Sharif University of Technology Scientia Iranica 1026-3098 32 8 2025 03 01 Unit Nadarajah and Haghighi distribution: Properties and applications in quality control 24029 10.24200/sci.2021.57302.5167 EN Ismail Shah Department of Statistics, Quaid-i-Azam University, Islamabad 45320, Pakistan. Brikhna Iqbal Department of Statistics, Quaid-i-Azam University, Islamabad 45320, Pakistan. Muhammad Farhan Akram Department of Statistics, Quaid-i-Azam University, Islamabad 45320, Pakistan. Sajid Ali Department of Statistics, Quaid-i-Azam University, Islamabad 45320, Pakistan. Sanku Dey Department of Statistics, St. Anthony's College, Shillong, India. Journal Article 2020 12 08 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, Cramer-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. https://scientiairanica.sharif.edu/article_24029_f9fc29138b61b3113be946d545d88b08.pdf