The Gamma process and its generalizations for describing age- and/or state dependent degradation phenomena

연사: Gianpaolo Pulcini (Istituto Motori, CNR, Napoli, Italy)
일시: 2013년 4월 11일(목) 오후 1시
장소: 종합과학관 B103호

The Gamma process is a widely used model for describing non-decreasing deterioration processes over time when the probability distribution of degradation growth during a future time interval depends on the current age and not on the current state of the unit (property of “independence of increments”).
However, the Gamma process is not a proper choice when there is empirical evidence that the variance-to-mean ratio of the degradation process varies with time, because the Gamma process implies a constant variance-to-mean ratio. In this case, a generalization of the non-stationary Gamma process, which is a time discretization of the extended Gamma process, can be used, allowing one to describe time-dependent degradation phenomena whose variance varies with time  , not necessarily in proportion to the mean.
In many cases, however, the distribution of the degradation growth during a future time interval depends on the current state of the unit (i.e., on the current degradation level), and not on its age. In these cases, a proper choice can the inverse Gamma processes, which is derived by assuming that the “inverse” time process is Gamma.
Finally, when the degradation growth depends both on the current age and on the current state of the unit, the Transformed Gamma process, which is obtained by a non linear transformation of the Gamma process and include as special case the Gamma process, can result in a suitable choice.
This presentation aims to present and briefly discuss both the well known Gamma process and these recently proposed generalizations of the Gamma process.