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When principal component analysis (PCA) is used for statistical process monitoring it relies on the assumption that data are time independent. However, industrial data will often exhibit serial correlation. Dynamic PCA (DPCA) has been suggested as a remedy for high-dimensional and time-dependent data. In DPCA the input matrix is augmented by adding time-lagged values of the variables. In building a DPCA model the analyst needs to decide on (1) the number of lags to add, and (2) given a specific lag structure, how many principal components to retain. In this article we propose a new analyst driven method to determine the maximum number of lags in DPCA with a foundation in multivariate time series analysis. The method is based on the behavior of the eigenvalues of the lagged autocorrelation and partial autocorrelation matrices. Given a specific lag structure we also propose a method for determining the number of principal components to retain. The number of retained principal components is determined by visual inspection of the serial correlation in the squared prediction error statistic, Q (SPE), together with the cumulative explained variance of the model. The methods are illustrated using simulated vector autoregressive and moving average data, and tested on Tennessee Eastman process data. [ABSTRACT FROM AUTHOR]

One of the basic assumptions for traditional univariate and multivariate control charts is that the data are independent in time. For the latter, in many cases, the data are serially dependent (autocorrelated) and cross-correlated because of, for example, frequent sampling and process dynamics. It is well known that the autocorrelation affects the false alarm rate and the shift-detection ability of the traditional univariate control charts. However, how the false alarm rate and the shift-detection ability of the Hotelling T² control chart are affected by various autocorrelation and cross-correlation structures for different magnitudes of shifts in the process mean is not fully explored in the literature. In this article, the performance of the Hotelling T² control chart for different shift sizes and various autocorrelation and cross-correlation structures are compared based on the average run length using simulated data. Three different approaches in constructing the Hotelling T² chart are studied for two different estimates of the covariance matrix: (i) ignoring the autocorrelation and using the raw data with theoretical upper control limits; (ii) ignoring the autocorrelation and using the raw data with adjusted control limits calculated through Monte Carlo simulations; and (iii) constructing the control chart for the residuals from a multivariate time series model fitted to the raw data. To limit the complexity, we use a first-order vector autoregressive process and focus mainly on bivariate data. [ABSTRACT FROM AUTHOR]

The article considers the use of a model fitting criterion in analyzing parsimonious time-series data, as well as in the decision-making process. The authors selected specific models based on the properties of the sample autocorrelation function (ACF) and the sample partial autocorrelation function (PACF). They also assesses the impulse response function for each model by reviewing time-series theory. Analyses of Internet server users are provided to expound some of the issues related to selecting an adequate model.

The article provides a detailed discussion about how to apply Box-Cox transformations to sales data. It discusses the forecasting model proposed by C. Chatfield and D. L. Prothero and the alternative model proposed by G. E. P. Box and G. M. Jenkins. It then evaluates the two models and interpret them to be able to understand why Chatfield and Prothero felt the autoregressive integrated moving average (ARIMA) approach did not provide sensible forecasts. It also discusses an unusual seasonal time series model proposed by G. T. Wilson.

The article examines how seasonal time series can be modeled and used for forecasting. The authors utilized the international airline data and modeled it with a seasonal autoregressive integrated moving average (ARIMA) time series model by Box and Jenkins to show how seasonal ARIMA models can be used to model cyclic data and how the model can be used for short-term forecasting. The most vital structural issue to consider about seasonal time series is that if the season is s periods long. Another consideration is that observations s time intervals apart are alike.

There is an increasing use of on-line data acquisition systems in industry. This usually leads to autocorrelated data and implies that the assumption of independent observations has to be re-examined. Most decision procedures for capability analysis assume independent data. In this article we present a new way of performing capability analysis when data are autocorrelated. This method is based on what can be called the ‘iterative skipping’ strategy. In that, by skipping a pre-determined number of observations, e.g. considering every fifth observation, the data set is divided into subsamples for which the independence assumption may be valid. For each such subsample of the data we estimate a capability index. Then traditional tests, assuming independence, can be performed based on each estimated capability index from the subsamples. By combining the information from each test statistic based on the subsamples in a suitable way, a new and efficient decision procedure is obtained. We discuss different ways of combining the information from these individual tests. A main appeal of our proposed method is that no time-series model is needed. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The article demonstrates how to characterize the behavior of a chemical manufacturing process using a time series model to control and adjust the manufacturing process. The authors discuss a different interpretation of the word control, and consider the situation where the process is adjusted whenever data coming from the process indicates that the process is too far from a given target value. They describe the idea behind time series control of a process and proceed more intuitively and use the chemical process as an illustrative example.

This article presents an analysis of time series data from industrial processes. The time series considered is consists of 197 consecutive concentration observations from a full-scale chemical process. Computation of the sample autocorrelation function is presented. It is concluded that the nonstationary model with the interpretation that the exponentially moving average represents is the best estimate of the current level of the process.

Characterizes the dynamic behavior of time series models. Dynamics of a stationary processes; Basic physics of a pendulum; Information on the impulse response function; Discussion on the superposition principle.

*Edited by Søren Bisgaard [ABSTRACT FROM AUTHOR]

There are two key reasons for aligning batch process data. The first is to obtain same-length batches so that standard methods of analysis may be applied, whilst the second reason is to synchronise events that take place during each batch so that the same event is associated with the same observation number for every batch. Dynamic time warping has been shown to be an effective method for meeting these objectives. This is based on a dynamic programming algorithm that aligns a batch to a reference batch, by stretching and compressing its local time dimension. The resulting ”warping function” may be interpreted as a progress signature of the batch which may be appended to the aligned data for further analysis. For the warping function to be a realistic reflection of the progress of a batch, it is necessary to impose some constraints on the dynamic time warping algorithm, to avoid an alignment which is too aggressive and which contains pathological warping. Previous work has focused on addressing this issue using global constraints. In this work, we investigate the use of local constraints in dynamic time warping and define criteria for evaluating the degree of time distortion and variable synchronisation obtained. A local constraint scheme is extended to include constraints not previously considered, and a novel method for selecting the optimal local constraint with respect to the two criteria is proposed. For illustration, the method is applied to real data from an industrial bacteria fermentation process. [ABSTRACT FROM AUTHOR]