  This paper introduces a popular dimension reduction method, sliced inverse
regression (SIR), into multivariate statistical process monitoring. Provides an
extension of SIR for the single-index model by adopting the idea from partial
least squares (PLS). Our partial sliced inverse regression (PSIR) method has
the merit of incorporating information from both predictors (x) and responses
(y), and it has capability of handling large, nonlinear, or "n<p" dataset. Two
statistics with their corresponding distributions and control limits are given
based on the X-space decomposition of PSIR for the purpose of fault detection
in process monitoring. Simulations showed PSIR outperformed over PLS and SIR
for both linear and nonlinear model.
