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Reliability Assessment Method Based on Small Sample Accelerated Life Test Data

EKSPLOATACJA I NIEZAWODNOSC-MAINTENANCE AND RELIABILITY 2025年第1期27卷

作者： You, Dazhang Liu, Shan Li, Fangke Liu, Hang Zhang, Yepeng Hubei Univ Technol Sch Mech Engn Hubei Peoples R China

Aiming at the problems of small sample size, few test failure data and low reliability evaluation efficiency in accelerated life test of high- reliability and long-life products, an improved virtual augmentation Bootstrap-Bayes reliability evaluation method based on small sample accelerated life test data was proposed. Firstly, the test data under various stress conditions are augmented by virtual fusion. Secondly, the empirical distribution function and bootstrap sampling method are improved, and the kernel density estimation method is used to fit the density distribution of test data as prior information. Then, the parameter estimates of the test data are obtained by Gibbs sampling combined with Bayes formula. Finally, the reliability index under normal stress level is obtained by accelerating model extrapolation. The feasibility of the proposed method is verified by the accelerated life test data of a type of Ship communication equipment.

关键词： reliability assessment accelerated life test virtual augmentation bootstrap sampling mcmc algorithm bayes

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Bayesian Analysis of Lifetime Delayed Degradation Process for Destructive/Nondestructive Inspection

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IEEE TRANSACTIONS ON RELIABILITY 2024年第2期73卷 990-1004页

作者： Chen, Siyi Lu, Zitong Hu, Qingpei Xie, Min Yu, Dan Chinese Acad Sci Acad Math & Syst Sci Beijing 100045 Peoples R China Univ Chinese Acad Sci Sch Math Sci Beijing 101408 Peoples R China City Univ Hong Kong Dept Syst Engn Hong Kong Peoples R China

Degradation has become the dominant failure mode for highly reliable engineering systems. Cracking, a fatigue phenomenon composed of sequential phases of crack initiation and propagation, is a major concern for critical aircraft structures. Traditional fracture mechanics analysis cannot fully meet the requirements for assessing reliability indicators from a reliability analysis perspective. Alternatively, the empirical Lifetime Delayed Degradation Process (LDDP) provides an explanatory framework for sequential hard&soft failure mode. This study further generalizes the LDDP framework by introducing the Bayesian method as a Bayes-LDDP model, which incorporates a weakly informative prior derived from historical data of similar systems for both non-destructive and destructive inspections. Additionally, we compare our proposed method to the LDDP approach using specific inspection datasets. Two practical applications are conducted to demonstrate the effectiveness of the Bayes-LDDP model for reliability monitoring and remaining useful life (RUL) prediction in critical aircraft structures using field data. The crack inspection datasets of a transport aircraft and an aircraft core automated maintenance system (CAMS) are utilized for non-destructive and destructive inspections, respectively. The Markov Chain Monte Carlo (mcmc) sampling algorithm is adopted for the Bayes-LDDP, improving the computational efficiency of model parameters estimation compared to the stochastic expectation maximum (SEM) algorithm. Furthermore, the Bayes-LDDP model enables precise inference including the mean time to failure (MTTF) of cracks for destructive inspections and the RUL for non-destructive inspections under the selected optimal model. This extended novel framework provides a clear depiction of the lifetime delayed degradation process from a Bayesian perspective.

关键词： Crack modeling delayed degradation lifetime distribution mcmc algorithm remaining useful life structure reliability weakly informative prior

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Compound negative binomial multivariate correlated frailty model for long-term survivors

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2024年第5期53卷 2261-2276页

作者： Dabade, Alok D. Univ Mumbai Dept Stat Mumbai Maharashtra India

In the correlated frailty models, it is believed that all the individuals in the population will eventually experience the event of interest. This may not always be the situation in reality. There may be a certain fraction of the population which is immune to the event and hence may not experience the event under study. For such individuals, frailty may not be active i.e., zero. Hence, frailty distribution should provide a positive mass at zero. In this article, a new correlated frailty model with compound negative binomial distribution as frailty distribution, is introduced to incorporate the non-susceptibility of individuals. The inferential problem is solved in a Bayesian framework using Markov Chain Monte Carlo methods. The proposed model is then applied to a real life data set.

关键词： Bayesian estimation Compound negative binomial distribution Correlated frailty Generalized exponential distribution mcmc algorithm

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Statistical Inference and Simulation for the Maxwell-Boltzmann Distribution

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ADVANCED THEORY AND SIMULATIONS 2025年

作者： Shams, Mehdi Mirzaie, Mohammad Ali Univ Kashan Dept Math Kashan *** Iran

Statistical simulation is one approach to problem solving without experimental testing. In this paper, a method for simulating the distribution of the Maxwell-Boltzmann distribution with mcmc approach by truncated Rayleigh distribution is presented and generated a random sample from this distribution by rejection sampling method. Some statistical inference properties for the parameter of the Maxwell-Boltzmann distribution such as maximum likelihood estimator, method of moments estimator, uniformly minimum variance unbiased estimator and minimum risk equivariant estimator, and the relationship between maximum likelihood estimator, uniformly minimum variance unbiased estimator, and also minimum risk equivariant estimator are found. Also, the hypothesis testing is discussed and the uniform most powerful test, generalized likelihood ratio test, uniformly most powerful unbiased test and uniformly most powerful invariant test and also confidence interval with equal tails, the shortest confidence interval, unbiased confidence interval and asymptotic confidence interval for the parameter of the Maxwell-Boltzmann model are found. By the way, a new method based on stochastic methods for finding the shortest and the unbiased confidence interval for the parameter of the Maxwell-Boltzmann model is introduced and it is shown that with a very close approximation, it leads to the same results of previous researches that are solved by numerical methods. It is proved that the Kullback-Leibler divergence between two Maxwell-Boltzmann distributions with different parameters is a convex function of the ratio of the parameters and then, the Hellinger distance between these two distributions is also calculated. By selecting the multiplicative group action, the discussion of invariance is followed and maximal invariant statistics and weakly equivariant estimators are found. Next, the uniformly most powerful invariant test critical region is performed using bootstrap. In the end, using two

关键词： equivariant estimators Kullback-Leibler divergence mcmc algorithm maximal invariant estimator maximum likelihood estimator uniformly minimum variance unbiased estimator

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Bayesian inferences and prediction of exponentiated exponential distribution based on multiple interval censored data

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COMPUTATIONAL STATISTICS 2025年第5期40卷 2635-2655页

作者： Agnihotri, Shubham Singh, Sanjay Kumar Singh, Umesh Banaras Hindu Univ Inst Sci Dept Stat Varanasi 221005 India

This article carefully defines a multiple interval censoring plan, and its scope of application in the Bayesian setup is demonstrated. The Bayes estimators of shape and scale parameters of the exponentiated exponential distribution are obtained under symmetric and asymmetric loss functions. Additionally, the credible intervals for both parameters are obtained. The performances of Bayes estimators and credible intervals are investigated through the appropriate Monte Carlo method. Furthermore, the authors also considered the prediction of future samples as well as the prediction interval. Lastly, a real-world example is presented in order to illustrate the effectiveness of the proposed methods.

关键词： Multiple interval censoring plan Bayesian prediction Exponentiated exponential distribution mcmc algorithm

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Research on recovering scattering obstacles in inhomogeneous medium based on Bayesian method

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APPLICABLE ANALYSIS 2024年第17期103卷 3197-3212页

作者： Yin, Weishi Shi, Xingyu Meng, Pinchao Qu, Fuheng Changchun Univ Sci & Technol Sch Math & Stat Changchun Peoples R China Changchun Univ Sci & Technol Sch Comp Sci & Technol Changchun Peoples R China

In this paper, the problem of acoustic wave scattering by obstacles in the two-dimensional inhomogeneous medium is considered. When the refractive index is a binary function, a hybrid method for reconstructing multiple impenetrable obstacles is proposed. The obstacle number is predicted based on the measured far-field data by using the neural network method. And then, it is used as the prior information of Bayesian method, the shape and position parameters of multiple obstacles are reconstructed using Markov chain Monte Carlo algorithm. The results of numerical experiments show that this method can effectively reconstruct the number, shape and position of obstacles in the inhomogeneous medium.

关键词： Inhomogeneous medium inverse obstacle scattering bayesian method mcmc algorithm

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Accounting for network noise in graph-guided Bayesian modeling of structured high-dimensional data

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BIOMETRICS 2024年第1期80卷 ujae012页

作者： Li, Wenrui Chang, Changgee Kundu, Suprateek Long, Qi Univ Penn Dept Biostat Epidemiol & Informat Philadelphia PA 19104 USA Indiana Univ Sch Med Dept Biostat & Hlth Data Sci Indianapolis IN 46202 USA Univ Texas MD Anderson Canc Ctr Dept Biostat Houston TX 77030 USA

There is a growing body of literature on knowledge-guided statistical learning methods for analysis of structured high-dimensional data (such as genomic and transcriptomic data) that can incorporate knowledge of underlying networks derived from functional genomics and functional proteomics. These methods have been shown to improve variable selection and prediction accuracy and yield more interpretable results. However, these methods typically use graphs extracted from existing databases or rely on subject matter expertise, which are known to be incomplete and may contain false edges. To address this gap, we propose a graph-guided Bayesian modeling framework to account for network noise in regression models involving structured high-dimensional predictors. Specifically, we use 2 sources of network information, including the noisy graph extracted from existing databases and the estimated graph from observed predictors in the dataset at hand, to inform the model for the true underlying network via a latent scale modeling framework. This model is coupled with the Bayesian regression model with structured high-dimensional predictors involving an adaptive structured shrinkage prior. We develop an efficient Markov chain Monte Carlo algorithm for posterior sampling. We demonstrate the advantages of our method over existing methods in simulations, and through analyses of a genomics dataset and another proteomics dataset for Alzheimer's disease.

关键词： adaptive Bayesian shrinkage latent scale network model mcmc algorithm noisy graph structured high-dimensional prediction

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On partially observed competing risks model for Chen distribution under generalized progressive hybrid censoring

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STATISTICA NEERLANDICA 2024年第1期78卷 105-135页

作者： Singh, Kundan Mahto, Amulya Kumar Tripathi, Yogesh Mani Indian Inst Technol Patna Dept Math Bihta India Indian Inst Technol Mandi Sch Math & Stat Sci Kamand India Indian Inst Technol Mandi Sch Math & Stat Sci Kamand 175005 India

In this paper, we discuss the inference for the competing risks model when the failure times follow Chen distribution. With assumption of two causes of failures, which are partially observed, are considered as independent. The existence and uniqueness of maximum likelihood estimates for model parameters are obtained under generalized progressive hybrid censoring. Also, we discussed the classical and Bayesian inferences of the model parameters under the assumption of restricted and nonrestricted parameters. Performance of classical point and interval estimators are compared with Bayesian point and interval estimators by conducting extensive simulation study. In addition to that, for illustration purpose, a real life example is discussed. Finally, some concluding remarks, regarding the presented model, are made.

关键词： asymptotic confidence interval Bayes estimates Chen distribution competing risk model generalized progressive hybrid censoring maximum likelihood estimation mcmc algorithm

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Compound negative binomial shared frailty model with random probability of susceptibility

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JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION 2024年第4期94卷 843-861页

作者： Dabade, A. D. Univ Mumbai Dept Stat Mumbai India

The shared frailty models are now popular for modelling heterogeneity in survival analysis. It assumes that the same frailty is shared by all individual members within the families. Also, it is believed that all the individuals in the population are susceptible to the event of interest and will eventually experience the event. This may not always be the situation in reality. There may be a certain fraction of the population which is non-susceptible for an event and hence may not experience the event under study. Non-susceptibility is modelled by frailty models with compound frailty distribution. Further, susceptibility may be different for different families. This can be attained by randomizing the parameter of frailty distribution. This paper incorporates both the things, non-susceptibility and different susceptibility for different families by considering compound negative binomial distribution with random probability of susceptibility as frailty distribution. The inferential problem is solved in a Bayesian framework using Markov Chain Monte Carlo methods. The proposed model is then applied to a real-life data set.

关键词： Bayesian estimation beta distribution compound negative binomial distribution shared frailty generalized exponential distribution mcmc algorithm

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Bayesian heterogeneous degradation performance modeling with an unknown number of sub-populations

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QUALITY AND RELIABILITY ENGINEERING INTERNATIONAL 2023年第7期39卷 2686-2705页

作者： Nguyen, Hung Sun, Xuxue Lu, Qing Zhang, Qiong Li, Mingyang Univ S Florida Dept Ind & Management Syst Engn Tampa FL USA Univ Zhejiang Coll Media Engn Commun Hangzhou Zhejiang Peoples R China Univ S Florida Dept Civil & Environm Engn Tampa FL USA Univ S Florida Dept Ind & Management Syst Engn 4202 E Fowler Ave Tampa FL 33620 USA

Successful modeling of degradation data is of great importance for both accurate reliability assessment and effective maintenance decision-making. Many of existing degradation performance modeling approaches either assume a homogeneous population of units or characterize a heterogeneous population with some restrictive assumptions, such as pre-specifying the number of sub-populations. This paper proposes a Bayesian heterogeneous degradation performance modeling framework to relax the conventional modeling assumptions. Specifically, a Bayesian non-parametric model formulation and learning algorithm are proposed to characterize the historical degradation data of a heterogeneous population of units with an unknown number of homogeneous sub-populations and allowing the joint model estimation and sub-population number identification. Based on the off-line population-level model, an on-line individual-level degradation model with sequential model updating is further developed to improve remaining useful life prediction of individual units with sparse data. A real case study using the heterogeneous degradation data of deteriorating roads is provided to illustrate the proposed approach and demonstrate its validity.

关键词： Bayesian approach degradation modeling heterogeneity mcmc algorithm sequential learning

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