Abstract: Practical Engineering situations are very often uncertain in a number of ways. Randomness and fuzziness are two types of uncertainty. The first type of uncertainty is described by stochastic models. The second type of uncertainty is solved by the theory of fuzzy sets. Although the theory of fuzzy sets is relatively new, the calculus of fuzzy sets is well developed with various applications in engineering. The fuzzy sets theory can make it possible to study complex and ill - defined system which include uncertainties caused by fuzziness or vagueness. In this work, the reliability assessment of process equipment was studied by using the theory of fuzzy sets such as fuzzy synthetic evaluation and extrama of fuzzy function. The research results were successfully used in engineering practice.