Analysis of Weibull Lifetime Data via Quantile Regression under Progressive Type-II Censoring  
Author Huizhong Lin

 
Co-Author(s) Liang Wang; Yuhlong Lio

 
Abstract In this paper, quantile regression (QR) is implemented to analyze ALT data, where as a basic tool for estimating conditional quantiles of a response variable, the QR can characterize the entire conditional distribution of the outcome variable appearing more robust to outliers and mis-specification of error distribution. Due to the cost and time limitations, constant-stress ALT is conducted under progressive Type- II censoring, when the lifetime of products follow Weibull distribution. Under the assumption of acceleration model between population quantile and stress, parameter estimation of the unknown model parameter as well as quantile quantities is established. Maximum likelihood estimators along with existence and uniqueness are established for the Weibull parameters, and the coefficient parameters in quantitie acceleration model are established by using an iterative reweighted least squares approach numerically. Moreover, the Bootstrap confidence intervals are constructed in consequence based on bootstrap sampling technique. Alternatively, another generalized point and interval estimates of model parameters under different acceleration stages are further constructed based on the proposed pivotal quantities and QR approach for comparison. In addition, due to the limitation that there is only a quantity estimate available under use condition, an inverse estimation approach is proposed, then the Weibull parameters under use condition has been estimated and the reliability indices are also obtained in consequence. Finally, extensive simulation studies are carried out to evaluate the performances of the proposed different methods, and a real life data is also evaluated for application illustration.

 
Keywords Quantile regression, Progressive Type-II censoring data, Weibull distribution, Maximum likelihood estimation, Generalized pivotal quantity estimation, Iterative reweighted least squares approach
   
    Article #:  RQD27-42
 

Proceedings of 27th ISSAT International Conference on Reliability & Quality in Design
Virtual Event
August 4-6, 2022