A pseudo-likelihood estimation method for nonhomogeneous gamma process model with random effects

We study a semiparametric pseudo-likelihood inference for nonhomogeneous Gamma process with random effects for degradation data. The setting for degradation data, is one in which n indepemdent subjects, each with a nonhomogeneous Gamma process, are observed at possible different times. The random effects are used to represent heterogeneity of degradation paths. To obtain the maximum pseudo-likelihood estimator, we use the Pool Adjacent Violators Algorithm. We study the asymptotic properties for this estimator. A simulation study is conducted to validate the method and its application is illustrated by using degradation data of a civil engineering structure to estimate its reliability.