00454 0cb01177d79802c7554a961014c51c

A Graphical Aid for Analyzing Autocorrelated Dynamics! Systems 459

Outliers will tend to "permanently" shift or rotate any pattem while mis-recorded data will tend to plot off the pattem and then back on the pattem.

The Varian Sputterer SPC Data Set

The author has used the univariate phase map movie to examine some new data sets. Two of them in particular will be presented here: the Varian SPC data set and the Sonic Log data set.

In the first case, the author was examining some industrial process control data. The Varian data consists of averages of nine measurements madę on a sputterer process under a statistical process control program. As is typical under such programs, the process is allowed to drift within the control limits until a "signal" of an out of control condition occurs. Such a signal may be due to process changes such as the target degrading over time. In such a case, the operator may take control of the system for a number of runs until maintenance can Schedule the downtime for repairs.

A time order plot of the Varian SPC data is presented in Figurę 20. In addition, plots of the autocorrelations and partial autocorrelations are presented in Figurę 21. These plots suggest that this data is not strongly autocorrelated. As was true for the plant yield data, nonę of the plots suggest that there is any unusual behavior to be found in the data set.

When examined with the univariate phase map movie however, the movie changed from appearing to be nearly random the majority of the time to having a very strong pattem for between 15 to 20 observations. The pattem then disappears completely only to reappear later in the data set. The pattems that appear are strongly suggestive of traditional autoregressive models e.g., and AR(2) with negative coefficients or AR(3) with positive coefficients, see Figurę 22 below.

A morę typical extract from the movie is shown in Figurę 23 below. In the typical extract, there are no readily noticeable pattems to be seen. It should be remarked that in this particular case, the two time periods with the strong pattems are immediately obvious to anyone watching the movie.

In addition, the two segments of the process control data that show strong autocorrelation pattems have suggested pattems that correspond well with how the eąuipment is actually operated as the target begins to wear out. Although the operators normally don't make freąuent process adjustments, when the process begins to drift due to the wear-out of the target, they look at the last two or three data points and make their process adjustments. After the target is replaced the process is operated normally.