 This paper introduces a new family of distributions called the Marshall-Alcon Weibull-Generated Family, which can capture high degree of skewness and kurtosis and enhance the goodness of fit in empirical distribution. The proposed family is a combination of Marshall-Alcon Transformation and the Weibull-Generated Family. Two special members of this family are investigated, and their mathematical properties are derived. The estimation for the parameters is obtained via maximum likelihood method, and simulation studies are conducted to examine the performance of the estimators. Additionally, a log Marshall-Alcon Weibull-Weibull Regression Model for censored data is proposed based on this family. Finally, COVID-19 data and three lifetime data sets are used to demonstrate the importance of this family of distributions in providing a better fit compared to other competitive distributions. This article was authored by Hadeel Klakatawi, Dala Al Salami, Mervat ABD-Eelul, and others.