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.
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