Via the literature of statistical studies, many continuous distributions have been presented that can help in many scientific and applied areas. on the other hand, variant properties of those distributions are derived and studied. However, there is a need to obtain highly flexible distributions to match different types of real data. For that purpose, new families of distributions have been established to have the best flexibility when dealing with variant kinds of data. In this study, a proposed family of continuous distributions is presented by fitting the Exponentiated Weibull distribution with the Exponentiated Chen G-family to obtain the new distribution namely the Exponentiated Chen Exponentiated Weibull distribution. The cumulative distribution function (CDF) and the probability density function (PDF) have been derived. Also, some important functions such as the characteristic function, the quantile, the skewness, and kurtosis have been derived. Using real engineering data and data generated by the statistical software R and comparing the results with eight competing distributions, the suggested distribution showed highly flexible, efficient, and suitable for different real data sets using some statistical criteria such as AIC, AICC, BIC, and HQIC and more.