Guide to Advanced Empirical
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| 5.4. Process Control The other major use of dynamic, temporally oriented data is in determining that there is not change overtime. This is the area of statistical process control. A process is performing effectively if its behavior only changes under conscious direction left alone it should remain stable, and measurements made on it should remain the same apart from the inevitable and unimportant random variation. In the s Walter Shewhart at Western Electric devised a statistical method for quantifying and monitoring the stability of a process, the control chart, examples of which are shown in Fig. 7. As can be seen, the control chart looks very much like a trend chart, except that it is based on a defined control level or expected value of the measurements (the These accuracy measures can also be used in assessing the fit of models to static data, of course, but in the latter case there are more useful global goodness-of-fit measures such as R 2 which are used instead. Such measures are not available for forecasting dynamic data. 6 Statistical Methods and Measurement solid line, as well as control limits (the dashed lines, which define the range of values that are expected to be observed if the process is operating stably at the control level (and thus differences in observed measurements are due simply to random variation. There are different types of control chart, depending on the kind of measurement being tracked, such as continuous measures, counts, or proportions. Multivariate control charts track several measurements jointly. The overall principle is the same in each case a baseline control level is established by a series of measurements of the process, and control limits are defined in terms of the observed variability of the process (and possibly also the desired variability. One then plots measurements of the process taken at regular intervals and looks either for measurements lying outside the control limits (and thus indicating that the process is operating outside of its normal range, presumably because of some interfering factor, or for patterns in the measurements which suggest that the observed variability is not random, but is due to some factor or factors affecting the process. Figure a illustrates a process that is under statistical control Fig. b shows one that is out of control and Fig. a shows one that, while apparently under control (being inside the control limits, shows patterns in the measurements that deserve investigation. In the decades since they were first developed, there have been many different variations developed to handle the variety of process control situations that arise. One of the most useful variants is the cumulative sum or cusum chart, which is more sensitive at detecting changes in the level of process measurements. Cusum charts work by accumulating the deviations from the baseline expected value of the process if the variation is truly random, the variations in one direction counterbalance those in the opposite direction and the cumulative sum remains close to zero. If, on the other hand, variations in the process are biased even slightly in one direction or the other, then the cumulative sum will advance towards the upper or lower control limit. This accumulation of small biases allows the trend to be detected earlier than would be the case with a standard control chart. Figure 8 shows both a standard chart and a cusum chart fora process that is drifting slowly out of control. The theory and practice of control charts is highly developed and remains a central part of quality engineering. Good references are Montgomery (1996) and Duncan (1986). More recently, Box and Luceño (1997) have elaborated the relationship between statistical process control and engineering control theory. Download 1.5 Mb. Share with your friends:
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