Remaining useful life prediction based on nonlinear random coefficient regression model with fusing failure time data

Remaining useful life(RUL) prediction is one of the most crucial elements in prognostics and health management(PHM). Aiming at the imperfect prior information, this paper proposes an RUL prediction method based on a nonlinear random coefficient regression(RCR) model with fusing failure time data.Firstly, some interesting natures of parameters estimation based on the nonlinear RCR model are given. Based on these natures,the failure time data can be fused as the prior information reasonably. Specifically, the fixed parameters are calculated by the field degradation data of the evaluated equipment and the prior information of random coefficient is estimated with fusing the failure time data of congeneric equipment. Then, the prior information of the random coefficient is updated online under the Bayesian framework, the probability density function(PDF) of the RUL with considering the limitation of the failure threshold is performed. Finally, two case studies are used for experimental verification. Compared with the traditional Bayesian method, the proposed method can effectively reduce the influence of imperfect prior information and improve the accuracy of RUL prediction.

Reliability evaluation of bladder accumulator with no failure data

As a bladder accumulator is a high reliable and long life component in a hydraulic system,its cost is high and it takes a lot of time to test its reliability,therefore,a reliability test with small sample is performed,and no failure data is obtained using the method of fixed time truncation. In the case of Weibull distribution,a life reliability model of bladder energy storage is established by Bayesian method using the optimal confidence intervals method,a model of one-sided lower confidence intervals of the reliability and one-sided lower confidence intervals model of the reliability life are established. Results of experiments show that the evaluation method of no failure data under Weibull distribution is a good way to evaluate the reliability of the accumulator,which is convenient for engineering application,and the reliability of the accumulator has theoretical and practical significance.

Reliability Assessment for the Solenoid Valve of a High-Speed Train Braking System under Small Sample Size

Reliability assessment of the braking system in a high?speed train under small sample size and zero?failure data is veryimportant for safe operation. Traditional reliability assessment methods are only performed well under conditions of large sample size and complete failure data,which lead to large deviation under conditions of small sample size and zero?failure data. To improve this problem,a new Bayesian method is proposed. Based on the characteristics of the solenoid valve in the braking system of a high?speed train,the modified Weibull distribution is selected to describe the failure rate over the entire lifetime. Based on the assumption of a binomial distribution for the failure probability at censored time,a concave method is employed to obtain the relationships between accumulation failure prob?abilities. A numerical simulation is performed to compare the results of the proposed method with those obtained from maximum likelihood estimation,and to illustrate that the proposed Bayesian model exhibits a better accuracy for the expectation value when the sample size is less than 12. Finally,the robustness of the model is demonstrated by obtaining the reliability indicators for a numerical case involving the solenoid valve of the braking system,which shows that the change in the reliability and failure rate among the di erent hyperparameters is small. The method is provided to avoid misleading of subjective information and improve accuracy of reliability assessment under condi?tions of small sample size and zero?failure data.

Hierarchical Bayesian Estimation of the Products Reliability Based on Zero-Failure Data

With the development of science and technology, the products reliability is higher and higher. So for high reliability products, zero\|failure data situation appears often in the time ended reliability tests. In this paper, the hierarchical Bayesian estimation of the products reliability is given under the conditions of the Binomial distribution with zero\|failure data and the prior distribution of the reliability being quasi\|Beta distribution. The authors also give a practical calculating example using the theory.

Progressive prediction method for failure data with small sample size

The small sample prediction problem which commonly exists in reliability analysis was discussed with the progressive prediction method in this paper.The modeling and estimation procedure,as well as the forecast and confidence limits formula of the progressive auto regressive(PAR) method were discussed in great detail.PAR model not only inherits the simple linear features of auto regressive(AR) model,but also has applicability for nonlinear systems.An application was illustrated for predicting the future fatigue failure for Tantalum electrolytic capacitors.Forecasting results of PAR model were compared with auto regressive moving average(ARMA) model,and it can be seen that the PAR method can be considered good and shows a promise for future applications.

Reliability analysis of DOOF for Weibull distribution

Hierarchical Bayesian method for estimating the failure probability Pi under DOOF by taking the quasi-Beta distribution B(pi-1 , 1,1, b ) as the prior distribution is proposed in this paper. The weighted Least Squares Estimate method was used to obtain the formula for computing reliability distribution parameters and estimating the reliability characteristic values under DOOF. Taking one type of aerospace electrical connectoras an example, the correctness of the above method through statistical analysis of electrical connector acceler-ated life test data was verified.

Marginal Accelerated Hazard Model with Multivariate Failure Time Data

Multivariate failure time data are frequently encountered in biomedical research.In this article,we model marginal hazards with accelerated hazards model to analyze multivariate failure time data.Estimating equations are derived analogous to generalized estimating equation method.Under certain regular conditions,the resultant estimators for the regression parameters are shown to be asymptotically normal.Furthermore,we also establish the weak convergence of estimators for the baseline cumulative hazard functions.

Discussion of Fan et al.’s paper “Gaining effciency via weighted estimators for multivariate failure time data”

In the analysis of correlated data, it is ideal to capture the true dependence structure to increase effciency of the estimation. However, for multivariate survival data, this is extremely

Maximum Likelihood Estimation for the Pooled Repeated Partly Interval-Censored Observations Logistic Regression Model

Often in longitudinal studies, some subjects complete their follow-up visits, but others miss their visits due to various reasons. For those who miss follow-up visits, some of them might learn that the event of interest has already happened when they come back. In this case, not only are their event times interval-censored, but also their time-dependent measurements are incomplete. This problem was motivated by a national longitudinal survey of youth data. Maximum likelihood estimation (MLE) method based on expectation-maximization (EM) algorithm is used for parameter estimation. Then missing information principle is applied to estimate the variance-covariance matrix of the MLEs. Simulation studies demonstrate that the proposed method works well in terms of bias, standard error, and power for samples of moderate size. The national longitudinal survey of youth 1997 (NLSY97) data is analyzed for illustration.

Discussion on “Gaining Effciency via Weight Estimators for Multivariate Failure Time Data” by Fan, Zhou and Chen

The survival analysis literature has always lagged behind the categorical data literature in developing methods to analyze clustered or multivariate data. While estimators based on

Rejoinder for Gaining effciency via weighted estimators for multivariate failure time data

We thank all the discussants for their interesting and stimulating contributions. They have touched various aspects that have not been considered by the original articles.

Analysis of Field Data on Computer Failures

This paper emphasizes the importance of making field measurements for effective and realistic dependability evaluations.Two examples are given,both based on real data from IBM mainframes.The first evaluates the impact of the operating environment on system failure characteristics and the second shows how an accurate model depicting this interaction can be extracted from real data.

A Semiparametric Additive Rates Model for Clustered Recurrent Event Data

Recurrent event data often arises in biomedical studies, and individuals within a cluster might not be independent. We propose a semiparametric additive rates model for clustered recurrent event data, wherein the covariates are assumed to add to the unspecified baseline rate. For the inference on the model parameters, estimating equation approaches are developed, and both large and finite sample properties of the proposed estimators are established.

Nutritional epidemiology methods and related statistical challenges and opportunities

The public health importance of nutritional epidemiology research is discussed,along withmethodological challenges to obtaining reliable information on dietary approaches to chronicdisease prevention.Measurement issues in assessing dietary intake need to be addressed toobtain reliable disease association information.Self-reported dietary data typically incorporatemajor random and systematic biases.Intake biomarkers offer potential for more reliable analyses,but biomarkers have been established only for a few dietary variables,and these may be tooexpensive to apply to all participants in large epidemiologic cohorts.A possible way forwardinvolves additional nutritional biomarker development using high-dimensional metabolomicprofiling,using blood and urine specimens,in conjunction withfurther development of statisticalapproaches for accommodating measurement error with failure time response data.Statisticianshave the opportunity to contribute greatly to worldwide public health through the development of statistical methods to address these nutritional epidemiology research challenges,asis elaborated in this contribution.