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

Area of Science:

• Statistics
• Survey Methodology

Background:

• Estimating finite population means is crucial in statistical analysis.
• Non-response in surveys introduces bias and reduces efficiency.
• Existing estimators have limitations in handling non-response and incorporating auxiliary information.

Purpose of the Study:

• To develop a novel hybrid log-exponential estimator for finite population mean estimation under non-response.
• To enhance estimation by incorporating auxiliary information and sample size efficiently.
• To improve flexibility and stability compared to traditional estimators.

Main Methods:

• Developed a hybrid log-exponential estimator combining logarithmic and exponential transformations.
• Derived theoretical properties (bias, MSE) using first-order Taylor series approximation.
• Utilized K-nearest neighbour imputation for missing data under a Missing Completely at Random (MCAR) mechanism.
• Assessed performance via Monte Carlo simulations and empirical studies on diverse datasets.

Main Results:

• The proposed estimator demonstrated consistently lower Mean Squared Error (MSE).
• Achieved higher percentage relative efficiency compared to existing estimators, often exceeding 50%.
• Performance gains were particularly notable under moderate to high non-response rates and strong correlations.

Conclusions:

• The hybrid log-exponential estimator is a reliable and practical alternative for finite population mean estimation.
• The inclusion of sample size parameter enhances variance stabilization and finite sample performance.
• The estimator offers improved flexibility and stability in various sampling conditions.