Potentiality of 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 is used as a model of damage accumulation with a time-dependent probability density distribution. 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 non-stationary function of time. The parameters of damage distribution function can be determined from the data of non-destructive testing using the maximum likelihood method or the method of moments. The potentiality and features of the proposed method 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 various 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 most strongly affects the damage probability. The main difference between the proposed methodology and other schemes and methods of 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 given service interval of technical objects. The proposed technique can be adapted for other types of damage, in particular for processes of long-term damage with the growth of corrosion, corrosion-fatigue and fatigue cracks.

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