Monitoring charts

Fig. 3 shows g and 7 monitoring charts (dotted line 99% confidence limit)... 

Vendor reports, field analysis sheets, monitoring charts, in-house software program results and printouts, laboratory results. 

Simple graphical procedures [monitoring charts) are used to emulate hypothesis testing. 

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. 

Moving Average Monitoring Charts for Individual Measurements... 

The effects of autocorrelation on monitoring charts have also been reported by other researchers for Shewhart [186] and CUSUM [343, 6] charts. Modification of the control limits of monitoring charts by assuming that the process can be represented by an autoregressive time series model (see Section 4.4 for terminology) of order 1 or 2, and use of recursive Kalman filter techniques for eliminating autocorrelation from process data have also been proposed... 

Figure 2.5. CUSUM monitoring charts of exit temperature residuals (a) Level (mean), (b) Spread.

If the process is out-of-control, the next step is to find the source cause of the deviation (fault diagnosis) and then to remedy the situation. Fault diagnosis can be conducted by associating process behavior patterns to specific faults or by relating the process variables that have significant deviations from their expected values to various equipment that can cause such deviations as discussed in Chapter 7. If the latter approach is used, univariate charts provide readily the information about process variables with significant deviation. Since multivariate monitoring charts summarize the information from many process variables, the variables that inflate... 

Multivariate SPM methods with PCs can employ various types of monitoring charts. If only a few PCs can describe the process behavior in a satisfactory manner, biplots could be used as visual aids that are easy to interpret. Such biplots can be generated by projecting the data to two dimensional surfaces as PC versus PC2, PC versus SPE, and PC2-SPE as illustrated in Figure 5.1. 

Multivariate monitoring charts based on Hotelling s statistic (T ) and squared prediction errors SPEx and SPEy) are constructed using the PLS models. Hotelling s statistic for a new independent t vector is [298]... 

Moving-window PCA (MWPCA) has been proposed to monitor time-varying processes where both the PCA model and the statistical confidence intervals of the monitoring charts are adapted [316]. MWPCA provides recursive adaptation within the moving window to adapt the mean and variance of process variables, the correlation matrix, and the PCA model by recomputing the decomposition. MWPCA is compared to recursive... 

FIGURE 7.2 NIRS calibration validation and monitoring chart. 

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