  We study sequential cost-efficient design in a situation where each update of
covariates involves a fixed time cost typically considerable compared to a
single measurement time. The problem arises from parameter estimation in
switching measurements on superconducting Josephson junctions which are
components needed in quantum computers and other superconducting electronics.
In switching measurements, a sequence of current pulses is applied to the
junction and a binary voltage response is observed. The measurement requires a
very low temperature that can be kept stable only for a relatively short time,
and therefore it is essential to use an efficient design. We use the dynamic
programming principle from the mathematical theory of optimal control to solve
the optimal update times. Our simulations demonstrate the cost-efficiency
compared to the previously used methods.
