Optimal experimental design for the calibration of irreversible, binary-state sensors

Many temperature, pressure, and gas sensors behave as irreversible switches. Once a threshold magnitude of the stimulus is reached, the sensor exhibits an irreversible change in some property. The hysteresis in the response of such irreversible, binary-state sensors (IBSS’s) is often desirable. For example, a color-switching temperature IBSS may indicate whether or not the temperature in a dishwasher exceeded a certain value required for sanitization.

The calibration of a new class of IBSS’s constitutes finding the threshold stimulus that causes the sensor to switch states. We present a dynamic programming method to obtain a policy tree giving the optimal, adaptive experimental design strategy for IBSS calibration. Specifically, we present an algorithm to adaptively determine the sequence of stimuli to expose to the IBSS to find the threshold stimulus with the minimal number of experiments, when multiple IBSS's are at our disposal.