Univariate SPM Techniques

Since in most chemical processes each measurement is made only once at each sampling time (no repeated measurements), all univariate monitoring charts will be developed for single observations except for Shewhart charts. 

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Some statistics concepts such as mean, range, and variance, test of hypothesis, and Type I and Type II errors are introduced in Section 2.1. Various univariate SPM techniques are presented in Section 2.2. The critical assumptions in these techniques include independence and identical distribution [iid) of data. The independence assumption is violated if data are autocorrelated. Section 2.3 illustrates the pitfalls of using such SPM techniques with strongly autocorrelated data and outlines SPM techniques for autocorrelated data. Section 2.4 presents the shortcomings of using univariate SPM techniques for multivariate data. 

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... 

Models between groups of variables such as process measurements x xi and quality variables y xi be developed by using various regression techniques. Here, the subscripts indicate the vector dimensions (number of variables). If n samples have been collected for each group of variables, the data matrices are X xm and Y xg- The existence of a model provides the opportunity to predict process or product variables and compare the measured and predicted values. The residuals between the predicted and measured values of the variables can be used to develop various SPM techniques (residuals-based univariate SPM was discussed in Section 2.3.1) and tools for identification of variables that have contributed to the out-of-control signal. 

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