A hybrid approach for modeling degradation processes with a degradation free stage

The delay time model is typically used to optimize an inspection scheme. A challenging issue with this model is that the exact defect initiation time and failure time are often not available. However, it is possible to build a delay time model for the situation where the degradation process has a degradation free stage. In this paper, we develop a hybrid approach to model a delay time model based on a set of incomplete data. The degradation data considered in this paper are obtained through destructive tests. The sample size is small and information is incomplete. A two-step modeling approach is proposed to model the data. In the first step we estimate the degradation initiation time distribution using mean pseudo-initiation time and implicit censoring information; and in the second stage we estimate the failure time distribution based on a non-homogeneous normal process model with a power-law mean value function. Application of the resulting model is also discussed.