A Bayesian Approach for Lifetime Modeling and Prediction with Multi-Type Group-Shared Missing Covariates

In the field of reliability engineering, covariate information shared among product units within a specific group (e.g., a manufacturing batch, an operating region), such as operating conditions and design settings, exerts substantial influence on product lifetime prediction. The covariates shared within each group may be missing due to sensing limitations and data privacy issues. The missing covariates shared within the same group commonly encompass a variety of attribute types, such as discrete types, continuous types, or mixed types. Existing studies have mainly considered single-type missing covariates at the individual level, and they have failed to thoroughly investigate the influence of multi-type group-shared missing covariates. Ignoring the multi-type group-shared missing covariates may result in biased estimates and inaccurate predictions of product lifetime, subsequently leading to suboptimal maintenance decisions with increased costs. To account for the influence of the group-shared missing covariates with different structures, a new flexible lifetime model with multi-type group-shared latent heterogeneity is proposed. We further develop a Bayesian estimation algorithm with data augmentation that jointly quantifies the influence of both observed and multi-type group-shared missing covariates on lifetime prediction. A tripartite method is then developed to examine the existence, identify the correct type, and quantify the influence of group-shared missing covariates. To demonstrate the effectiveness of the proposed approach, a comprehensive simulation study is carried out. A real case study involving tensile testing of molding material units is conducted to validate the proposed approach and demonstrate its practical applicability.