Prefix Treatment and Bayesian Pooling for Early-Stage Lifetime Prediction from Degradation Data

Abstract

Early-stage lifetime prediction depends not only on model form but also on how the observed prefix of degradation data is converted into a forecast. That second issue has received far less direct attention in controlled comparisons. This paper examines the effect of prefix treatment using the GaAs laser degradation data of Meeker and Escobar. A fixed early-stage protocol is imposed in which only the first six measurements of each device are available for prediction, while the complete trajectories are retained as a common full-history reference. Under a common power-law pseudo-lifetime map, five estimators are compared: an early global fit, a window-median estimator, two prefix-emphasis rules, and a partial-pooling Bayesian estimator. The comparison isolates a specific research gap by holding the lifetime map fixed and varying only the way the same observation prefix is aggregated or regularized. The results show that heuristic emphasis on the earliest local windows systematically shifts predictions upward and substantially increases absolute error, whereas Bayesian pooling provides the most stable predictions across devices and across tested prefix lengths. The contribution is therefore methodological: the paper identifies prefix treatment as a first-order component of early-stage lifetime prediction and shows that, for this dataset, transparent pooling is more defensible than heuristic weighting.