In practice, the data related to rates and proportion may have excess of ones wherein the beta distribution does not fit well. To deal with the inflation of ones, this article introduces unit Nadarajah and Haghighi distribution. Besides deriving statistical properties of the proposed distribution, several estimation methods are discussed. In particular, maximum likelihood estimation, least squares estimation, weighted least squares estimation, maximum product of spacing, minimum spacing absolute distance estimation, minimum spacing absolute log-distance estimation, Cramér-Von-Mises, Anderson-Darling method and right-tail Anderson-Darling method are considered. Using real data sets, it is shown that the new distribution outperforms some well-known existing distributions. Furthermore, the application of the proposed distribution in quality control is also discussed. A control chart using unit Nadarajah and Haghighi distribution is constructed and its performance is evaluated using the average run length."