical EWMA chart and other schemes being investigated. Besides pointing out some erroneous ARL and standard deviation of the run length (SDRL) computations in Abbas et al., this paper presents a Markov chain approach for computing the ARL, percentiles of the run length (RL) distribution and SDRL, for the two runs rules schemes of Abbas et al. Using Markov chain, we also propose two combined runs rules EWMA schemes to quicken the two schemes of Abbas et al. in responding to large shifts. The runs rules (basic and combined rules) EWMA schemes will be compared with some existing control charting methods, where the former charts are shown to prevail.

A Data-Driven Monitoring Technique for Enhanced Fall Events Detection

Fall detection is a crucial issue in the health care of seniors. In this work, we propose an innovative method for detecting falls via a simple human body descriptors. The extracted features are discriminative enough to describe human postures and not too computationally complex to allow a fast processing. The fall detection is addressed as a statistical anomaly detection problem. The proposed approach combines modeling using principal component analysis modeling with the exponentially weighted moving average (EWMA) monitoring chart. The EWMA scheme is applied on the ignored principal components to detect the presence of falls. Using two different fall detection datasets, URFD and FDD, we have demonstrated the greater sensitivity and effectiveness of the developed method over the conventional PCA-based methods.

Run length quantiles of EWMA control charts monitoring normal mean or/and variance

Exponentially weighted moving average (EWMA) control charts are well-established devices for monitoring process stability. Typically, control charts are evaluated by considering their Average Run Length (ARL), that is the expected number of observations or samples until the chart signals. Because of the limitations of an average, various papers also dealt with the run length distribution and quantiles. Going beyond these papers, we develop algorithms for and evaluate the quantile performance of EWMA control charts with variance adjusted control limits and with fast initial response features, of EWMA charts based on the sample variance, and of EWMA charts simultaneously monitoring mean and variance. Additionally, for the mean charts we consider medium, late and very late process changes and their impact on appropriately conditioned run length quantiles. It is demonstrated that considering run length quantiles can protect from constructing distorted EWMA designs while optimising their zero-state ARL performance. The implementation of all the considered measures in the R package ‘spc’ allows any control chart user to consider EWMA schemes from the run length quantile prospective in an easy way.

Optimal EWMA of linear combination of Poisson variables for multivariate statistical process control

In this paper, we propose a new process control chart for monitoring correlated Poisson variables, the EWMA LCP chart. This chart is the exponentially weighted moving average (EWMA) version of the recently proposed LCP chart. The latter is a Shewhart-type control chart whose control statistic is a linear combination of the values of the different Poisson variables (elements of the Poisson vector) at each sampling time. As a Shewhart chart, it is effective at signalling large process shifts but is slow to signal smaller shifts. EWMA charts are known to be more sensitive to small and moderate shifts than their Shewhart-type counterparts, so the motivation of the present development is to enhance the performance of the LCP chart by the incorporation of the EWMA procedure to it. To ease the design of the EWMA LCP chart for the end user, we developed a user-friendly programme that runs on Windows© and finds the optimal design of the chart, that is, the coefficients of the linear combination as well as the EWMA smoothing constant and chart control limits that together minimise the out-of-control ARL under a constraint on the in-control ARL. The optimization is carried out by genetic algorithms where the ARLs are calculated through a Markov chain model. We used this programme to evaluate the performance of the new chart. As expected, the incorporation of the EWMA scheme greatly improves the performance of the LCP chart.

An accurate evaluation of adaptive exponentially weighted moving average schemes

As a natural generalization of the conventional Exponentially Weighted Moving Average (EWMA) monitoring scheme, the Adaptive EWMA (AEWMA) scheme has received a great deal of attention. The Markov chain method was originally used to approximate the average run length performance of the AEWMA chart; however, this method may suffer from the issue of slow convergence and unstable approximation due to kernel discontinuity. In order to overcome this issue, this article extends the piecewise collocation method and the Clenshaw–Curtis (CC) quadrature (method) to the evaluation of AEWMA chart performance. It is shown that both the collocation and CC quadrature methods are very competitive and can provide more accurate and fast approximation to the run length performance of AEWMA charts than the conventional Markov chain approach.

Design of Exponentially Weighted Moving Average Scheme for Standardized Means

Exponentially Weighted Moving Average (EWMA) scheme in monitoring process mean is favored because it remembers the past information and detects the small shifts in the mean of a sequence of independent normal variates. However the design procedure of the EWMA scheme was complex till Crowder (1989) presents a simplified scheme for monitoring process mean. Currently standardizing the variables and monitoring them jointly is widely practiced and many schemes are presented under joint quality monitoring. Therefore a need arises to design EWMA schemes for monitoring standardized process means which will easier the work of monitoring more than one process variable at a time. In this paper an alternative design of such a scheme is presented. The new scheme is easy to apply and is independent of sample size. The scheme parameters are the same for any process if the in-control average run length (ARL) and the shifts in means to be detected are the same. In industrial application this property is more beneficial for monitoring few variables in one display. DOI: http://dx.doi.org/10.4038/sljastats.v14i2.6221

Improved Fast Initial Response Features for Exponentially Weighted Moving Average and Cumulative Sum Control Charts

Exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) control charts have found extensive applications in industry. The sensitivity of these quality control schemes can be increased by using fast initial response (FIR) features. In this paper, we introduce some improved FIR features for EWMA and CUSUM control charts and evaluate their performance in terms of average run length. We compare the proposed FIR‐based EWMA and CUSUM control schemes with some existing control schemes, that is, EWMA, FIR‐EWMA, CUSUM, and FIR‐CUSUM. It is noteworthy that the proposed control schemes are uniformly better than the other schemes considered here. An illustrative example is also given to demonstrate the implementation of the proposed control schemes. Copyright © 2013 John Wiley & Sons, Ltd.

Efficient Computer Network Anomaly Detection by Changepoint Detection Methods

We consider the problem of efficient on-line anomaly detection in computer network traffic. The problem is approached statistically, as that of sequential (quickest) changepoint detection. A multi-cyclic setting of quickest change detection is a natural fit for this problem. We propose a novel score-based multi-cyclic detection algorithm. The algorithm is based on the so-called Shiryaev-Roberts procedure. This procedure is as easy to employ in practice and as computationally inexpensive as the popular Cumulative Sum chart and the Exponentially Weighted Moving Average scheme. The likelihood ratio based Shiryaev-Roberts procedure has appealing optimality properties, particularly it is exactly optimal in a multi-cyclic setting geared to detect a change occurring at a far time horizon. It is therefore expected that an intrusion detection algorithm based on the Shiryaev-Roberts procedure will perform better than other detection schemes. This is confirmed experimentally for real traces. We also discuss the possibility of complementing our anomaly detection algorithm with a spectral-signature intrusion detection system with false alarm filtering and true attack confirmation capability, so as to obtain a synergistic system.

Likelihood-Based EWMA Charts for Monitoring Poisson Count Data With Time-Varying Sample Sizes

Many applications involve monitoring incidence rates of the Poisson distribution when the sample size varies over time. Recently, a couple of cumulative sum and exponentially weighted moving average (EWMA) control charts have been proposed to tackle this problem by taking the varying sample size into consideration. However, we argue that some of these charts, which perform quite well in terms of average run length (ARL), may not be appealing in practice because they have rather unsatisfactory run length distributions. With some charts, the specified in-control (IC) ARL is attained with elevated probabilities of very short and very long runs, as compared with a geometric distribution. This is reflected in a larger run length standard deviation than that of a geometric distribution and an elevated probability of false alarms with short runs, which, in turn, hurt an operator's confidence in valid alarms. Furthermore, with many charts, the IC ARL exhibits considerable variations with different patterns of sample sizes. Under the framework of weighted likelihood ratio test, this article suggests a new EWMA control chart which automatically integrates the varying sample sizes with the EWMA scheme. It is fast to compute, easy to construct, and quite efficient in detecting changes of Poisson rates. Two important features of the proposed method are that the IC run length distribution is similar to that of a geometric distribution and the IC ARL is robust to various patterns of sample size variation. Our simulation results show that the proposed chart is generally more effective and robust compared with existing EWMA charts. A health surveillance example based on mortality data from New Mexico is used to illustrate the implementation of the proposed method. This article has online supplementary materials.

Modified exponentially weighted moving average (EWMA) control chart for an analytical process data

This article introduces modified exponentially weighted moving average (modified EWMA) control chart. The modified EWMA control chart is very effective in detecting small and abrupt shifts in monitoring process mean. This chart is based on modified EWMA control chart statistic, which is a correction of EWMA chart statistic and it is free from inertia problem. The advantage of using modified EWMA chart is its good performance for observations that are autocorrelated or independently normal distributed. The performances of Modified EWMA chart are illustrated along with EWMA chart for the two types of analytical process data. The average run length (ARL) properties of modified EWMA scheme are derived using Markov Chain approach. Key words: Abrupt change, autocorrelated, average run length, exponentially weighted moving average (EWMA), modified.

EWMA Charts for the Weibull Shape Parameter

This article discusses exponentially weighted moving average (EWMA) charts for monitoring the Weibull shape parameter β. The charts are based on the sample range of the logarithms of the data and an unbiased estimator of 1β. The average run length (ARL) of the proposed chart is determined by β and the sample size n. Hence, the design of a chart is based on the β of interest, n, and the desired in-control ARL. Two-sided charts are derived, as well as one-sided charts for detecting specific shifts in β. These charts are compared with the cumulative sum chart of Page (1954), which is known to have optimality properties. The EWMA schemes studied here are ARL unbiased in the sense that they are expected to detect shifts sooner than the in-control ARL. The proposed schemes are applied to monitoring the Weibull shape parameter of the strength distribution of a carbon fiber used in composite materials.

Accurate ARL Calculation for EWMA Control Charts Monitoring Normal Mean and Variance Simultaneously

Exponentially weighted moving average (EWMA) control charts designed for monitoring the variance or the mean and the variance of a normally distributed variable are either based on the log transformation of the sample variance S 2 or provide only rough average run length (ARL) results. Gan (1995), as the most prominent example for the simultaneous case, calculated ARL values precisely for -ln S 2 EWMA schemes. The results in Knoth and Schmid (2002) for -S 2 ones are less accurate than the former one. The reason behind the lack of precision is that the methods usually applied for ARL calculation are not able to handle the restricted support of the chart statistic (S 2 and, of course, S and the range R are nonnegative random variables). While in Knoth (2005) this problem is treated for single variance monitoring by solving integral equations with collocation methods, this paper employs collocation and ideas similar to Gan (1995) in order to obtain accurate ARL values of -S 2 EWMA control charts. Additionally, the appropriate choice of the nonsymmetric control limits for the S 2 part of the scheme is addressed.

Design and investigation of EWMA and double EWMA with quadratic process model in R2R controllers

In the last few years, “Run-to-Run” (R2R) control techniques have been developed and used to control various processes in industries. These techniques combine control engineering and statistical process control techniques. The R2R controller is basically consists of a linear regression model that relates the input variables to the output variables using Exponentially Weighted Moving Average (EWMA) or double EWMA (dEWMA) scheme. In this paper, we have developed a quadratic R2R controller model as an extension of Box, Luceno and Del Castillo models. The validity and performance of the developed models were tested in the magnetic ceramic process. By this study we have found that the quadratic model improves capability of process and applying dEWMA procedure decreases variance of the response variables. The results of the study shows that the quadratic R2R control models outperform linear R2R controls in the certain manufacturing process.

Fast initial response features for EWMA control charts

The exponentially weighted moving average (EWMA) control chart became very popular during the last decade. It is characterized by simple handling and good performance. It turns out, however, that the most popular EWMA scheme with fixed-width control limits—the asymptotic control limits are taken and do not change over time—detects early changes rather slowly. For the competing CUSUM chart the so-called fast initial response (head-start) feature is developed which permits rapid response to an initial out-of-control situation. Meanwhile, in some papers similar modifications for EWMA schemes are described. We compare these approaches by using precise computation techniques, which are based on numeric quadrature rules and allow higher accuracy than earlier studies. Moreover, previous comparisons are restricted to the evaluation of the detection speed by comparing the average run lengths (ARLs), that is, the parameter of interest is constant during the whole monitoring period. Here, we consider more possible change point locations, which gives the EWMA control chart user a better insight into the scheme performance for early changes. *** DIRECT SUPPORT *** A00T7005 00004

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.

Statistical tool breakage detection schemes based on vibration signals in NC milling

We develop a vibration sensor-based tool breakage detection system for NC milling operations. The system obtains the time-domain vibration signal from the sensor attached on the spindle bracket of our CNC machine and declares tool failures through the on-line monitoring schemes. For the on-line detection, our approach is to use the statistical process control methods where control limits or thresholds are automatically calculated independently of cutting conditions. The main thrust of this paper is to compare the performance of the proposed statistical process monitoring methods including the X-bar control scheme, the exponentially weighted moving average (EWMA) scheme, and the adaptive EWMA scheme. The performance of the control schemes are compared in terms of the type I and II errors calculated from the experiment data.

EWMA Control Charts with Time-Varying Control Limits and Fast Initial Response

The control limits of an exponentially weighted moving average (EWMA) control chart should vary with time, approaching asymptotic limits as time increases. However, previous analyses of EWMA charts consider only asymptotic control limits. In this article, the run length properties of EWMA charts with time-varying control limits are approximated using non-homogeneous Markov chains. Comparing the average run lengths (ARL's) of EWMA charts with time-varying control limits and results previously obtained for asymptotic EWMA charts shows that using time-varying control limits is akin to the fast initial response (FIR) feature suggested for cumulative sum charts. The ARL of the EWMA scheme with time-varying limits is substantially more sensitive to early process shifts, especially when the EWMA weight is small. An additional improvement in FIR performance can be achieved by further narrowing the control limits for the first twenty observations. The methodology is illustrated assuming a normal process with known standard deviation where we wish to detect shifts in the mean.