Towards Improved Analysis Methods for Two-Level Factorial Experiments with Time Series Responses Erik Vanhatalo, a * † Bjarne Bergquist a and Kerstin Vännman b,c,d Dynamic processes exhibit a time delay between the disturbances and the resulting process response. Therefore, one has to acknowledge process dynamics, such as transition times, when planning and analyzing experiments in dynamic processes. In this article, we explore, discuss, and compare different methods to estimate location effects for two-level factorial experiments where the responses are represented by time series. Particularly, we outline the use of intervention-noise modeling to estimate the effects and to compare this method by using the averages of the response observations in each run as the single response. The comparisons are made by simulated experiments using a dynamic continuous process model. The results show that the effect estimates for the different analysis methods are similar. Using the average of the response in each run, but removing the transition time, is found to be a competitive, robust, and straightforward method, whereas intervention-noise models are found to be more comprehensive, render slightly fewer spurious effects, find more of the active effects for unreplicated experi- ments and provide the possibility to model effect dynamics. Copyright © 2012 John Wiley & Sons, Ltd. Keywords: two-level factorial design; time series analysis; intervention-noise model; location effects; simulation 1. Introduction M any industrial processes exhibit a dynamic behavior, and combined with typical high measurement sampling frequencies, the measurement series become autocorrelated. In fact, many industrial processes are unstable by nature and never truly exhibit a state of statistical control. Even so, using basic concepts such as randomization and replication of runs makes it possible to conduct experiments on these processes (see Bisgaard et al. 1 ). Autocorrelation in logged process data is especially evident in process industry, where process dynamics contribute to slow-moving propagations of disturbances. When experimenting on such systems, the observed responses naturally become represented by time series. When analyzing these experiments, our experience is that the time series aspects are often disregarded and instead a single response value (e.g. the run average) is assigned to each experimental run (see Figure 1). However, analysis procedures that completely disregard the dynamic nature of the responses may be ineffective or even erroneous. Disregarding the time series characteristics by, for example, averaging out the entire time series in the run, including the transition periods when the process reacts to different treatments, is a poor alternative because it likely leads to the underestimation of location effects and the overestimation of variation effects. We argue that a discussion of how to analyze experiments with time series responses may be valuable for many experimenters. This article relates the analysis of two-level factorial designs to time series analysis methods. More specifically, we outline a method based on transfer function-noise modeling, with the purpose of analyzing and estimating location effects for two-level factorial experiments with time series responses. The performance of this new proposed method is compared with approaches using the averages of the experimental runs, with or without removing the process’ transition periods when going from one run to the next. The analysis methods under consideration are outlined in Section 2. Performance comparisons are made by analyzing simulated replicated and unreplicated 2 3 factorial experiments with known effect sizes and dynamic behavior. Because of time concerns, we limit our study to location effects of sizes of 0, 0.5, 1.0, and 2.0 times the process’ standard deviation under normal operation. Important assumptions for the process model used during the simulations are given in Section 3. Sections 4–7 illustrate how the methods work and test their performance using simulated examples. Concluding remarks and a discussion of the results are given in Section 8. a Quality Technology and Management, Luleå University of Technology, SE-97187, Luleå, Sweden b Department of Statistics, Umeå University, Umeå, Sweden c Department of Engineering Sciences and Mathematics, Luleå University of Technology, Luleå, Sweden d Department of Engineering Science, University West, Trollhättan, Sweden *Correspondence to: Erik Vanhatalo, Quality Technology and Management, Luleå University of Technology, SE-97187, Luleå, Sweden. † E-mail: erik.vanhatalo@ltu.se Copyright © 2012 John Wiley & Sons, Ltd. Qual. Reliab. Engng. Int. 2012 Research Article (wileyonlinelibrary.com) DOI: 10.1002/qre.1424 Published online in Wiley Online Library