Bivariate Analysis of Incomplete Degradation Observations Based on Inverse Gaussian Processes and Copulas

Modern engineering systems are generally composed of multicomponents and are characterized as multifunctional. Condition monitoring and health management of these systems often confronts the difficulty of degradation analysis with multiple performance characteristics. Degradation observations generally exhibit an s-dependent nature and sometimes experience incomplete measurements. These issues necessitate investigating multiple s-dependent degradations analysis with incomplete observations. In this paper, a new type of bivariate degradation model based on inverse Gaussian processes and copulas is proposed. A two-stage Bayesian method is introduced to implement parameter estimation for the bivariate degradation model by treating the degradation processes and copula function separately. Degradation inferences for missing observation points, and for future observation points are investigated. A simulation study is presented to study the effectiveness of the dependence modeling and degradation inference of the proposed method. For demonstration, a bivariate degradation analysis of positioning accuracy and output power of heavy machine tools subject to incomplete measurements is provided.