  In the manufacturing industry, it is often necessary to repeat expensive
operational testing of machine in order to identify the range of input
conditions under which the machine operates properly. Since it is often
difficult to accurately control the input conditions during the actual usage of
the machine, there is a need to guarantee the performance of the machine after
properly incorporating the possible variation in input conditions. In this
paper, we formulate this practical manufacturing scenario as an Input Uncertain
Reliable Level Set Estimation (IU-rLSE) problem, and provide an efficient
algorithm for solving it. The goal of IU-rLSE is to identify the input range in
which the outputs smaller/greater than a desired threshold can be obtained with
high probability when the input uncertainty is properly taken into
consideration. We propose an active learning method to solve the IU-rLSE
problem efficiently, theoretically analyze its accuracy and convergence, and
illustrate its empirical performance through numerical experiments on
artificial and real data.
