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

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.

[1]  R. Arabi Belaghi,et al.  Estimation based on progressively type-I hybrid censored data from the Burr XII distribution , 2019 .

[2]  Debanjan Mitra,et al.  Analysis of left truncated and right censored competing risks data , 2017, Comput. Stat. Data Anal..

[3]  Debanjan Mitra,et al.  EM-based likelihood inference for some lifetime distributions based on left truncated and right censored data and associated model discrimination , 2014 .

[4]  W. Nelson.  Statistical Methods for Reliability Data , 1998 .

[5]  Gordon Johnston,et al.  Statistical Models and Methods for Lifetime Data , 2003, Technometrics.

[6]  Takeshi Emura,et al.  Estimation and Model Selection for Left-truncated and Right-censored Lifetime Data with Application to Electric Power Transformers Analysis , 2016, Commun. Stat. Simul. Comput..

[7]  Debashis Kushary,et al.  Bootstrap Methods and Their Application , 2000, Technometrics.

[8]  Yili Hong,et al.  Prediction of remaining life of power transformers based on left truncated and right censored lifetime data , 2009, 0908.2901.

[9]  Pao-Sheng Shen,et al.  Estimation in the Cox proportional hazards model with doubly censored and truncated data , 2011 .

[10]  Pao-Sheng Shen,et al.  Analysis of left-truncated right-censored or doubly censored data with linear transformation models , 2012 .

[11]  Pao-sheng Shen,et al.  The Cox-Aalen model for left-truncated and mixed interval-censored data , 2019, Statistics.

[12]  A. Cohen.  Truncated and Censored Samples , 1991 .

[13]  J. Bert Keats,et al.  Statistical Methods for Reliability Data , 1999 .

[14]  Debanjan Mitra,et al.  Left truncated and right censored Weibull data and likelihood inference with an illustration , 2012, Comput. Stat. Data Anal..

[15]  Debanjan Mitra,et al.  Statistical inference based on left truncated and interval censored data from log-location-scale family of distributions , 2019, Commun. Stat. Simul. Comput..

[16]  G. McLachlan,et al.  The EM algorithm and extensions , 1996 .

[17]  Janez Puhan,et al.  Grid Restrained Nelder-Mead Algorithm , 2006, Comput. Optim. Appl..

[18]  R. Arabi Belaghi,et al.  On the estimation of the extreme value and normal distribution parameters based on progressive type-II hybrid-censored data , 2016 .

[19]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[20]  Debanjan Mitra,et al.  Likelihood inference for lognormal data with left truncation and right censoring with an illustratio , 2011 .

[21]  Xingwei Tong,et al.  Efficient estimation for the additive hazards model in the presence of left-truncation and interval censoring , 2015 .

[22]  Debanjan Mitra,et al.  Bayesian inference of Weibull distribution based on left truncated and right censored data , 2016, Comput. Stat. Data Anal..

[23]  Ülkü Gürler,et al.  Full and conditional likelihood approaches for hazard change-point estimation with truncated and censored data , 2011, Comput. Stat. Data Anal..

[24]  Xu Liu,et al.  A note on estimation of the mean residual life function with left-truncated and right-censored data , 2013 .

[25]  Marc Teboulle,et al.  A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems , 2009, SIAM J. Imaging Sci..

[26]  Wen-Harn Pan,et al.  Semiparametric regression analysis for left-truncated and interval-censored data without or with a cure fraction , 2019, Comput. Stat. Data Anal..