Potentiality of the Probabilistic Risk Analysis of Damaged Technical Objects Using the Gamma Model

A technique for probabilistic risk analysis of technical objects with accumulated irreversible damage is proposed. Damage is considered as a stochastic irreversible cumulative process with an absorbing boundary. The gamma process with a time-dependent probability density distribution is used as a damage accumulation model. The probability distribution function of life before failure and the probability (risk) of failure are determined by integrating the probability density of accumulated damage over the risk area. The damage accumulation rate is considered as a nonstationary function of time. The parameters of the damage distribution function can be determined from the data of nondestructive testing using the maximum likelihood method or the method of moments. The features and potentiality of the method proposed are exemplified in the risk analysis of the corrosion damage of critically important technical objects, e.g., offshore pipelines. The results of calculating the pipeline failure probability at different shape parameters and the scale parameter of the damage distribution function are presented. It is shown that the shape parameter, which directly depends on the time of damage accumulation, affects the damage probability most strongly. The main difference between the proposed technique and other schemes and methods of the damage risk analysis is the explicit time dependence of the gamma model parameters, which makes it possible to predict the probability of failure for a specified interval of service of technical objects. The technique proposed can be adapted to damage of other types, in particular, long-term damage with the growth of corrosion, corrosion-fatigue, and fatigue cracks.