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reliability Estimation from Linear Degradation and Failure Time Data With Competing Risks Under a Step-Stress Accelerated Degradation Test

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IEEE TRANSACTIONS ON reliability 2015年第3期64卷 960-971页

作者： Haghighi, Firoozeh Bae, Suk Joo Univ Tehran Dept Math Stat & Comp Sci Tehran Iran Hanyang Univ Dept Ind Engn Seoul 133791 South Korea

The accelerated degradation test (ADT) has become critical for product reliability assessment. In performing the ADT for newly developed products, a constant-stress ADT may be impractical or sometimes impossible where the available size of testing units and the testing duration are heavily bounded to meet the short development period of the products. As an alternative, a step-stress accelerated degradation test (SSADT) can be a useful tool for satisfying the test limitation, and for making up for uncertainty in selecting appropriate levels of stress. Occasionally, the elevated stress under SSADT not only accelerates the performance degradation of products, but it may also expedite traumatic failures. This paper proposes a modeling approach to simultaneously analyze linear degradation data and traumatic failures with competing risks in an SSADT experiment. Under the modeling approach, a cumulative exposure model is considered. The failure rate corresponding to each failure mode is described as a function of the degradation level at the moment of failure. No parametric assumptions are made regarding the failure-time distribution to extend the proposed method to more general cases. We derive maximum likelihood estimates of the model parameters, then estimate failure rates and product reliability based on the degradation level to failure. Asymptotic properties of the maximum likelihood estimates are also discussed. The proposed model is applied to accelerated degradation data from plastic substrate active matrix light-emitting diodes (AMOLEDs), along with sensitivity analysis.

关键词： Accelerated degradation tests competing risk conditional reliability function cumulative exposure model step-stress

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Optimal Control of Partially Observable Semi-Markovian Failing Systems: An Analysis Using a Phase Methodology

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OPERATIONS RESEARCH 2021年第4期69卷 1282-1304页

作者： Khaleghei, Akram Kim, Michael Jong Univ Toronto Rotman Sch Business Toronto ON M5S 3E6 Canada Univ British Columbia Sauder Sch Business Columbia BC V6T 1Z2 Canada

We formulate a maintenance control model as an optimal stopping problem under partial observations. The key challenge in our formulation is that the underlying state process is not restricted to be Markovian but rather is allowed to follow a semi-Markov process, which is more realistic in practice. Consequently, the stopping problem is not representable as a partially observable Markov decision process (POMDP) with finite state space, a commonly adopted modeling framework in the maintenance optimization literature;it constitutes a partially observable semi-Markov decision process (POSMDP), a problem class that in general is both computationally intractable and not amenable to structural analysis. In this paper, we develop a new analysis approach based on a phase methodology where the idea is to view the intractable POSMDP as the limiting problem of a sequence of tractable POMDPs. We show how this approach allows us to (i) characterize the structural form of the optimal policy and (ii) efficiently compute the optimal policy and associated optimal value via successive approximation. In particular, we show that the optimal control policy can be represented as a control limit policy that monitors the estimated conditional reliability at each decision epoch, and, by exploiting this structure, we develop an efficient computational approach to solve for the optimal control limit and corresponding optimal value. Numerical comparisons are provided that show substantial improvement over existing policies.

关键词： condition-based maintenance partially observable semi-Markov decision process likelihood ratio ordering Bayesian control chart conditional reliability function

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reliability of the bi-stable piezoelectric energy harvester under random excitation

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JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES 2023年第12期34卷 1378-1388页

作者： Dong, Hao Du, Lin Hu, Rongchun Zhang, Shuo Deng, Zichen Northwestern Polytech Univ Sch Math & Stat Xian Peoples R China MIIT Key Lab Dynam & Control Complex Syst Xian Peoples R China Northwestern Polytech Univ Sch Mech Civil Engn & Architecture Xian Peoples R China Northwestern Polytech Univ Sch Math & Stat Changan Campus Xian 710129 Shaanxi Peoples R China

The bi-stable piezoelectric energy harvester can produce higher voltage and efficiency than traditional energy harvester. In this manuscript, the reliability of the bi-stable piezoelectric energy harvester excited by Gaussian white noise is investigated. The equivalent uncoupled equation of system is deduced on the basis of the generalized harmonic transformation for the bi-stable piezoelectric energy harvester original coupling system. The averaged stochastic differential equation for system energy of the equivalent uncoupled system is established using the stochastic averaging method. The conditional reliability function and the mean first-passage time are derived through the backward Kolmogorov equation and the generalized Pontryagin equation associated with the averaged stochastic differential equation. The influences of noise intensity, electromechanical coupling coefficient, and time constant ratio on the conditional reliability function and mean first-passage time are discussed. The analytical results are highly consistent with the numerical results that are obtained by the Monte Carlo numerical simulation.

关键词： Piezoelectric energy harvester generalized harmonic transformation conditional reliability function first-passage time

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Dynamical reliability of internally resonant or non-resonant strongly nonlinear system under random excitations

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MECHANICAL SYSTEMS AND SIGNAL PROCESSING 2019年 118卷 767-780页

作者： Wu, Yongjun Shanghai Jiao Tong Univ Sch Naval Architecture Ocean & Civil Engn Dept Engn Mech Shanghai 200240 Peoples R China

The dynamical reliability of multi-degrees-of-freedom (MDOF) strongly nonlinear system under Gaussian white noise excitations is studied, including resonance and nonresonance. Firstly, the equations of motion of the original system with or without internal resonance are reduced to a set of Ito stochastic differential equations after stochastic averaging. Then, the backward Kolmogorov equation and the Pontryagin equation associated with the resonantly or non-resonantly averaged Ito stochastic differential equations, which determine the conditional reliability function and the mean first-passage time of the original random system, are constructed under appropriate boundary and (or) initial conditions, respectively. In particular, if the non-resonantly averaged system is completely decoupled, the conditional reliability function and the mean first-passage time of the original nonresonant system can be obtained by solving a set of simplified backward Kolmogorov equations. A system comprising two weakly coupled and strongly nonlinear mechanical oscillators is given as a concrete example to show the application of the proposed method. The 1:1 internal resonance or non-resonance is discussed. The corresponding high-dimensional backward Kolmogorov equation and Pontryagin equation are established and solved numerically. All theoretical results are validated by a Monte Carlo digital simulation. (C) 2018 Elsevier Ltd. All rights reserved.

关键词： Gaussian white noise Internal resonance Stochastic averaging method conditional reliability function Mean first- passage time

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reliability estimation of a system subject to condition monitoring with two dependent failure modes

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IIE TRANSACTIONS 2016年第11期48卷 1058-1071页

作者： Khaleghei, Akram Makis, Viliam Univ Toronto Dept Mech & Ind Engn Toronto ON Canada

A new competing risk model is proposed to calculate the conditional Mean Residual Life (CMRL) and conditional reliability function (CRF) of a system subject to two dependent failure modes, namely, degradation failure and catastrophic failure. The degradation process can be represented by a three-state continuous-time stochastic process having a healthy state, a warning state, and a failure state. The system is subject to condition monitoring at regular sampling times that provides partial information about the system is working state and only the failure state is observable. To model the dependency between two failure modes, it is assumed that the joint distribution of the time to catastrophic failure and sojourn time in the healthy state follow Marshal-Olkin bivariate exponential distributions. The Expectation-Maximization algorithm is developed to estimate the model's parameters and the explicit formulas for the CRF and CMRL are derived in terms of the posterior probability that the system is in the warning state. A comparison with a previously published model is provided to illustrate the effectiveness of the proposed model using real data.

关键词： Competing risk conditional reliability function dependent failure modes Expectation-Maximization algorithm mean residual life

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An Advanced Framework for Predictive Maintenance Decisions: Integrating the Proportional Hazards Model and Machine Learning Techniques under CBM Multi-Covariate Scenarios

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APPLIED SCIENCES-BASEL 2024年第13期14卷 5514页

作者： Godoy, David R. Mavrakis, Constantino Mena, Rodrigo Kristjanpoller, Fredy Viveros, Pablo Univ Tecn Federico Santa Maria Dept Ind Engn Predict Lab Ave Santa Maria 6400 Santiago 7630000 Chile

Under Condition-Based Maintenance, the Proportional Hazards Model (PHM) uses Cox's partial regression and vital signs as covariates to estimate risk for predictive management. However, maintenance faces challenges when dealing with a multi-covariate scenario due to the impact of the conditions' heterogeneity on the intervention decisions, especially when the combined measurement lacks a physical interpretation. Therefore, we propose an advanced framework based on a PHM-machine learning formulation integrating four key areas: covariate prioritization, covariate weight estimation, state band definition, and the generation of an enhanced predictive intervention policy. The paper validates the framework's effectiveness through a comparative analysis of reliability metrics in a case study using real condition monitoring data from an energy company. While the traditional log-likelihood minimization may fall short in covariate weight estimation, sensitivity analyses reveal that the proposed policy using IPOPT and a non-scaler transformation results in consistent prediction quality. Given the challenge of interpreting merged covariates, the scheme yields improved results compared to expert criteria. Finally, the advanced framework strengthens the PHM modeling by coherently integrating diverse covariate scenarios for predictive maintenance purposes.

关键词： proportional hazards model condition-based maintenance multi-covariate scenarios machine learning conditional reliability function remaining useful life predictive maintenance decisions

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A recursive method for the health assessment of systems using the proportional hazards model

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reliability ENGINEERING & SYSTEM SAFETY 2022年第0期221卷 108379-108379页

作者： Zheng, Rui Najafi, Seyedvahid Zhang, Yingzhi Hefei Univ Technol Sch Management Hefei 230009 Peoples R China Univ Toronto Dept Mech & Ind Engn Toronto ON M5S 3G8 Canada Jilin Univ Sch Mech & Aerosp Engn Changchun 130022 Peoples R China

The failure of many practical systems is dependent on both age and a diagnostic covariate process. Cox's proportional hazards model is widely adopted to describe the failure rate of such systems. If the covariate state space is large, it is computationally not feasible to use an analytical method for health assessment at inspection epochs. Existing approximation methods, although can address the above problem, fail to satisfy the critical requirements of modern health management in terms of accuracy, memory storage, and computational speed. This paper develops a novel recursive method to approximately assess the health indices of the proportional hazards model with a Markovian covariate process. The method discretizes age into equidistant and small subintervals. Over each subinterval, an incomplete state transition matrix is constructed with each element measured by its upper and lower bounds. The consideration of dual bounds makes our model more robust than previous methods considering only an upper bound. Then the recursive formulas of various health indices are derived based on the matrixes of consecutive subintervals. Two practical examples demonstrate that the proposed method can produce accurate assessment results with higher efficiency and less memory compared with existing approximation methods.

关键词： Health assessment Mean residual life Proportional hazards model Recursive method conditional reliability function

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