Weibull distribution is one of the most widely applied statistical distributions in various fields, especially in reliability and lifetime analysis. It has monotonically increasing, monotonically decreasing, and constant hazard rate; these however, partly limits its applications. This limitation undoubtedly inspired researchers to develop generalized Weibull distribution that can exhibit unimodal or bathtub hazard rate. In this article, a new family of continuous distributions based on the Weibull random variable called the Reflected Kumaraswamy Weibull-X {Exponential} family of distributions was introduced. General statistical properties of the new family were established and discussed, general expressions for the ordinary and incomplete moments, the generating function, quantile function, and order statistics were also provided. The maximum likelihood method of estimation was used to estimate the model parameters. In addition, the asymptotic confidence intervals for the parameters were derived from the Fisher information matrix. Real-life application to three datasets were provided and comparison was made with respect to some existing families of distributions in the literature. [ABSTRACT FROM AUTHOR]