The purpose of this paper is to develop a program -target strategy of quality management in Industry 4.0 and formation of cognitive economy based on industrial and manufacturing engineering in the Russian Federation and countries of the EU. Originality of this research consists in the following. Firstly, the authors specify the essence, distinguish and determine the elements of quality in Industry 4.0, offer estimate indicators and use them to perform a polycriterial evaluation of quality in Industry 4.0, and determine and substantiate the sources of its increase in the Russian Federation and countries of the EU. Secondly, the authors study and prove the strong influence of the factors of industrial and manufacturing engineering on successes in formation of cognitive economy in the Russian Federation and countries of the EU and determine the perspectives of optimizing the influence of these factors of in the interests of formation of cognitive economy. Thirdly, the specifics of causal connections of quality management in Industry 4.0 in countries of Western and Eastern Europe are determined, due to which this research has high empirical value, for its allows developing the specific programs of development of Industry 4.0 in countries of Europe in view of their specific features. Fourthly, the issues of quality management in Industry 4.0 and formation of cognitive economy based on industrial and manufacturing engineering are studied consistently, due to which a general program-target strategy for the Russian Federation and countries of the EU is developed.