In the article the set of models of quality evaluation of the lifecycle of the cyberphysical systems, which are the basis for building and evolution of the Industry 4.0 is presented. The model is the next development of structure of quality indicators of the lifecycle of difficult objects and defines the unified structure for quantitative assessment of quality of systems, which are parts of the System of systems, throughout whole its lifecycle, which is defined by dual-V process model. In the study the set-theoretical definition of the quality model of the lifecycle of the System of systems is generalized. Based on the definitions and reference model, which are given in family of standards ISO 25000, the hierarchical structure of the model of quality indicators and math model of quality evaluation is built. The generalized expressions for quantitative assessment of complex quality indicators of the lifecycles and phases of the cyberphysical system as a part of the System of systems are offered. The expressions for quantitation of quality indicators of the processes of validation and confirmation according to the model of inner and outer quality and quality during usage are offered. The decomposition of the process V-model of quality of the generalized process of the lifecycle is done and the analysis of the phases of the processes as objects of the lowest level is executed. The expressions for quantitation of complex quality indicators of the lifecycle and the process phases are offered. The graphical visualization of the mathematical model of quality evaluation of the lifecycle of the cyberphysical systems is given, integration phases and validation (CQM verification and validation), phases of development and determination (CQM lowest configuration items), phases of development and determination (CQM processes). The mathematical model of quality evaluation of the lifecycle, which is received as a result of the research, gives the possibility of automated building of the general tree of quality of the System of systems and subtrees of quality of the explored cyberphysical system and its subsystems.