Prediction of Remaining Lifetime Distribution From Functional Trajectories Under Censoring Data

Sozucok Izzet ； Shan Sun ； Huitian Lu

《International Journal of Intelligent Technologies and Applied Statistics》 13卷4期 (2020/12) Pp. 347-367

https://doi.org/10.6148/IJITAS.202012_13(4).0003

摘要

Motivations: The purpose of this study is to estimate the mean remaining lifetime and the distribution function of the remaining lifetime using co-variate trajectories. In engineering systems, the co-variate trajectories are taken as degradation signals under observed condition-based signals. Methods: There are two major steps to accomplish our goal. The first step is to express the remaining lifetime as linear combinations of random scores. These random scores (as functional principal components) are determined using numerical integration of integrated function of observed/incomplete co-variate trajectories. The second step is to estimate the coefficients of the random scores in the remaining lifetime via local linear regression based on Nadaraya-Watson weighted kernel estimates. Findings: In this paper, we apply our proposed methods to a degradation signal based on censored co-variate trajectories obtained in engineering system. The performance of the method is discussed using simulated degradation signals. Originality: In this paper, (1) the functional model we developed can apply not only to the completely observed co-variate trajectories, but also to incomplete/censored co-variate trajectories and (2) the method allows for straightforward inclusion of more than one predictor co-variate trajectory per subject. Implications: Our proposed methods reduce the durability of each component of the system, according to our simulation results.

關鍵字

Functional predictors ； Principal component scores ； Survival function and residual life distribution