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 situa-tions, 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 pa-rameters are then estimated and the effect of covariate is analyzed.