Sampling inspection for the evaluation of time-dependent reliability of deteriorating systems under imperfect defect detection

The paper presents a sampling-inspection strategy for the evaluation of time-dependent reliability of deteriorating systems, where the deterioration is assumed to initiate at random times and at random locations. After initiation, defects are weakening the system's resistance. The system becomes unacceptable when at least one defect reaches a critical depth. The defects are assumed to initiate at random times modeled as event times of a non-homogeneous Poisson process (NHPP) and to develop according to a non-decreasing time-dependent gamma process. The intensity rate of the NHPP is assumed to be a combination of a known time-dependent shape function and an unknown proportionality constant. When sampling inspection (i.e. inspection of a selected subregion of the system) results in a number of defect initiations, Bayes’ theorem can be used to update prior beliefs about the proportionality constant of the NHPP intensity rate to the posterior distribution. On the basis of a time- and space-dependent Poisson process for the defect initiation, an adaptive Bayesian model for sampling inspection is developed to determine the predictive probability distribution of the time to failure. A potential application is, for instance, the inspection of a large vessel or pipeline suffering pitting/localized corrosion in the oil industry. The possibility of imperfect defect detection is also incorporated in the model.