Discussion on “Real-time monitoring of events applied to syndromic surveillance”

Abstract

I discuss the article “Real-time monitoring of events applied to syndromic surveillance” by Sparks and collaborators. This discussion focuses on how statistical network modeling and inference can be used to augment the analysis done in their paper. In particular I describe what network models can be used to characterize the dynamics and interactions of Twitter users, and more broadly how network analysis can be used to benefit statistical process monitoring. I hope to not only provide readers a new perspective on how to approach statistical process monitoring in the context of social interactions, but also to motivate future research that address the unique challenges facing quality engineers.     

A control scheme for monitoring the frequency and magnitude of an event

While many control charts have been developed for monitoring the time interval (t) between the occurrences of an event, many other charts are employed to examine the magnitude (x) of the event. These two types of control charts have usually been investigated and applied separately with limited syntheses in conventional statistical process control (SPC) methods. This article presents an SPC method for simultaneously monitoring the time interval t and magnitude x. It, essentially, combines a t chart and an x chart, and is therefore referred to as a t&x chart. The new chart is more effective than an individual t chart or individual x chart for detecting the out-of-control status of the event, in particular for detecting downward shifts (sparse occurrence and/or small magnitude). More profound is that, compared with an individual t or x chart, the detection effectiveness of the t&x chart is more invariable against different types of shifts, i.e. t shift, x shift and joint shift in t and x. The t&x chart has demonstrated its potential not only for manufacturing systems, but also for non-manufacturing sectors such as supply chain management, office administration and health care industry.     

A triple exponentially weighted moving average control chart for monitoring time between events

Time between events (TBE) charts are used in high-yield processes where the rate of occurrences is very low. In the current article, we propose a triple exponentially weighted moving average control chart to monitor TBE (regarded as triple exponentially weighted moving average TEWMA-TBE chart) modeled by a gamma distribution. One- and two-sided schemes of the proposed chart are designed and compared with the double EWMA DEWMA-TBE and EWMA-TBE charts. It is shown that the lower- and two-sided TEWMA-TBE charts outperform its competitors, especially for small to moderate downward shifts, while the upper-sided TEWMA-TBE chart has very good detection ability for small shifts. We also study the robustness of the proposed chart when the true distribution is a Weibull or a lognormal and it is found that the TEWMA-TBE chart has better robustness properties than its competitors, especially for small shifts. Two illustrative examples from airplane accidents and earthquakes are also provided to display the application of the proposed chart.     

A CUSUM chart for detecting the intensity ratio of negative events

This paper developed a single cumulative sum (CUSUM) scheme, called the UCUSUM chart, for simultaneously detecting the size N and time interval T of an event. The new chart used the information of size and frequency of the event and the UCUSUM chart is carried out using the only one statistic U, which contains both T and N; on the other hand, the UCUSUM chart could allocate the detection power to the T shifts and the N shifts. The results present that the UCUSUM chart is significantly powerful compared to other charts which are in the current research with either the time interval T or with the size N. The UCUSUM chart could be applied in many areas including industries and non-industries and the performance of the new chart shows it is much effective in example.     

Properties of the exponential EWMA chart with parameter estimation

Count rates may reach very low levels in production processes with low defect levels. In such settings, conventional control charts for counts may become ineffective since the occurrence of many samples with zero defects would cause control statistic to be consistently zero. Consequently, the exponentially weighted moving average (EWMA) control chart to monitor the time between successive events (TBE) or counts has been introduced as an effective approach for monitoring processes with low defect levels. When the counts occur according to a Poisson distribution, the TBE observations are distributed as exponential. Although the assumption of exponential distribution is a reasonable choice as a model of TBE observations, its parameter, i.e. the mean (also the standard deviation), is rarely known in practice and its estimate is used in place of the unknown parameter when constructing the exponential EWMA chart. In this article, we investigate the effects of parameter estimation on the performance measures (average run length, standard deviation, and percentiles of the run length distribution) of the exponential EWMA control chart. A comprehensive analysis of the conditional performance measures of the chart shows that the effect of estimation can be serious, especially if small samples are used. An investigation of the marginal performance measures, which are calculated by averaging the conditional performance measures over the distribution of the parameter estimator, allows us to provide explicit sample size recommendations in constructing these charts to reach a satisfactory performance in both the in‐control and the out‐of‐control situation. Copyright © 2009 John Wiley & Sons, Ltd.     

A control chart based on likelihood ratio test for monitoring process mean and variability

Recently, monitoring the process mean and variance simultaneously by using a single chart has drawn more and more attention. In this paper, we propose a new single chart that integrates the EWMA procedure with the generalized likelihood ratio (GLR) test statistics for jointly monitoring both the process mean and variance. It can be easily designed and constructed, and its average run length can be evaluated by a two‐dimensional Markov chain model. Owing to the good properties of the GLR test and EMWA, computation results show that it provides quite a robust and satisfactory performance in various cases, including the detection of the decrease in variability and the individual observation at the sampling point, which are very important in many practical applications but may not be well handled by the existing approaches in the literature. The application of our proposed method is illustrated by a real data example from chemical process control. Copyright © 2009 John Wiley & Sons, Ltd.     

SPC with correlated observations for the chemical and process industries

In the use of statistical control charts, violating the basic assumption of independent or uncorrelated data results in a chart that exhibits poor statistical performance, resulting in an increased number of false alarms. Autocorrelated data requires modifications to traditional control chart techniques. A method based on the exponentially weighted moving average that uses variable control limits is presented. Using simulation, we explore the shift detection properties of this moving centre-line technique and will show how the detection capability of the procedure can be enhanced using supplemental tracking signal tests. Guidelines and conditions for use are also presented.     

New EWMA control charts for monitoring process dispersion using auxiliary information

The exponentially weighted moving average (EWMA) control chart is a well‐known statistical process monitoring tool because of its exceptional pace in catching infrequent variations in the process parameter(s). In this paper, we propose new EWMA charts using the auxiliary information for efficiently monitoring the process dispersion, named the auxiliary‐information–based (AIB) EWMA (AIB‐EWMA) charts. These AIB‐EWMA charts are based on the regression estimators that require information on the quality characteristic under study as well as on any related auxiliary characteristic. Extensive Monte Carlo simulation are used to compute and study the run length profiles of the AIB‐EWMA charts. The proposed charts are comprehensively compared with a recent powerful EWMA chart—which has been shown to be better than the existing EWMA charts—and an existing AIB‐Shewhart chart. It turns out that the proposed charts perform uniformly better than the existing charts. An illustrative example is also given to explain the implementation and working of the AIB‐EWMA charts.     

Statistical monitoring performance for startup operations in a feedback control system

Previously, it has been held that statistical process control (SPC) and engineering process control (EPC) were two distinct domains for process improvement. However, we specifically consider the impact for integrating the two approaches on a first‐order dynamic system with ARIMA disturbances. We show how to model and analyze this system over a range of practical conditions. Our work results in a set of response surfaces that characterize the performance of the integrated design. We also compare these results to the case where the SPC and EPC policies are applied separately. In general, we find that the EPC approach performs best in terms of minimizing error, but that we can reduce the number and magnitude of adjustments using the integrated monitoring and control approach. This work also further supports our earlier findings that the integrated design is effective on complex dynamic systems during the initial transient or startup period. Copyright © 2001 John Wiley & Sons, Ltd.     

Real-time process monitoring using kernel distances

Real-time monitoring is an important task in process control. It often relies on estimation of process parameters in Phase I and Phase II and aims to identify significant differences between the estimates when triggering signals. Real-time contrast (RTC) control charts use classification methods to separate the Phase I and Phase II data and monitor the classification probabilities. However, since the classification probability statistics take discretely distributed values, the corresponding RTC charts become less efficient in the detection ability. In this paper, we propose to use distance-based RTC statistics for process monitoring, which are related to the distance from observations to the classification boundary. We illustrate our idea using the kernel linear discriminant analysis (KLDA) method and develop three distance-based KLDA statistics for RTC monitoring. The performance of the KLDA distance-based charting methods is compared with the classification probability-based control charts. Our results indicate that the distance-based RTC charts are more efficient than the class of probability-based control charts. A real example is used to illustrate the performance of the proposed method.     

A new adaptive EWMA control chart for monitoring the process dispersion

The exponentially weighted moving average (EWMA), cumulative sum (CUSUM), and adaptive EWMA (AEWMA) control charts have had wide popularity because of their excellent speed in tracking infrequent process shifts, which are expected to lie within certain ranges. In this paper, we propose a new AEWMA dispersion chart that may achieve better performance over a range of dispersion shifts. The idea is to first consider an unbiased estimator of the dispersion shift using the EWMA statistic, and then based on the magnitude of this shift, select an appropriate value of the smoothing parameter to design an EWMA chart, named the AEWMA chart. The run length characteristics of the AEWMA chart are computed with the help of extensive Monte Carlo simulations. The AEWMA chart is compared with some of the existing powerful competitor control charts. It turns out that the AEWMA chart performs substantially and uniformly better than the EWMA‐S², CUSUM‐S², existing AEWMA, and HHW‐EWMA charts when detecting different kinds of shifts in the process dispersion. Moreover, an example is also used to explain the working and implementation of the proposed AEWMA chart.     

Novel Bayesian CUSUM and EWMA control charts via various loss functions for monitoring processes

In this work, both the cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) control charts have been reconfigured to monitor processes using a Bayesian approach. Our construction of these charts are informed by posterior and posterior predictive distributions found using three loss functions: the squared error, precautionary, and linex. We use these control charts on count data, performing a simulation study to assess chart performance. Our simulations consist of sensitivity analysis of the out-of-control shift size and choice of hyper-parameters of the given distributions. Practical use of theses charts are evaluated on real data.     

Economic design of exponential charts for time between events monitoring

The occurrence of defects or non-conformities in manufacturing processes can usually be modeled by a homogeneous Poisson process. However, the process parameter may change over time and it can be monitored with statistical process control techniques. Control charts based on an exponential distribution, called exponential charts in this paper, can be developed to monitor the occurrence rate of such events. For manufacturers, the economic objective of production is very important and has to be optimized. An economic approach is developed in this paper for the design of exponential charts. We compare and contrast the performances of statistical design, economic design and economic–statistical design. The usefulness of the proposed economic design approach is justified. The relationships among these designs are illustrated through numerical examples. In particular, the economic–statistical design approach is interpreted from a multi-objective optimization viewpoint. The limitations of the approach as well as future research are also discussed.     

Exponential CUSUM Charts with Estimated Control Limits

Exponential CUSUM charts are used in monitoring the occurrence rate of rare events because the interarrival times of events for homogeneous Poisson processes are independent and identically distributed exponential random variables. In these applications, it is assumed that the exponential parameter, i.e. the mean, is known or has been accurately estimated. However, in practice, the in‐control mean is typically unknown and must be estimated to construct the limits for the exponential CUSUM chart. In this article, we investigate the effect of parameter estimation on the run length properties of one‐sided lower exponential CUSUM charts. In addition, analyzing conditional performance measures shows that the effect of estimation error can be significant, affecting both the in‐control average run length and the quick detection of process deterioration. We also provide recommendations regarding phase I sample sizes. This sample size must be quite large for the in‐control chart performance to be close to that for the known parameter case. Finally, we provide an industrial example to highlight the practical implications of estimation error, and to offer advice to practitioners when constructing/analyzing a phase I sample. Copyright © 2013 John Wiley & Sons, Ltd.     

Registration‐free monitoring of multimode near‐circular shape profiles

Traditional shape profile monitoring of product geometric features mostly focuses on one type or mode of shapes in the discrete‐part manufacturing. Little attention has been paid to monitoring of multimode shape profiles, where different modes of shapes appear in a sample in the batch production process. Motivated by a real example of a powder material production process, we exploit the statistical process monitoring of multimode near‐circular shape profiles. First, we develop a feature extraction approach that is invariant to shape rotation and thus requires no registration for a mixture of different modes of shape profiles. The extracted feature vectors capture shape features well, based on which different modes of shape profiles are separated into several clusters. This enables us to build a Gaussian mixture model for the multimodality in the feature vector space. In process surveillance, a control chart is constructed based on the likelihood ratio test for detecting shifts in both the proportions and the shape features of multimode near‐circular shape profiles. Numerical simulations and real case studies demonstrate the effectiveness of our proposed chart.     

Evaluation of Shewhart time-between-events-and-amplitude control charts for correlated data

In recent years, several techniques based on control charts have been developed for the simultaneous monitoring of the time interval T and the amplitude X of events, known as time-between-events-and-amplitude (TBEA) charts. However, the vast majority of the existing works have some limitations. First, they usually focus on statistics based on the ratio $\frac{X}{T}$, and second, they only investigate a reduced number of potential distributions, that is, the exponential distribution for T and the normal distribution for X. Moreover, until now, very few research papers have considered the potential dependence between T and X. In this paper, we investigate three different statistics, denoted as Z₁ , Z₂ , and Z₃ , for monitoring TBEA data in the case of three potential distributions (gamma, normal, and Weibull), for both T and X, using copulas as a mechanism to model the dependence. An illustrative example considering times between machine breakdowns and associated maintenance illustrates the use of TBEA control charts.     

Bayesian monitoring to detect a shift in process mean

A Bayesian analogue of the Shewhart X‐bar chart is defined and compared with cumulative sum charts. The comparison identifies types of production process where the Bayesian chart has better expected performance than the cumulative sum chart. Implementing the Bayesian chart requires more detailed knowledge of the process structure than is required by the best‐known types of charts, but acquiring this information can yield tangible benefits. Copyright © 2007 John Wiley & Sons, Ltd.     

Parameter Selection for a Robust Tracking Signal

Tracking signals use past forecast errors to monitor and control a forecasting process. In this study, the cumulative‐sum tracking signal and the smoothed‐error tracking signal are evaluated on their ability to aid in shift (process upset) detection. The moving‐centerline EWMA control chart technique is coupled with these tracking signals to enhance the monitoring of autocorrelated processes. The analysis characterizes two prevalent time series models: AR(1) and ARMA(1,1). The goal of this paper is to explore the capabilities of the tracking signals and the moving‐centerline EWMA when the smoothing constants are varied and a shift is introduced into the process. The tracking signals are evaluated based on average run length (ARL) and false alarm rate (FA). Copyright © 2005 John Wiley & Sons, Ltd.     

Real-time synchronization of batch trajectories for on-line multivariate statistical process control using Dynamic Time Warping

This paper addresses the real-time monitoring of batch processes with multiple different local time trajectories of variables measured during the process run. For Unfold Principal Component Analysis (U-PCA)—or Unfold Partial Least Squares (U-PLS)-based on-line monitoring of batch processes, batch runs need to be synchronized, not only to have the same time length, but also such that key events happen at the same time. An adaptation from Kassidas et al.'s approach [1] will be introduced to achieve the on-line synchronization of batch trajectories using the Dynamic Time Warping (DTW) algorithm. In the proposed adaptation, a new boundaries definition is presented for accurate on-line synchronization of an ongoing batch, together with a way to adapt mapping boundaries to batch length. A relaxed greedy strategy is introduced to avoid assessing the optimal path each time a new sample is available. The key advantages of the proposed strategy are its computational speed and accuracy for the batch process context. Data from realistic simulations of a fermentation process of the Saccharomyces cerevisae cultivation are used to illustrate the performance of the proposed strategy.