Failure Analysis for Truncated and Fully Censored Lifetime Data With a Hierarchical Grid Algorithm

Qi Li,Bing Huang,Zengqiang Jiang,Jing Ma,Mingcheng E.,Dongdong Li

doi:10.1109/access.2020.2974266

Abstract

In the field of failure analysis and reliability evaluation, truncated and censored lifetime data due to observational constraints and periodic inspection schemes are highly common. The expectation-maximization algorithm is a widely employed approach for the parameter estimations of truncated and censored lifetime data. In this study, a new hierarchical grid algorithm is proposed to estimate the model parameters based on left-truncated and fully-censored data. An improved expectation-maximization algorithm is also adapted under incomplete information. These two methods are compared using Monte Carlo simulations. The confidence intervals corresponding to different quantile methods of the nonparametric bootstrap are compared in terms of coverage probabilities. In a case study, the failure analysis and prediction intervals for individual coupler knuckles of rail wagons are discussed. This simulation study and case study verify the effectiveness of the proposed framework.

Highlights

Lifetime data has been used to evaluate the time-to-failure distribution and to predict remaining useful life (RUL) for a long time in the field of reliability
To verify the proposed hierarchical grid (HG) algorithm in the case of lefttruncated and right-censored data, the EM algorithm of lognormal distribution introduced by Balakrishnan and Mitra [4] is employed for comparison
The HG algorithm only needs four iterations to reach a tolerance of less than 0.001. These results reveal that the HG algorithm converges more rapidly than does the improved EM algorithm

Summary

INTRODUCTION

Lifetime data has been used to evaluate the time-to-failure distribution and to predict remaining useful life (RUL) for a long time in the field of reliability. Q. Li et al.: Failure Analysis for Truncated and Fully Censored Lifetime Data With a Hierarchical Grid Algorithm TABLE 1. Shen et al [16] proposed an EM algorithm based on left-truncated and interval-censored data for obtaining the conditional maximum likelihood estimator (cMLE). The inference of parameter estimation methods and their applications to left-truncated and fully censored data have not been studied extensively. A. REALISTIC LEFT-TRUNCATED AND FULLY CENSORED DATA SCENARIO The lifetime data of coupler knuckles is collected from a rail wagon maintenance factory, which was established in 2015. Q. Li et al.: Failure Analysis for Truncated and Fully Censored Lifetime Data With a Hierarchical Grid Algorithm. An improved version of the EM algorithm that can handle fully censored data is presented for comparison purposes

PROPOSED HIERARCHICAL GRID ALGORITHM

NUMERICAL VALIDATION BASED ON LEFT-TRUNCATED AND RIGHT-CENSORED DATA

CASE STUDY

CONCLUSION