Time-dependent covariates in the Transformed Gamma degradation process

This paper introduces time-dependent covariates in the Transformed Gamma degradation process, a continuous, non decreasing Markovian process recently proposed to describe degradation phenomena with dependent increments. In general, the introduction of time-dependent covariates does not preserve the mathematical and statistical tractability of the Transformed Gamma process. However, in some specific situations, that are identified and discussed in this paper, the tractability properties are preserved. A real case study is considered, that is constituted by the wear process of the cylinder liners of a cargo ship’s diesel engine. The wear process underwent a sudden change on January 2004, when the diesel fuel used until then was changed to a new one with lower sulfur content. The type of fuel is modeled as a single-step time-dependent covariate, a situation where the mathematical tractability of the Transformed Gamma process is retained. The model parameters are then estimated and the effect of covariate is analyzed