Some problems in engineering and applied science require building a mo
del of a newly observed phenomenon and extrapolating that model beyond
the regime in which data has been gathered. A simple example is accel
erated testing, in which devices are stressed at extreme conditions fo
r a short time-for example, months-in order to build a model of how th
ey behave over decades under moderate stress. In such a situation, cho
osing the wrong model can cause costly errors in estimating reliabilit
y By integrating physical and statistical thinking, we have developed
a strategy for identifying certain kinds of modeling errors. In this p
aper, we give one example in which we have experimental indications of
such an error that would not have been identified without our new app
roach. We also list some examples that gave no such indications.