  This paper proposes a new methodology to predict and update the residual
useful lifetime of a system using a sequence of degradation images. The
methodology integrates tensor linear algebra with traditional location-scale
regression widely used in reliability and prognosis. To address the high
dimensionality challenge, the degradation image streams are first projected to
a low-dimensional tensor subspace that is able to preserve their information.
Next, the projected image tensors are regressed against time-to-failure via
penalized location-scale tensor regression. The coefficient tensor is then
decomposed using CANDECOMP/PARAFAC (CP) and Tucker decompositions, which
enables parameter estimation in a high-dimensional setting. Two optimization
algorithms with a global convergence property are developed for model
estimation. The effectiveness of our models is validated using a simulated
dataset and infrared degradation image streams from a rotating machinery.
