The problem of statistical inference of Kumaraswamy distribution (KD) based on a progressive first-failure censoring scheme (PFFCS) is discussed in this article. The population parameters as well as the reliability and hazard rate functions are estimated by using the maximum likelihood method for point and interval estimation. Both point and interval-credible estimations of parameters are obtained using the Bayes method. In the Bayes method, we use the Markov chain Monte Carlo (MCMC) technique. The Bayes estimates results are obtained under symmetric and asymmetric loss functions. We also obtained an exact confidence interval (ECI) and an exact joint confidence region (EJCR) of parameters. Real-life data is analyzed for illustrative purposes. By applying Monte Carlo simulation analysis, some comparisons between the different proposed methods are investigated.