The priority of the quality improving  of machine parts, providing their operational characteristics and specified reliability parameters during the design of oil and gas and mechenical engineering equipment was established. The dominance of the criterion of technological inheritability for all stages of the Life Cycle of a Part was noted. The current state of providing of the quality parameters of a part and its operational characteristics by means of the technological inheritabilty was analyzed. Algorithms for technological providing of quality parameters, operational characteristics and reliability indicators of parts are considered. Approaches for estimation of the degree of material degradation, worked-out and anticipated (residual) part lifetime were described. Object, subject and research tasks were installed. The deformation and energy criteria for evaluation of degree of material damageability  are presented. The specificity of SADT-technology for the analysis and synthesis of the technological processes is described and the advantages, disadvantages, scope of its application are noted. A systematic approach  for the joint using of continuum media mechanics, continuous damage mechanics and fracture mechanics is proposed. During the study of the process of metal plastic molding in a certain focus of deformation the properties of the surface layer are considered as a the result of this molding. And the process  of part exploitation are considered as the continuing the change of these properties. That approach allows to use the parameters of the deformation mechanics as the degree of shear deformation  and the degree of exhaustion of the plasticity reserve  for the analysis of physical phenomena. The Life Cycle of a Part is analyzed as an integrated process of exhaustion of the metal plasticity stock under the influence of the specified load programs in according to the technological inheritability of its properties. An advanced structural model of the Life Cycle of a Part by means of the technological inheritability mechanics is offered.