"Maximum Likelihood Estimation (MLE): Theory, Practical Calculations, and Applications in Textile Spinning"

This paper provides a comprehensive review of Maximum Likelihood Estimation (MLE), covering its theoretical foundations, derivation of key formulas, and practical calculation examples. It highlights R. A. Fisher’s seminal contributions, including Fisher information, sufficiency, efficiency, and asymptotic properties. Practical examples using normal and exponential distributions illustrate the mechanics of MLE. The paper then applies MLE to the textile spinning industry, showing how it can improve quality control, optimize machine settings, and enhance reliability. By combining theory with industrial applications, the article serves as a reference for researchers and practitioners seeking to leverage MLE for data-driven decision-making.