In this paper, borrowing the intuition in Rao et al. (2004), we introduce a CUMULATIVE version of the inaccuracy measure (CIM). Also we obtain interesting and applicable properties of CIM for different cases based on the residual, past and inter-val lifetime random variables. Relying on various applications of stochastic classes in reliability and information theory fields, we study new classes of the lifetime in terms of the CIM along with their relations with other famous aging classes. Furthermore, some characterization results are obtained under the proportional reversed hazard rate model. Finally, considering that the time t changes in the range (t1; t2), an extension of the CIM, called the interval CUMULATIVE residual (past) inaccuracy (ICR(P)I), is de-rived. We investigate the ICRI’ s relation with its analogous version based on Shannon entropy.