How to Faster Test a Device for Different Combinations of Parameters

Authors

Francisco Zapata, The University of Texas at El PasoFollow
Luis C. Gutierrez, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

8-2013

Comments

Technical Report: UTEP-CS-13-49

To appear in Journal of Uncertain Systems, 2014, Vol. 8.

Abstract

A device has to function properly under all possible conditions: e.g., for all temperatures within a given range, for all possible humidity values within a given range, etc. Ideally, it would be nice to be able to test a device for all possible combinations of these parameters, but the number of such combinations is often so huge that such an exhaustive testing is not possible. Instead, it is reasonable to check the device for all possible values of each parameter, for each possible pairs of values of two parameters, and, in general, for all possible combinations of values of k parameters for some k. For n parameters, a straightforward testing design with this property contains O(n^k) * N^k experiments, where N is the number of tested values of each parameter. We show that, by using a more sophisticated testing design, we can decrease the number of experiments to a much smaller number (log(n))^k-1 * N^k.