Minimizing scatter in experimental data sets

Thermal transient data collected to characterize packaged semiconductor devices is often acquired from a number of individual samples that then must be averaged together. Yet each individual transient curve has a relatively large experimental uncertainty which is usually a combination of unmeasurable initial transient thermal response (related to electrical transients which cannot be separated from the thermal signal), coupled with mounting variability not fairly attributable to the device itself being tested (but is rather due to differences in test board characteristics, solder thickness variation, etc.). When a limited range of the data is believed to accurately represent device-only dependence, a useful, simple, yet rigorous method has been developed to allow the analyst to minimize the scatter in the data set, while preserving the average value in the specified range. Application of this method to actual data is presented for purposes of illustration, and additional implications in the use of the method are discussed. Although this method was developed and is applied here in the context of thermal transient characterization, it is universal in potential application; the underlying mathematical "theorem" is completely general.