[under construction]
Things to consider:
The usual assumptions for standard SPC charts apply (independent observations; identically distributed)
Is there cross-correlation between streams?
StatSoft Online Help - Multiple Stream Processes
Book: "Innovative Control Charting: Practical Spc Solutions for Today's Manufacturing Environment" (on Amazon.com)
ISBN-10: 0873893859
ISBN-13: 978-0873893855
Group Control Charts (GCC)
proposed by Boyd (1950)
described in Burr (1976), Pyzdek (1992, Chapter 21) and Montgomery (1997, Section 8.3)
Article: Statistical Process Control of Multiple Stream Processes
Authors - Mortell, Robert R.; Runger, George C.
ASQ QICID: 11395
"A model that allows correlation between the streams is described and a simple control strategy is recommended. Performance comparisons are provided."
Article: SPC of Multiple Stream Processes - a chart for enhanced detection of shifts in one stream
Based on a Residuals Group Control Chart
For an example of a univariate residuals control chart, see Example - SPC on Regression Residuals