The high availability of technological systems like aerospace, defense, petro-chemistry and automobile, is an important major goal of earlier recent developments in system design technology. In petrochemical industries, pipelines are the principal element of hydrocarbon transport systems. They are crucial for human activities since they serve to transport oil, water, and natural gases from sources to all sites of consumers. A new analytic prognostic model is developed in this paper and applied to three cases of pipes subject to internal pressure, to the effects of corrosion, and to soil loading. This will initiate micro-cracks in the tubes body that can propagate suddenly and lead to failure. The increase of pipes performance, availability, and the reduction of their global mission cost, need to develop a suitable prognostic process. Consequently, a new approach based on analytic laws of degradation is proposed in this paper. From a predefined threshold of degradation D, the Remaining Useful Lifetime (RUL) is estimated from this prognostic model.