Segmental Viterbi estimation using transition constraints for covariate-dependent hidden semi-Markov degradation models with right censoring

Accelerated degradation tests often end before late degradation states are observed, weakening multistage first passage prediction under right censoring. Fixed segmentations treat persistent threshold crossings as complete paths, whereas unconstrained sequence estimators can admit unsupported transitions. We formulate segmental Viterbi estimation for a four-state covariate-dependent hidden semi-Markov model (HSMM) that converts persistent crossing intervals and censoring exclusions into transition constraints and propagates the fitted state and residence age into ordered reliability predictions. Evaluation used 300 independent simulations (100 at each dropout level of 20%, 50%, and 80%), 19 laser diode folds that withheld one unit, four folds that withheld one current stratum, and a public 77-cell battery extension. Survival-terminal simulation continuous ranked probability scores were 16.94, 17.68, and 18.39 h. Fixed and optimized segmentation yielded scores of 45.51 and 46.10 h under unit holdout. In the battery extension with training histories limited to 1000 cycles, survival-terminal scoring reduced the score from 166.47 to 105.01 cycles relative to completed-terminal scoring, with the comparison against accelerated failure-time prediction depending on duration regularization. The results distinguish the effects of operational constraints, state-age filtering and terminal censoring treatment, with limitations from sparse late events and extrapolation.