‎In this paper‎, ‎first‎, ‎we investigate probability density function and the failure rate function of some families of exponential distributions‎. ‎Then we present their features such as expectation‎, ‎variance‎, ‎moments and maximum likelihood estimation and we identify the most flexible distributions according to the figure of probability density function and the failure rate function and finally we offer practical examples of them‎.