The basis of reliability engineering is reliability theory. Reliability analysis is critical for developing different alternatives for system improvement during the design, configuration, and tuning stages, which are essential to the efficient operation of a complicated system. This paper deals with the estimation of the reliability of a degradable system with imperfect coverage and uncertain information about system components. The Weibull intuitionistic fuzzy set (WIFS) concept was used to deal with the uncertainties in the data. The knowledge of a trapezoidal intuitionistic fuzzy number (TrIFN) is presented, as well as its arithmetic operations. Trapezoidal intuitionistic fuzzy numbers (TrIFN) are applied to signify the failure rate of system.