Batch processes are ubiquitous and valuable to the chemical, pharmaceutical and semiconductor manufacturing industries. Data from batch processes are naturally arranged in three-way data tables (batch process time by variable by batch number). This is in contrast to continuous processes where the data are arranged as simple two-dimensional tables (process time by variable). However, a complication for process monitoring and fault detection is that batch processing time generally varies resulting in data records of variable length. This is a complication because many multivariate and multi-way data analysis methods require that the data from each batch be of consistent record length. Many strategies have been forwarded for dealing with this “batch data problem” and several are explored in this talk. These include methods for standardizing the record length through various warping strategies (e.g. Correlation Optimized Warping), interpolating to an indicator variable (e.g. extent of reaction or predicted batch time), and batch alignment and truncation.

Methods for describing batches using alternate descriptor variables are considered in more detail. These methods break up the time record by various means (including some of the strategies listed above) and then summarize the process behavior in each segment using descriptor variables. For example, for processes with several steps it is possible to summarize the behavior in each step by calculating variable means, ranges, variances, slope, and step length. The original data is then replaced with the descriptor set resulting in equal length records for each batch, and data that are more amenable to analysis. Advantages to this approach include 1) reduction of data set size, easing analysis from both a computer power and human perspective, 2) descriptor variables often make it easier to pinpoint which variables are contributing to process faults, and 3) descriptors can capture phenomena not easily derived from the original data (for instance, variance during a step). The methods considered in this study are demonstrated on data from a semiconductor etch process.