Predictive Quality Control Charts for Variables Results - Prediction Tab

Select the Prediction tab of the Predictive Quality Control Charts for Variables Results dialog box to access options to study in detail any autocorrelations and periodic recurrent patterns in the chart statistics (e.g., means, ranges) over the samples in the control charts. As described in the Introductory Overview, it is generally assumed in quality control charting that the consecutive sample means and ranges are independent; in practice, however, this is often not the case.

Individual charts

Select this check box to display the individual control charts for each variable in the analysis.

Autocorrelations

Select this check box to compute (when you click the Summary button) the autocorrelation functions for the sample statistics for all variables and charts (see also the Time Series module documentation, in particular Time Series Analysis - Autocorrelations). In general, large autocorrelations with a particular lag indicate that consecutive sample points (e.g., means or ranges) are not independent but correlated. For example, if the autocorrelation for a lag 1 is sizeable (significantly different from 0), that means that consecutive or adjacent sample measurements are more similar to each other than what would be expected by chance (assuming independence). This could indicate slow machine wear or other systematically changing conditions that affect sample measurements that are taken close to each other (in time) in a similar manner.

Note: these statistics are computed based on the sample statistics (e.g., means and ranges, not for the raw data) for all variables selected for the analysis. Use the Number of lags edit field to set the maximum number of lags for which to compute the autocorrelations (the program will compute autocorrelations to a lag of at least 10, regardless of the setting of the Number of lags parameter).

Cross-correlations

Select this check box to compute the (lagged) cross-correlation functions for all predictor variables and all chart (dependent) variables (based on the sample statistics, e.g., means, ranges, etc.). Cross-correlations are computed for a lag of -k through +k, where k is the number specified in the Number of lags box (see below). The spreadsheet will contain the cross-correlations and their standard errors. In general, the cross-correlation is the correlation of a series with another series, shifted by a particular number of observations. For details regarding the computations of the cross-correlations and their standard errors refer to Time Series Analysis - Cross-correlations. Correlations that are greater than 2 times their respective standard errors are highlighted in the results spreadsheets.

Note: these statistics are computed based on the sample statistics (e.g., means and ranges, not for the raw data) for all variables selected for the analysis. Use the Number of lags edit field to set the maximum number of lags for which to compute the autocorrelations (the program will compute autocorrelations to a lag of at least 10, regardless of the setting of the Number of lags parameter).

Partial autocorrelations

Select this check box to compute the partial autocorrelation functions for the sample statistics for all variables and charts (see also the documentation for the Time Series module documentation, in particular Time Series Analysis - Partial Autocorrelations). The partial autocorrelation is the correlation of a series with itself, shifted by a particular lag of k observations, and controlling for the correlations for all shifts of 1 through k-1. Hence, these statistics are useful in order to evaluate whether there are autocorrelations at different lags, after controlling for all other autocorrelations (at lower lags), e.g., in order to detect seasonal autocorrelations in the data (if a machine begins to deteriorate every day after a particular number of hours, etc.).

Note: these statistics are computed based on the sample statistics (e.g., means and ranges, not for the raw data) for all variables selected for the analysis. Use the Number of lags edit field to set the maximum number of lags for which to compute the autocorrelations (the program will compute autocorrelations to a lag of at least 10, regardless of the setting of the Number of lags parameter).

Fourier decomposition

Fourier or spectral decomposition analysis is discussed in detail in the documentation for the Time Series module (see Spectral (Fourier) Analysis). In general, these analyses enable you to identify cyclical or recurrent patterns in the data. If this check box is selected, the program will perform spectral analyses based on the sample statistics (e.g., means, ranges) computed for all samples and variables. Use the results to determine whether there are any such patterns in the consecutive "plot points" for the quality control charts.

Number of lags

Specify here the number of lags to be used for 1) computing the autocorrelations and cross-correlation functions, and 2) for fitting neural networks-based models to the consecutive plot points in the charts. For example, if you set this value to 2, the autocorrelations and cross-correlations will be computed for a lag of 1 and 2, and the time series neural network will include lagged predictors for each lag 1 and 2.

Specify neural network prediction

The options in this group box are described below:

Neural network

Select this check box to fit a neural network to the sample statistics for all variables in the analysis; select the Do not save network option button to fit a network to the data without saving it; select the Open network option button to apply a previously saved network to the current data to compute predictions; select the Save network option button to fit a network to the data and save it to a file for future analyses (e.g., for computing forecasts).

In general, the program will find the best time series network for sample statistics for the user-defined Number of lags. Note that a single neural network will be constructed for sample means (X-bar, or X) and sample variability estimates (ranges or standard deviations). Hence, complex interactions and lagged effects between the two (e.g., ranges and means) can be modeled.

After clicking the Summary button, the program will compute (fit) the best neural network for the requested Number of lags, based on the sample statistics (e.g., means, ranges) found in the range of samples as specified in the Fit model from sample and Fit model to sample fields. In other words, the neural network can be fitted to a particular range of samples only, saved, and applied to data as new samples are gathered.

Fit model from sample/Fit model to sample

These options are only applicable when fitting a neural network with lagged indicator variables to the data (see the Fit neural network option description). The neural networks will be fitted from the sample number specified in the Fit model from sample field to the sample number specified in the Fit model to sample next field.

Do not save network

Select this option button to estimate a network from the current data (sample statistics). The best network will then be used to compute predicted values (e.g., means, ranges, etc.), but it will not be saved. Select the Save network option button to save the best network for future use (e.g., to predict values for new data).

Open network

Select this option button to open an existing network file (e.g., previously created via the Save network option). The program will not estimate a new (best) network for the data, but instead will use the selected network (file) to compute predicted values and forecasts. Click the icon next to this option to display a standard file selection dialog where you can select the network file for the current analysis (predictions and forecasting). Note that these files can also be saved via the STATISTICA Neural Networks facilities.

Save network

Select this option button to estimate a network from the current data (sample statistics), and to save that network in a file. Click the icon next to this option to display a standard file selection dialog box, where you can select the file to save. Note that these files can also be created via the STATISTICA Neural Networks facilities.