RELIABILITY ESTIMATION OF INCOMPLETE FAILURE TIME DATA USING SPLINES

Abstract

This thesis proposes several novel nonparametric and semiparametric models for making statistical inference on incomplete lifetime data. Particularly, we focus on three popular types of failure time data collected within window observations: left-truncated and right-censored data, window-observation recurrence data with and without covariates. We accordingly develop different yet coherent sieve estimation frameworks using splines and design efficient algorithms for estimating model parameters. The proposed spline-based estimators are proved to enjoy superior asymptotic properties than existing alternatives. Simulation studies are presented to verify the established theoretical guarantees, and, to illustrate the substantial gain in finite-sample estimation accuracy of the proposed methods. We showcase the wide applicability of our models in real applications via case studies on high-voltage power transformers, high-transaction printer repairable systems and water pipe recurrent failure data. The great flexibility and interpretability of the proposed approaches are highlighted by comparing with conventional methods.