  Accelerated destructive degradation tests (ADDT) are widely used in industry
to evaluate materials' long term properties. Even though there has been
tremendous statistical research in nonparametric methods, the current
industrial practice is still to use application-specific parametric models to
describe ADDT data. The challenge of using a nonparametric approach comes from
the need to retain the physical meaning of degradation mechanisms and also
perform extrapolation for predictions at the use condition. Motivated by this
challenge, we propose a semi-parametric model to describe ADDT data. We use
monotonic B-splines to model the degradation path, which not only provides
flexible models with few assumptions, but also retains the physical meaning of
degradation mechanisms (e.g., the degradation path is monotonically
decreasing). Parametric models, such as the Arrhenius model, are used for
modeling the relationship between the degradation and accelerating variable,
allowing for extrapolation to the use conditions. We develop an efficient
procedure to estimate model parameters. We also use simulation to validate the
developed procedures and demonstrate the robustness of the semi-parametric
model under model misspecification. Finally, the proposed method is illustrated
by multiple industrial applications.
