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A basic assumption when using principal component analysis (PCA) for inferential purposes, such as in statistical process control (SPC), is that the data are independent in time. In many industrial processes, frequent sampling and process dynamics make this assumption unrealistic rendering sampled data autocorrelated (serially dependent). PCA can be used to reduce data dimensionality and to simplify multivariate SPC. Although there have been some attempts in the literature to deal with autocorrelated data in PCA, we argue that the impact of autocorrelation on PCA and PCA-based SPC is neither well understood nor properly documented. This article illustrates through simulations the impact of autocorrelation on the descriptive ability of PCA and on the monitoring performance using PCA-based SPC when autocorrelation is ignored. In the simulations, cross-correlated and autocorrelated data are generated using a stationary first-order vector autoregressive model. The results show that the descriptive ability of PCA may be seriously affected by autocorrelation causing a need to incorporate additional principal components to maintain the model's explanatory ability. When all variables have equal coefficients in a diagonal autoregressive coefficient matrix, the descriptive ability is intact, while a significant impact occurs when the variables have different degrees of autocorrelation. We also illustrate that autocorrelation may impact PCA-based SPC and cause lower false alarm rates and delayed shift detection, especially for negative autocorrelation. However, for larger shifts, the impact of autocorrelation seems rather small. © 2015 The Authors. Quality and Reliability Engineering International published by John Wiley & Sons Ltd. [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]

In many industrial applications, autocorrelated data are becoming increasingly common due to, for example, on-line data collection systems with high-frequency sampling. Therefore, the basic assumption of independent observations for process capability analysis is not valid. The purpose of this article is to compare decision methods using the process capability index Cpk when data are autocorrelated. This is done through a case study followed by a simulation study. In the simulation study the actual significance level and power of the decision methods are investigated. The outcome of the article is that two methods appeared to be better than the others. [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.

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]

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.

The article uses an example from economics to show how regression analysis can be misleading if the assumption of independence of the errors is violated. It says that the issue of autocorrelation is of importance when one uses regression to estimate input-output relationships from process data sampled over time that likely may be autocorrelated.

*Edited by Søren Bisgaard [ABSTRACT FROM AUTHOR]