Failure Time Data Research Articles

Reliability Evaluation of Smart Meter Based on Multiple Type-I Censored Data

Smart meter is an integral part of our state smart grid, which involves the interests of millions of households. Reliability evaluation based on operating data is an important problem in the implementation of smart grid operation and maintenance management. In view of the data characteristics of the same type and the same batch of smart meter with multiple Type-I censored data, i.e., unequal time censored data, this paper introduces Weibull distribution to model its failure time data. Then, this paper applies the maximum likelihood method to estimate unknown parameters of the distribution. Moreover, the reliability evaluation model of the smart meter is established, and partial failure data of meters from one region is collected to verify the effectiveness of the proposed method.

Goodness‐of‐fit test for semiparametric copula models with bivariate interval‐censored data

This paper discusses the goodness‐of‐fit test of semiparametric copula models when one faces bivariate interval‐censored failure time data, which often occur in many areas including epidemiological and medical studies as well as social science experiments. For the problem, three test statistics or procedures are proposed: two based on the pseudo in‐and‐out‐sample approach and one based on the information ratio criterion. The asymptotic properties of the proposed test procedures are established, and in particular, the three methods are shown to be asymptotically equivalent. To assess the empirical performance of the proposed methods, an extensive simulation study is conducted and indicates that they work well in practical situations. An application to a Signal–Tandmobiel study is provided.

A New Model-Free Feature Screening Procedure for Ultrahigh-Dimensional Interval-Censored Failure Time Data

A New Model-Free Feature Screening Procedure for Ultrahigh-Dimensional Interval-Censored Failure Time Data

A Bayesian Mixture Cure Rate Model for Estimating Short-Term and Long-Term Recidivism

Mixture cure rate models have been developed to analyze failure time data where a proportion never fails. For such data, standard survival models are usually not appropriate because they do not account for the possibility of non-failure. In this context, mixture cure rate models assume that the studied population is a mixture of susceptible subjects who may experience the event of interest and non-susceptible subjects that will never experience it. More specifically, mixture cure rate models are a class of survival time models in which the probability of an eventual failure is less than one and both the probability of eventual failure and the timing of failure depend (separately) on certain individual characteristics. In this paper, we propose a Bayesian approach to estimate parametric mixture cure rate models with covariates. The probability of eventual failure is estimated using a binary regression model, and the timing of failure is determined using a Weibull distribution. Inference for these models is attained using Markov Chain Monte Carlo methods under the proposed Bayesian framework. Finally, we illustrate the method using data on the return-to-prison time for a sample of prison releases of men convicted of sexual crimes against women in England and Wales and we use mixture cure rate models to investigate the risk factors for long-term and short-term survival of recidivism.

A Semiparametric Bayesian Joint Modelling of Skewed Longitudinal and Competing Risks Failure Time Data: With Application to Chronic Kidney Disease

In clinical and epidemiological studies, when the time-to-event(s) and the longitudinal outcomes are associated, modelling them separately may give biased estimates. A joint modelling approach is required to obtain unbiased results and to evaluate their association. In the joint model, a subject may be exposed to more than one type of failure event (competing risks). Considering the competing event as an independent censoring of the time-to-event process may underestimate the true survival probability and give biased results. Within the joint model, longitudinal outcomes may have nonlinear (irregular) trajectories over time and exhibit skewness with heavy tails. Accordingly, fully parametric mixed-effect models may not be flexible enough to model this type of complex longitudinal data. In addition, assuming a Gaussian distribution for model errors may be too restrictive to adequately represent within-individual variations and may lack robustness against deviation from distributional assumptions. To simultaneously overcome these issues, in this paper, we presented semiparametric joint models for competing risks failure time and skewed-longitudinal data by using a smoothing spline approach and a multivariate skew-t distribution. We also considered different parameterization approaches in the formulation of joint models and used a Bayesian approach to make the statistical inference. We illustrated the proposed methods by analyzing real data on a chronic kidney disease. To evaluate the performance of the methods, we also carried out simulation studies. The results of both the application and simulation studies revealed that the joint modelling approach proposed in this study performed well when the semiparametric, random-effects parameterization, and skew-t distribution specifications were taken into account.

Estimation of linear transformation cure models with informatively interval-censored failure time data

Linear transformation models have been one type of models commonly used for regression analysis of failure time data partly due to their flexibility. More recently they have been generalised to the case where there may exist a cured subgroup or the censoring may be informative. In this paper, we consider a more complicated and general situation where both a cured subgroup and informative censoring, or more specifically informative interval censoring, exist. As pointed out in the literature, the analysis that fails to take into account either the cured subgroup or the informative censoring can yield biased estimation or misleading conclusions. For the problem, a three-component mixture cure model is presented and we develop a two-step estimation procedure with the use of B-splines to approximate unknown functions. The proposed approach is quite flexible and can be easily implemented. Also the proposed estimators of regression parameters are shown to be consistent and asymptotically normal. An extensive simulation study is conducted and suggests that the method works well for practical situations. Furthermore a real application is provided to illustrate the proposed methodology.

Remaining useful life prediction of implicit linear Wiener degradation process based on multi-source information

Accurate remaining useful life (RUL) prediction is helpful to improve the reliability and safety of complex systems. However, in practical engineering applications, it often occurs imperfect or scarce prior degradation information for the degradation system with measurement error (ME). In order to solve this problem, based on the implicit linear Wiener degradation process, a RUL prediction method which reasonably fuses failure time data or multi-source information is proposed in this paper. Firstly, based on the implicit linear Wiener degradation process, we obtain the relationship between the natures of parameters estimation and degradation data by theoretical derivation, which provides a theoretical basis regarding how to fuse multi-source information. Secondly, according to the natures of parameters estimation, we use field degradation data and historical degradation data to estimate the fixed parameters of the two prediction cases respectively, and fuse failure time data into the degradation model by the expectation maximization (EM) algorithm. Then, the Kalman filtering algorithm is used to online update the drift parameter based on field degradation data. Finally, we use some simulation experiments to further verify the natures of parameters estimation, and two practical case studies to verify the superiority of the proposed method.

Inference on semi-parametric transformation model with a pairwise likelihood based on left-truncated and interval-censored data

Semi-parametric transformation models provide a general and flexible class of models for regression analysis of failure time data and many methods have been developed for their estimation. In particular, they include the proportional hazards and proportional odds models as special cases. In this paper, we discuss the situation where one observes left-truncated and interval-censored data, for which it does not seem to exist an established method. For the problem, in contrast to the commonly used conditional approach that may not be efficient, a pairwise pseudo-likelihood method is proposed to recover some missing information in the conditional method. The proposed estimators are proved to be consistent and asymptotically efficient and normal. A simulation study is conducted to assess the empirical performance of the method and suggests that it works well in practical situations. This method is illustrated by using a set of real data arising from an HIV/AIDS cohort study.

Discussion of signature‐based models of preventive maintenance

Discussion of signature‐based models of preventive maintenance

Regression Analysis of Multivariate Interval-Censored Failure Time Data under Transformation Model with Informative Censoring

We consider a regression analysis of multivariate interval-censored failure time data where the censoring may be informative. To address this, an approximated maximum likelihood estimation approach is proposed under a general class of semiparametric transformation models, and in the method, the frailty approach is employed to characterize the informative interval censoring. For the implementation of the proposed method, we develop a novel EM algorithm and show that the resulting estimators of the regression parameters are consistent and asymptotically normal. To evaluate the empirical performance of the proposed estimation procedure, we conduct a simulation study, and the results indicate that it performs well for the situations considered. In addition, we apply the proposed approach to a set of real data arising from an AIDS study.

Joint modeling of generalized scale-change models for recurrent event and failure time data.

Recurrent event and failure time data arise frequently in many clinical and observational studies. In this article, we propose a joint modeling of generalized scale-change models for the recurrent event process and the failure time, and allow the two processes to be correlated through a shared frailty. The proposed joint model is flexible in that it requires neither the Poisson assumption for the recurrent event process nor a parametric assumption on the frailty distribution. Estimating equation approaches are developed for parameter estimation, and the asymptotic properties of the resulting estimators are established. Simulation studies are conducted to evaluate the finite sample performances of the proposed method. An application to a medical cost study of chronic heart failure patients is provided.

Efficient estimation for accelerated failure time model with interval-censored data in the presence of a cured subgroup

As the alternative of Cox model, the accelerated failure time (AFT) model, which simply regresses the logarithm of the survival time over the covariates, is commonly used in the analysis of interval-censored data. In this paper, we propose a novel two-component mixture-cure model for the interval-censored failure time data in the presence of a cure fraction. Specifically, the first component is a logistic regression model that describes the cure rate, and the second component is a semiparametric accelerated failure time model that describes the failure time of interest for the uncured subjects. An efficient semiparametric procedure is developed to estimate parameters in the considered model. We propose a penalized sieve maximum likelihood estimation approach with Bernstein polynomials to estimate the regression parameters quickly and accurately and the proposed procedure does not rely on the assumption of the distribution of the measurement error. The asymptotic properties of the resulting estimators are established. Extensive simulation studies conducted indicate that the proposed procedure works well for practical situations. In addition, AIDS data analysis is provided for illustration of the proposed method.

Adaptive Residual Life Prediction for Small Samples of Mechanical Products Based on Feature Matching Preprocessor-LSTM

In order to solve the problem of predicting the residual life of mechanical products accurately based on small-sample data, this paper proposes a small-sample adaptive residual life prediction model of mechanical products based on feature matching preprocessor-LSTM. First, aiming at the problem of low accuracy of remaining life prediction for small samples of mechanical products caused by multiple time scales and multiple fault states, the failure time data and performance degradation data are fused, and the failure rate and standard deviation are used as the remaining life prediction criteria to intuitively reflect The possibility of failure of a component or system at a certain point in time. Considering the demand of adaptive small-sample residual life prediction data, this paper establishes the adaptive matching pre-processor model of life characteristics. On this basis, the LSTM neural network is used to establish a small-sample adaptive residual life prediction model. Then, the XJTU-SY bearing life data set and the test data of the small-sample life characteristics measured by the RV reducer are used as the research objects, and a small amount of the data set is randomly selected. The remaining life expectancy is predicted from the sample data and compared with its standard remaining life, respectively. The comparison results show that the overall prediction error is small. This study shows that the remaining life prediction model established can better predict the remaining life of mechanical product sub-sample data and provides a feasible method for predicting the remaining life of mechanical product sub-samples.

Variable selection for nonparametric additive Cox model with interval-censored data.

The standard Cox model is perhaps the most commonly used model for regression analysis of failure time data but it has some limitations such as the assumption on linear covariate effects. To relax this, the nonparametric additive Cox model, which allows for nonlinear covariate effects, is often employed, and this paper will discuss variable selection and structure estimation for this general model. For the problem, we propose a penalized sieve maximum likelihood approach with the use of Bernstein polynomials approximation and group penalization. To implement the proposed method, an efficient group coordinate descent algorithm is developed and can be easily carried out for both low- and high-dimensional scenarios. Furthermore, a simulation study is performed to assess the performance of the presented approach and suggests that it works well in practice. The proposed method is applied to an Alzheimer's disease study for identifying important and relevant genetic factors.

Bivariate-Dependent Reliability Estimation Model Based on Inverse Gaussian Processes and Copulas Fusing Multisource Information

Reliability estimation for key components of a mechanical system is of great importance in prognosis and health management in aviation industry. Both degradation data and failure time data contain abundant reliability information from different sources. Considering multiple variable-dependent degradation performance indicators for mechanical components is also an effective approach to improve the accuracy of reliability estimation. This study develops a bivariate-dependent reliability estimation model based on inverse Gaussian process and copulas fusing degradation data and failure time data within one computation framework. The inverse Gaussian process model is used to describe the degradation process of each performance indicator. Copula functions are used to capture the dependent relationship between the two performance indicators. In order to improve the reliability estimation accuracy, both degradation data and failure time data are used simultaneously to estimate the unknown parameters in the degradation model based on the likelihood function transformed using the zeros-ones trick. A simulation study and a real application in the reliability estimation of mechanical seal used in airborne hydraulic pump are conducted to validate the effectiveness and accuracy of the proposed model compared with existing reliability models.

Joint analysis of informatively interval-censored failure time and panel count data.

Interval-censored failure time and panel count data, which frequently arise in medical studies and social sciences, are two types of important incomplete data. Although methods for their joint analysis have been available in the literature, they did not consider the observation process, which may depend on the failure time and/or panel count of interest. This study considers a three-component joint model to analyze interval-censored failure time, panel counts, and the observation process within a unique framework. Gamma and distribution-free frailties are introduced to jointly model the interdependency among the interval-censored data, panel count data, and the observation process. We propose a sieve maximum likelihood approach coupled with Bernstein polynomial approximation to estimate the unknown parameters and baseline hazard function. The asymptotic properties of the resulting estimators are established. An extensive simulation study suggests that the proposed procedure works well for practical situations. An application of the method to a real-life dataset collected from a cardiac allograft vasculopathy study is presented.

A method for obtaining the preventive maintenance interval in the absence of failure time data

One of the ways to reduce greenhouse gas emissions and other polluting gases caused by ships is to improve their maintenance operations through their life cycle. The maintenance manager usually does not modify the preventive intervals that the equipment manufacturer has designed to reduce the failure. Conditions of use and maintenance often change from design conditions. In these cases, continuing using the manufacturer's preventive intervals can lead to non-optimal management situations. This article proposes a new method to calculate the preventive interval when the hours of failure of the assets are unavailable. Two scenarios were created to test the effectiveness and usefulness of this new method, one without the failure hours and the other with the failure hours corresponding to a bypass valve installed in the engine of a maritime transport surveillance vessel. In an easy and fast way, the proposed method allows the maintenance manager to calculate the preventive interval of equipment that does not have installed an instrument for measuring operating hours installed.

Description of survival data extended to the case of competing risks: a teaching approach based on frequency tables

Survival analysis is a powerful statistical tool to study failure-time data. In introductory courses students learn how to describe right-censored survival time data using the product-limit estimator of the survival function on a given end-point relying on a product of conditional survival probabilities. In the case of a composite end-point, the next step is to account for the presence of competing risks. The complement to one of the survival function is decomposed into the sum of cause-specific incidences, which are obtained as sum of unconditional probabilities due to the single competing risk. However, this algebraic decomposition is not straightforward, given the difference between the structure of the involved estimators. In addition, one is tempted to use the Kaplan-Meier estimator, leading to an erroneous decomposition of the overall incidence. Here we discuss a simple reinterpretation of the Kaplan-Meier formula in terms of sum of non-conditional probabilities of developing the end-point in time, adjusted for the presence of censoring. This approach could be used for describing survival data through simple frequency tables which are directly generalized to the case of competing risks. In addition, it makes clear how the estimation of the single cause-specific incidence through the Kaplan-Meier estimator, simply considering the occurrence of competing events as censored data, leads to an overestimation of the cause-specific incidence. Two examples are provided to support the explanation: the first one, could help to clarify the procedure described by the formulas; the second one, simulates real data in order to present graphically the results.

Burr XII Distribution for Disease Data Analysis in the Presence of a Partially Observed Failure Mode

Modeling competing failure modes is an important problem in engineering and survival analyses. Competing failure modes are partially observed in many applications and often pose a modeling challenge. This study discusses the inference for partially observed failure modes assuming a Burr XII distribution. In particular, we consider two failure modes, and the failure time data are collected under a hybrid type I censoring scheme. The model parameters are estimated using maximum likelihood and Bayesian methods under a symmetric squared error loss function, whereas the intervals estimation is done with three methods: asymptotic and credible confidence intervals. Besides a simulation study, a real-life data set is taken from individuals who live in an environment with several diseases to present the utility of the work. Additionally, a simulation study is constructed to measure and compare different estimation methods.

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

Survival and reliability analyses deal with incomplete failure time data, such as censored and truncated data. Recently, the classical left-truncation scheme was generalized to analyze “field data”, defined as samples collected within a fixed period. However, existing competing risks models dealing with left-truncated field data are not flexible enough. We propose copula-based competing risks models for latent failure times, permitting a flexible parametric form. We formulate maximum likelihood estimation methods under the Weibull, lognormal, and gamma distributions for the latent failure times. We conduct simulations to check the performance of the proposed methods. We finally give a real data example. We provide the R code to reproduce the simulations and data analysis results.