  The efficiency of an experimental design is ultimately measured in terms of
time and resources needed for the experiment. Optimal sequential (multi-stage)
design is studied in the situation where each stage involves a fixed cost. The
problem is motivated by switching measurements on superconducting Josephson
junctions. In this quantum mechanical experiment, the sequences of current
pulses are applied to the Josephson junction sample and a binary response
indicating the presence or the absence of a voltage response is measured. The
binary response can be modeled by a generalized linear model with the
complementary log-log link function. The other models considered are the logit
model and the probit model. For these three models, the approximately optimal
sample size for the next stage as a function of the current Fisher information
and the stage cost is determined. The cost-efficiency of the proposed design is
demonstrated in simulations based on real data from switching measurements. The
results can be directly applied to switching measurements and they may lead to
substantial savings in the time needed for the experiment.
