Module 1: Introduction to Experimental Techniques
  Lecture 5: Design of experiments
 

Clearly an optimum exists. The optimum time duration is found using the following criterion. If is the variance in the data of , that in will be

where

Hence, minimizing is equivalent to maximizing the quantity with respect to experimental test time and so

This can be simplified to the integral equation

and the test duration can be found by a root-finding procedure.