Non-response adjusted mean estimation using tool wear and torque data in predictive maintenance systems

The study provides a hybrid log-exponential estimator for estimating the finite population mean under non-response, which incorporates auxiliary information and sample size efficiently within a coherent and mathematically structured framework. Unlike traditional ratio, exponential, and logarithmic estimators, the suggested estimator combines logarithmic and exponential transformations into a single functional form, which improves flexibility and stability under changing sampling conditions. Theoretical properties, such as bias and mean squared error are derived using first-order Taylor series approximation, and optimal conditions are obtained by minimizing mean squared error, providing a clear justification for the estimator's efficiency gains. In particular, the inclusion of the sample size parameter contributes to variance stabilization and improved performance in finite samples. To ensure methodological consistency, both theoretical research and simulation design assume a Missing Completely at Random mechanism, with missing data handled via K-nearest neighbour imputation. The suggested estimator's performance is assessed using comprehensive Monte Carlo simulations and empirical tests on a variety of real-world datasets, including radiation data, agricultural labour data, and tool wear and torque data from predictive maintenance systems. The results show that the proposed estimator consistently achieves lower MSE and higher percentage relative efficiency than existing estimators, with improvements frequently exceeding 50%, especially under moderate to high non-response rates and strong correlation structures, making it a reliable and practical alternative for finite population mean estimation in real-world applications.