2 research outputs found
The transformed gamma process for degradation phenomena in presence of unexplained forms of unit-to-unit variability
The transformed gamma process is a suitable model for degradation phenomena
where damages accumulate gradually over time in a sequence of tiny increments.
Attractiveness of the transformed gamma process mainly lies in the fact
that it provides a relatively easy way for dealing with phenomena in which the
degradation increments over disjoint time intervals are not independent. The
transformed gamma process is also a very flexible model. In fact, it is indexed
by 2 functions, the âage functionâ and the âstate function,â whose mathematical
form can be chosen ad hoc for modeling the dependence of the future degradation
increment of a unit on its current age and state, respectively. In this
paper, the transformed gamma process is adopted to describe the degradation
paths of degrading units in the presence of an unexplained form of unitâtoâunit
variability. The degradation path of each unit is described via a transformed
gamma process. Heterogeneity among paths of different units is accounted for
by assuming that the scale parameters of the age and state functions vary randomly
from unit to unit. Under these assumptions, a quite mathematically tractable
model is obtained. The main properties of the proposed model are
discussed, and inferential procedures based on the maximum likelihood criterion
are implemented. A simple test is presented to check the goodness of fit
of the proposed model. Three applicative examples, based on real degradation
data, are developed