Exponentially Weighted Moving Average Schemes Research Articles

The estimation of the long-term drift of the inductance measurement standards

Inductance measurements are important in many fields, especially in electronics, electrical engineering, radio engineering, and other areas. The inductance is often an important parameter in a wide range of applications such as radio transmitters, power circuits, magnetic resonance pulsed sources, etc. The accuracy of the inductance affects the quality of products, especially in devices where inductors are used, such as filters, transformers, inverters, etc. High-precision inductance measurements are used for the product quality control to ensure that manufactured devices meet established specifications and standards.
 Drift is an undesirable property of all measuring instruments and measurement standards during their life cycle. The analysis of the instrumental drift of measurement standards is of great importance in metrology. Reliable drift accounting plays an important role in maintaining measurement accuracy. For electrical measurement standards, the long-term drift is predictable. The drift types and main methods of its estimation for measurement standards between their calibrations were analysed. The drift uncertainty can be evaluated from the history of successive calibrations, and in the absence of such history, the order of magnitude of the calibration uncertainty can be estimated.
 The results of the estimation of the long-term drift of the inductance measurement standards for high-precision calibration of measuring instruments and measurement standards by two methods, polynomial regression curves and Exponentially Weighted Moving Average (EWMA) schemes, are given. The EWMA schemes reduce the lag inherent in traditional moving averages by giving more weight to recent observations. It is shown that the use of the EWMA schemes compared to the regression analysis shows greater sensitivity to the drift changes in the last years of observations. This allows the laboratory to take this factor into account when calibrating measuring instruments and measurement standards.

Monitoring negative sentiment scores and time between customer complaints via one-sided distribution-free EWMA schemes

Customer complaints about a product or service can be evaluated using the sentiment intensity (S) and time interval (T) of negative reviews. Previous control chart-based research applied two-sided schemes to detect upward and downward shifts in S and T. However, managers are interested in shifts related to frequent and severe customer complaints. One-sided schemes focusing on specific shifts are preferable to traditional schemes focusing on all shifts. Therefore, we propose one-sided distribution-free exponentially weighted moving average (EWMA) schemes to detect these specific shifts, including the increase in S, the decrease in T, and the possible increase in the variability of either variable. We devise the schemes by combining the individual p-values of the modified Wilcoxon rank-sum and Mood test statistics. We provide detailed implementation steps and post-signal diagnostic plans. The proposed schemes can timely detect anomalies in customer complaints and diagnose the cause of variations. In the simulation study, the proposed schemes exhibit robustness under in-control cases and outperform the existing schemes under most out-of-control cases. Finally, we use JingDong (JD) laptop reviews to verify the effectiveness of the proposed method.

Distribution-free Phase-II monitoring of high-dimensional industrial processes via origin and modified interpoint distance based algorithms

Improvements in measuring devices, the development of sensing technologies, automated record-keeping and cloud storage facilities have offered us a large volume of data streams involving many variables for data-driven decision-making. Consequently, monitoring high-dimensional (HD) processes has become an essential and exciting topic in statistical process monitoring. HD monitoring poses a significant challenge because considerable uncertainty is involved in estimating process parameters when an adequately large reference sample is unavailable before monitoring. Thus, designing an effective, conveniently implementable monitoring scheme for the HD processes remains a challenging task that has yet to be effectively addressed. This paper develops two distribution-free exponentially weighted moving average (EWMA) schemes to monitor multivariate and HD processes based on origin and interpoint distances. Previous works on interpoint distance-based charts are generally not distribution-free unless only one reference point is used as a benchmark to compute the interpoint distances. We offer an improved and general way to achieve conditionally distribution-free properties closely. The proposal also combines the advantage of the nonparametric approaches for jointly monitoring the process location and scale parameters with the better shift detection performance of an EWMA scheme. The new EWMA schemes can be easily implemented even when the data dimension is large with a small number of Phase-I samples. Control limits using the median run length as a metric are evaluated and tabulated for some cases to implement the proposed chart quickly. Extensive comparative studies have been conducted to verify the efficacy of the proposed monitoring schemes. Finally, the proposed schemes are illustrated with a real problem of monitoring high-dimensional quality characteristics from semiconductor manufacturing processes.

Exponentially weighted moving average Lepage-type schemes based on the lower-order percentile of the run-length metrics and their use in monitoring time-occupancy in Google applications

ABSTRACT Many existing monitoring schemes in the literature are based on the in-control (IC) average or median run-length. Several Phase-II schemes frequently fail to protect against the high rate of early false alarms. The problem may worsen when the average run-length metric is used, and the scheme is based on unknown and estimated parameters. Early false alarms can be avoided using monitoring schemes based on the lower-order percentiles of the IC run-length distribution. The exponentially weighted moving average (EWMA)-Lepage scheme is presented in this paper. The new design is based on a percentile-based approach that can effectively reduce and control the rate of early false alarms. The run-length properties of the EWMA scheme with the lower-order percentile-based design were investigated and compared with the double EWMA-Lepage and homogeneously weighted moving average-Lepage schemes. Detailed simulation studies show no clear winner among the three schemes for given sample sizes for the unknown shift. Instead, the size of the Phase-I and Phase-II samples heavily influences the choice of a potentially beneficial scheme. A case study on monitoring the time occupation of users on the Google application is presented to demonstrate the design and implementation of lower-percentile-based techniques. Some future research directions are offered.

Proposed variable sampling interval maximum EWMA and distance EWMA charts with unknown process parameters

The variable sampling interval (VSI) exponentially weighted moving average (EWMA) chart which varies the chart's sampling interval according to the value of the current plotting statistic increases the speed of the standard EWMA chart in detecting shifts. Joint monitoring schemes use a single combined statistic for the mean and variance in process monitoring. To simultaneously monitor the mean and variance of a process from the normal distribution, two VSI EWMA schemes with unknown process parameters, based on (i) Maximum (Max) and (ii) Distance (Dis) type combining functions, are proposed in this paper. Each of these schemes uses a single plotting statistic. The effects of parameter estimation on the performance of the proposed VSI Max EWMA and VSI Dis EWMA schemes, in terms of the average time to signal, standard deviation of the time to signal, expected average time to signal and median time to signal criteria, are studied using Monte Carlo simulation. The results show that the proposed schemes can identify process shifts quicker than the existing Max/Dis Shewhart (SH), Max/Dis cumulative sum (CUSUM) and Max/Dis EWMA schemes. The implementation of the proposed schemes is demonstrated using a commercial dataset.

Performance of the Shiryaev‐Roberts‐type scheme in comparison to the CUSUM and EWMA schemes in monitoring weibull scale parameter based on Type I censored data

AbstractThis paper introduces a process monitoring scheme based on the Shiryaev‐Roberts (SR) procedure for Type I right‐censored Weibull lifetime data for detecting shifts in the scale parameter for a fixed value of the shape parameter. The performance of the new charting scheme is evaluated under different censoring rates and sample sizes via Monte Carlo simulation. Comparison with two existing schemes, namely, the exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) schemes, is performed in terms of average run length (ARL). Both zero‐state and steady‐state shifts are considered in this study for impartial comparisons. The numerical results based on simulation are highly encouraging in favour of the SR procedure. Our findings show that the new scheme outperforms the other two schemes in some cases. An illustrative example is given to illustrate the application of the proposed scheme.

A novel single composite Shewhart‐EWMA control chart for monitoring the process mean

AbstractStatistical process monitoring (SPM) literature recommends the combination of Shewhart and exponentially weighted moving average (EWMA) schemes to improve the ability of the standalone Shewhart and EWMA monitoring schemes in detecting small to large shifts. The resulting scheme is named combined (or composite) Shewhart‐EWMA (CSEWMA) scheme. In this paper, a new single composite Shewhart‐EWMA (denoted as SCSEWMA) scheme for monitoring the mean when the process parameters are known or unknown is proposed using an additive weighted model. The flexibility of the proposed scheme is made possible by an additional weighing parameter that regulates its sensitivity towards shifts of different sizes. The new scheme is compared to the existing Shewhart, EWMA and CSEWMA schemes, and the results reveal the superiority of the proposed scheme over the latter schemes. Simulated and real‐life data are used to demonstrate the application and implementation of the proposed scheme.

A new multivariate CUSUM chart for monitoring of covariance matrix with individual observations under estimated parameter

AbstractMultivariate charts for process dispersion detect changes in the variance‐covariance matrix of a process. Most of the existing multivariate charts for monitoring the dispersion of individual observations were designed based on exponentially weighted moving average (EWMA) charting schemes. However, an alternative to the EWMA scheme is the cumulative sum (CUSUM) control chart, which has proven to be better in some cases. In the last decades, few studies have been conducted on methods based on multivariate CUSUM (MCUSUM) schemes to monitor the covariance matrix of individual observations. Consequently, we propose a new MCUSUM dispersion chart. Besides, most of the existing methods have been developed by assuming that the process parameters are known and that the process distribution is normal; these assumptions are not always true in practice. Hence, we compare the performance of the proposed chart and its counterparts based on the estimation effects under normal and non‐normal distributions. The results show that the proposed chart outperforms the other charts in terms of minor shifts in the process. Similarly, the proposed chart is the most robust to the normality assumption among the compared charts. The average value of the conditional average run length was used as the performance measure. Finally, the proposed method was also implemented with a simulated dataset to support the stated proposal findings.

Run length distribution for a modified EWMA scheme fitted with a stationary AR(p) model

A modified exponentially weighted moving average (EWMA) scheme is a quality control chart which can quickly detect small shifts in autocorrelated data. In this article, an explicit formula is presented to calculate the average run length (ARL) for a modified EWMA chart with an autoregressive AR(p) model involving exponential white noise. Its performance is compared with a numerical integral equation method via a simulation study to determine whether the explicit formula can help decrease the processing time. Moreover, this scheme is tested against a classical EWMA control chart using the ARL and RMI results. Finally, the explicit formula for ARL is applied to a real numerical example from the health field to demonstrate the efficacy of our method.

Design of attribute EWMA type control charts with reliable run length performance

Attribute control charts assuming a Poisson (c chart) or a binomial distribution (np chart) are usually used when the quality characteristic cannot be measured on a continuous scale. For equivalent sample sizes, Shewhart type attribute control charts are known to be less efficient than their measurement counterparts (like the chart) and, for this reason, practitioners often compensate it by supplementing them with an EWMA (Exponentially Weighted Moving Average) scheme. However, because of the discrete nature of count data, it is unfortunately impossible to compute exactly and accurately (by means of Markov chain of integral equation methods) the run length (RL) properties, such as its mean (ARL) and its standard deviation (SDRL) of these EWMA attribute control charts and, consequently, it is impossible to efficiently design them in order to minimize some out-of-control characteristics. For this reason, we propose in this paper a dedicated approach called “continuousify” method which, coupled with a classical Markov chain technique, allows to compute the RL properties of any EWMA attribute control chart in a reliable way. A numerical comparison shows that the RL properties obtained by using the proposed “continuousify” approach are very much alike to the ones calculated via simulation and without the “continuousify” approach. Illustrative examples are also provided to show how the proposed method can be implemented in practice.

Effective monitoring of carbon emissions from industrial sector using statistical process control

The industrial sector is considered one of the fastest-growing sources of greenhouse gases, due to the excessive consumption of energy required to cope with the growing production of energy exhaustive products. The statistical process monitoring (SPM) can be an effective tool for monitoring and controlling carbon emissions from industries. This article presents an economic-statistical design of the combined Shewhart X¯ and exponentially weighted moving average (EWMA) scheme (X¯&EWMA scheme) for monitoring carbon emissions from industries to allow prompt action for controlling excessive emissions. The parameters of the proposed SPM scheme have been optimized for minimizing the expected total cost, including cost from carbon emissions and operational costs of the SPM scheme. The design of the X¯&EWMA scheme has been optimized considering a wide range of shifts in the mean of the emission process, and ensuring that the constraints on inspection rate, sample size, and false alarm rate are all satisfied. Comparative studies showed that the optimal X¯&EWMA scheme reduced the expected total cost by about 40%, 77%, and 28% compared with the basic X¯, EWMA, and X¯&EWMA schemes, respectively. The impact of the design parameters on the effectiveness of the proposed SPM scheme has also been investigated by sensitivity analysis. Finally, the application of the proposed SPM scheme is demonstrated by using real data for carbon emissions from different industrial facilities. This study is expected to considerably reduce the cost owing to excessive carbon emissions from industries and widen the literature on the utilization of SPM tools in managing the quality of the environment.

Joint monitoring of post-sales online review processes based on a distribution-free EWMA scheme

With the booming of online shopping, the post-sales online review process becomes a crucial activity in product life cycle management, as it provides abundant user-generated content (UGC) for e-commerce businesses to monitor customer satisfaction, identify potential recalls, and improve electronic Word of Mouth (eWOM). As the core of UGCs, online reviews are generally divided into negative reviews and non-negative reviews in terms of sentiment polarity. Quality issues, such as failures of products or services, are more likely to be hidden in negative reviews. Hence this paper focuses on detecting the abnormal changes of the time-between-review T and sentiment scores S of negative reviews. Due to the complexity and variability of online review processes, the distribution assumptions for S and T may be invalid in real cases. To overcome this problem, we design a distribution-free two-sided monitoring scheme by using the max-type combining function to combine the exponentially weighted moving average (EWMA)-based Wilcoxon rank-sum (WRS) statistics for S and T. The IC and OC performances of the proposed scheme are investigated via simulation study. The results indicate that the proposed scheme outperforms other schemes including a distribution-free EWMA scheme and three parametric Shewhart schemes. Finally, a real example from Ctrip is provided for illustrating the application of the proposed scheme in post-sales service monitoring.

Optimal one‐ and two‐sided adaptive EWMA scheme for monitoring Poisson count data

AbstractThe Poisson distribution assumption often arises in several industrial applications for modeling defects or nonconformities. In this work, we investigate the one‐ and two‐sided performance of a new adaptive EWMA (exponentially weighted moving average)‐type chart for monitoring Poisson count data. An appropriate discrete‐state Markov chain technique is provided to compute the exact ARL (average run length) properties. Moreover, comparative studies are conducted to demonstrate the higher sensitivity of the proposed chart in the detection of shifts with various magnitudes. Advices on how to select the appropriate chart parameters are provided and an illustrative numerical example is proposed.

Generally weighted moving average monitoring schemes: Overview and perspectives

AbstractAn overview of monitoring schemes from a class called generally weighted moving average (GWMA) is provided. A GWMA scheme is an extended version of the exponentially weighted moving average (EWMA) scheme with an additional adjustment parameter that introduces more flexibility in the GWMA model as it adjusts the kurtosis of the weighting function so that the GWMA scheme can be designed such that it has an advantage over the corresponding EWMA scheme in the detection of certain shift values efficiently. The parametric and distribution‐free GWMA schemes to monitor various quality characteristics and its existing enhanced versions (ie, double GWMA, composite Shewhart‐GWMA, mixed GWMA‐CUSUM, and mixed CUSUM‐GWMA) have better performance than their corresponding EWMA counterparts in many situations; hence, all such existing research works discussing GWMA‐related schemes (ie, 66 publications in total) are documented and categorized in such a manner that it is easy to identify research gaps. Finally, a number of possible future research ideas are provided.

Design and application of dual-EWMA scheme for anomaly detection in injection moulding process

Plastic injection moulding is one of the very challenging processes to yield products with good quality and low cost. This study presents an optimization model for designing an exponentially weighted moving average (EWMA) scheme consisting of two individual EWMA schemes (called dual-EWMA scheme) for efficient monitoring of a range of mean shifts in an injection moulding process producing plastic parts. The optimization design is conducted under the constraints of inspection resources (labor equipped with measurement instrumentation) and false alarm rate, which ensures that no extra manpower will be needed and the false alarm rate of the charting scheme will not be increased. The effectiveness of the optimal dual-EWMA scheme is investigated through a 23 factorial design considering different scenarios, which shows that the proposed charting scheme is significantly superior to its main competitor, the conventional dual-EWMA scheme, as well as other schemes. The impact of design specifications on the effectiveness of the proposed scheme is analyzed through a sensitivity study. The design and implementation of the proposed scheme are demonstrated through a case study. Finally, a design table is presented to ease the application of the proposed scheme in practice.

Comparisons of some distribution-free CUSUM and EWMA schemes and their applications in monitoring impurity in mining process flotation

Cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) schemes are widely used in monitoring small and persistent shifts in specific process characteristics. Nonparametric (Distribution-free) CUSUM and EWMA schemes are useful in detecting such changes when the underlying process distribution is unknown or complicated. The CUSUM-Wilcoxon rank-sum (CUSUM-WRS), CUSUM-Precedence, EWMA-WRS, and EWMA-Precedence are well-known distribution-free CUSUM and EWMA schemes for Phase-II monitoring of a shift in the unknown location parameter of a process. In this article, we compare their performances with two robust CUSUM and EWMA schemes based on the Hogg-Fisher-Randle (HFR) type statistic. We investigate the accomplishments of these CUSUM and EWMA schemes in detecting shifts of different sizes for various process distributions and show that the proposed CUSUM and EWMA HFR schemes perform favourably for highly skewed distributions. In this article, we also discuss the efficacy of these nonparametric CUSUM and EWMA schemes when the test sample size is small. We also outline the implementation strategies various plans with an illustration using a dataset from the iron ore mining plant. We offer some concluding remarks and future research problems.

Robust adaptive exponentially weighted moving average control charts with applications of manufacturing processes

Statistical process control (SPC) has its own importance in the field of quality control. In SPC, control charts are significant tools to monitor process parameters, and exponentially weighted moving average (EWMA) control chart is one such tool. It is a memory-type chart, which is used to target mainly the smaller shifts in the process parameters. Adaptive EWMA (AEWMA) scheme is used to identify small as well as large shifts. EWMA and AEWMA are based on the assumption of normality, which is quite hard to find in practice, and there are many situations where outliers are occasionally present. In the current study, we have proposed four robust adaptive EWMA schemes for monitoring process location parameter. We have investigated their performance under uncontaminated normal and contaminated normal environments. We have carried out comparisons amongst different competing charts based on average run length (ARL), standard deviation of run length (SDRL) and different percentiles of run length distribution. Two examples related to manufacturing processes are also provided for practical implementation of the proposed schemes.

An improved design of exponentially weighted moving average scheme for monitoring attributes

The Exponentially Weighted Moving Average (EWMA) schemes are a potent tool for monitoring small to moderate variations in the quality characteristics in production lines of manufacturing industries. Practitioners in various sectors widely use the EWMA schemes for scrutinising both the variables and attributes. In the present article, we investigate a modified EWMA scheme based on the power of the difference between the actual number of nonconforming items and its technical specification in an in-control (IC) situation. We abbreviate it as a wEWMA scheme and show that the traditional EWMA scheme is a particular case of the proposed scheme when the power is unity. We establish that the powers lower than unity are more effective for detecting smaller shifts, while for detecting substantial variations in process parameter, one should prefer higher powers greater than unity. Noting that possible magnitude of a shift is often unknown, we propose the optimal design procedure of the scheme, including the determination of its charting parameters to ensure the best overall performance. The results reveal that the optimal wEWMA schemes can be beneficial in detecting a shift very quickly when the sample size is small, particularly for high-precision production processes.

The effect of measurement errors on the adaptive EWMA chart

AbstractThe AEWMA chart is an Adaptive EWMA (Exponentially Weighted Moving Average)–type chart that combines the Shewhart and the classical EWMA schemes in a smooth way. Its performance has been studied under the assumption that there is no measurement error in the quality characteristic. In this paper, we investigate the performance of the AEWMA chart when measurement errors exist using a linearly covariate error model. The presence of measurement errors with a linearly increasing measurement error standard deviation is also investigated. It turns out that, with the existence of measurement errors, the efficiency of the AEWMA chart can be strongly affected, and the negative effect can be compensated by taking multiple measurements at each sample point. Comparisons with the classical EWMA scheme confirm the superiority of the AEWMA scheme in detecting a wide range of shifts even in the presence of measurement errors. An example is provided to illustrate the use of the AEWMA chart with measurement errors.

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.