Robust Quantile Regression Analysis on Experimental Design
摘要
The analysis of lifetime quantiles is crucial for improving product reliability. Traditional experimental design methods, such as maximum likelihood estimation and weighted least squares, often rely on assumptions about data distribution, which makes them inefficient and significantly limits their handling of heteroscedasticity and censored data. To address these challenges, this paper introduces quantile regression into factorial experiments for analyzing lifetime quantiles, effectively overcoming issues related to data distribution, heteroscedasticity, and censoring. Within the quantile regression framework, this study further proposes an adaptive weighted quantile regression model by incorporating an adaptive weight parameter to enhance the performance of the quantile regression model. The asymptotic normality of the coefficient estimates for the weighted quantile regression model is theoretically proved. Simulation results demonstrate that the weighted quantile regression model exhibits robustness to heteroscedasticity and data distribution and outperforms the traditional quantile regression model in terms of stability and accuracy. Finally, two experiments validate the feasibility and effectiveness of the proposed method, providing new insights and tools for reliability analysis.