  Sensitivity analysis (SA) is an important aspect of process automation. It
often aims to identify the process inputs that influence the process output's
variance significantly. Existing SA approaches typically consider the
input-output relationship as a black-box and conduct extensive random sampling
from the actual process or its high-fidelity simulation model to identify the
influential inputs. In this paper, an alternate, novel approach is proposed
using a sparse polynomial chaos expansion-based model for a class of
input-output relationships represented as directed acyclic networks. The model
exploits the relationship structure by recursively relating a network node to
its direct predecessors to trace the output variance back to the inputs. It,
thereby, estimates the Sobol indices, which measure the influence of each input
on the output variance, accurately and efficiently. Theoretical analysis
establishes the validity of the model as the prediction of the network output
converges in probability to the true output under certain regularity
conditions. Empirical evaluation on two manufacturing processes shows that the
model estimates the Sobol indices accurately with far fewer observations than a
state-of-the-art Monte Carlo sampling method.
