Limitations of Univariate Monitoring Techniques

In the era of single-loop control systems in chemical processing plants, there was little infrastructure for monitoring multivariable processes by using multivariate statistical techniques. A limited number of process and quality variables were measured in most plants, and use of univariate SPM tools for monitoring critical process and quality variables seemed appropriate. The installation of computerized data acquisition and storage systems, the availability of inexpensive sensors for typical process variables such as temperature, flow rate, and pressure, and the development of advanced chemical analysis systems that can provide reliable information on quality variables at high frequencies increased the number of variables measured at 

The appeal of multivariate process monitoring techniques is based on 

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The book follows a rational presentation structure, starting with the fundamentals of univariate statistical techniques and a discussion on the implementation issues in Chapter 2. After stating the limitations of univariate techniques, Chapter 3 focuses on a number of multivariate statistical techniques that permit the evaluation of process performance and provide diagnostic insight. To exploit the information content of process measurements even further. Chapter 4 introduces several modeling strategies that are based on the utilization of input-output process data. Chapter 5 provides statistical process monitoring techniques for continuous processes and three case studies that demonstrate the techniques. 

In this chapter, we first introduce traditional process monitoring techniques (Section 21.1) that are based on limit checking of measurements and process performance calculations. In Section 21.2, the theoretical basis of SPC monitoring techniques and the most widely used control charts are considered. We also introduce process capability indices and compare SPC with standard automatic feedback control. Traditional SPC monitoring techniques consider only a single measured variable at a time, a univariate approach. But when the measured... 

Figure 21.9 provides a general comparison of univariate and multivariate SPC techniques (Alt et al., 1998). When two variables, xi and X2, are monitored individually, the two sets of control limits define a rectangular region, as shown in Fig. 21.9. In analogy with Example 21.5, the multivariate control limits define the dark, ellipsoidal region that represents in-control behavior. Figure 21.9 demonstrates that the application of univariate SPC techniques to correlated multivariate data can result in two types of misclassification false alarms and out-of-control conditions that are not detected. The latter type of misclassification occurred at sample 8 for the two Shewhart charts in Fig. 21.8.

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