A hierarchical modeling approach for degradation data with mixed-type covariates and latent heterogeneity

Successful modeling of degradation data with covariates is essential for accurate reliability assessment of highly reliable product units. Due to the influences of different types of covariates, such as the external factors (e.g. accelerated operating conditions) and the internal factors (e.g. material microstructure characteristics), as well as latent heterogeneity due to the influences of the unobserved or unknown factors shared within each product unit, the degradation measurements of product units are highly heterogeneous over time. Many of existing degradation models often failed to simultaneously consider the influences of (i) both external accelerated conditions and internal material information, (ii) latent heterogeneity, and (iii) multiple material types. In this work, we propose a generic degradation modeling approach with mixed-type (e.g. both scalar and functional) covariates and latent heterogeneity to account for both the influences of observed internal and external factors as well as their interaction, and the influences of unobserved factors. Effective estimation algorithm is developed under expectation–maximization framework to jointly quantify the influences of mixed-type covariates and individual latent heterogeneity. The proposed algorithms further enables closed-form updating of model parameters at each iteration to ensure the estimation convenience. A real case study is provided to illustrate the proposed modeling approach and to demonstrate its effectiveness from both model prediction and interpretation perspectives.