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

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 expectationmaximization 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.

Left‐truncated and right‐censored field failure data: Review of parametric analysis for reliability

“…The EM-based method for left-truncated and interval-censored data was also developed for the log-location-scale family of distributions. 6,25 However, more case studies by real data will be required to demonstrate interval censoring. Moreover, it remains unclear if the EM algorithms are advantageous over the simpler NR algorithm.…”

“…The review consists of the well-established statistical and computational methodologies 1,[10][11][12][13][14][15] and very recent models and methods. 6,7,16,17,25,26 Our review also includes a real data example for studying the reliability of electric power transformers, 1,15 which illustrates the introduced models and methods. Readers interested in other engineering applications may study the data examples.…”

“…Many algorithms were proposed to compute θ: the NR algorithm, [12][13][14][15] EM-or EM-gradient algorithm, [10][11][12][13][14] stochastic EMalgorithm, 17,23,25 profile ML estimation algorithm, 17 and hierarchical grid (HG) algorithm. 6 All the algorithms use initial values and some iterations until they meet a convergence criterion. Below, we explain the NR and EM algorithms.…”

“…16 Therefore, the paper adds these recent developments to the previous review of Balakrishnan and Mitra. 14 The paper also discusses potential future works on this growing research area, including the emerging methods for interval censoring 6,25 and competing risks 26,27 for field failure data. Our focus is on the parametric methods that can be applicable for reliability engineering based on field failure data.…”

Likelihood Inference for Copula Models Based on Left-Truncated and Competing Risks Data from Field Studies

“…Hong et al [1] separated the samples into two parts: a truncated part (e.g., transformers installed before 1980) and an untruncated part (e.g., transformers installed after 1980), and then combined them into a single likelihood function. This type of truncated field data arises in many other practical applications, where there is a birth process (the installing process) of individuals and a certain data collection period of failure [6][7][8][9].…”