Exponential Dispersion Process for Degradation Analysis

Zhou, Shirong; Xu, Ancha

doi:10.1109/tr.2019.2895352

Cited by 46 publications

(21 citation statements)

References 43 publications

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“…The accuracy of the approximation method has been discussed in Duan and Wang 22 and Zhou and Xu. 23 The approximation results are exact in several special cases, such as the normal, IG distributions. In other cases, the approximation results are also accurate.…”

Section: Regular Ed Process Modelmentioning

confidence: 96%

“…Duan and Wang 22 gave a saddlepoint approximation of the probability density function (PDF) of the ED distribution, and evaluated the lifetime and residual lifetime of products based on the ED process with covariates and random effects. Zhou and Xu 23 built a nonlinear ED degradation process model. Chen et al 24 studied the ED degradation process model with a random drift parameter and measurement error, and Chen et al 25 further discussed the optimal degradation-based burn-in policy using the ED process model with measurement error.…”

Section: Introductionmentioning

confidence: 99%

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Generalized exponential‐dispersion process model for degradation analysis under nonlinear condition

Duan

Wang

2021

Quality & Reliability Eng

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The regular exponential-dispersion (ED) process with a nonlinear path can be used to model degradation processes of many products, while it has the shortage that the degradation increment is only age-dependent, which limits its application in some circumstances. To overcome this shortage, two extensions of the ED process are suggested. For many degradation phenomena with selfmodulating mechanisms, the degradation increment during the next time interval may depend on the current degradation state. To describe this degradation phenomenon, an improved ED process model with state-dependent degradation increment and a nonlinear path is proposed. Further, as an extension of the regular ED process and the improved ED process models, the generalized improved ED process is introduced, in which the degradation increment during an interval is both age-and state-dependent. For the three discussed models, the MLE method is applied to estimate the model parameters. The numerical integration and Monte Carlo (MC) simulation methods are used to evaluate the reliability.Finally, two sets of fatigue crack size data are used to illustrate the proposed models and methods.

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Section: Regular Ed Process Modelmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

Generalized exponential‐dispersion process model for degradation analysis under nonlinear condition

Duan

Wang

2021

Quality & Reliability Eng

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“…To compensate for that, the potential of the Tweedie exponential dispersion (TED) model, a variant of exponential dispersion models, whose variance function has power exponential form, has been investigated. Actually, the three first processes mentioned are shown to be special cases of TED process with specific values of the exponent in the power form of the variance function [19,20]. is ability to model several types of process, to be more generic, is of particular interest for our study since complicated degradation mechanisms are observed.…”

Section: Introductionmentioning

confidence: 99%

Durability and Reliability Estimation of Flax Fiber Reinforced Composites Using Tweedie Exponential Dispersion Degradation Process

Yan

Riahi

Benzarti

et al. 2021

Mathematical Problems in Engineering

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Flax fiber reinforced composites are demonstrating promising outcomes which make them potential candidates to replace synthetic composites in various industrial applications. However, there is limited information regarding their long-term performance, and it is usually acknowledged that natural fibers are less resistant than their synthetic counterparts. In this context, it is crucial to study their durability before considering their use for structural rehabilitation and strengthening in construction. This research aims to study and predict the performance of flax fiber reinforced polymer (FFRP) composites with a biobased epoxy matrix. The test program consists in exposing FFRP laminates and FFRP strengthened concrete slabs to different accelerated ageing conditions over a total period of two years. In the present study, not a single stress variable but various combinations and coupling of two environmental stress variables, temperature (T) and relative humidity (RH), are considered, thereby distinguishing this study from most of the works reported in the literature. Then, a series of mechanical destructive tests are performed periodically on aged samples to evaluate property evolutions over ageing time. The collected experimental data are analyzed to develop a performance evolution model and to evaluate the service lifetime performance of this new biobased FFRP composite. For that, the potential of the Tweedie exponential dispersion (TED) process model, which takes some famous stochastic processes (Wiener process, Gamma process, and inverse Gaussian process) as special cases, is investigated. The TED process modeling, particularly interesting in the cases of complicated degradation mechanisms, is written here for destructive tests and, finally, a reliability analysis based on the TED process model determined is carried out in order to update the FRP design equations provided by international codes in the specific case of FFRP.

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“…Birnbaum and Mccarty 21 further developed this model. Some literatures have studied inferential procedures of the reliability

R

under different stress and strength distributions, for example, normal distribution, 22, 23 Weibull distribution, 24–26 , Burr XII distribution, 27 Gamma distribution, 28 generalized exponential distribution, 29, 30 IG distribution, 31 among others. Kotz et al 32 provided many results and applications for stress–strength model.…”

Section: Introductionmentioning

confidence: 99%

Interval estimation for inverse Gaussian distribution

Wang

Pan

et al. 2021

Quality & Reliability Eng

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In this paper, we consider interval estimation for the inverse Gaussian (IG) distribution. Using generalized pivotal quantity method, we derive the generalized confidence intervals (GCIs) for the model parameters and some quantities such as the quantile, the reliability function of the lifetime, the failure rate function, and the mean residual lifetime. We verify that the GCI of the scale parameter is the same as its commonly used exact CI. We also obtain the generalized prediction intervals (GPIs) for future failure times based on the observed failure data set. In addition, we get the GCI for the reliability of the stress–strength model when the stress and strength variables follow the IG distributions with different parameters. We compare the proposed GCIs and GPIs with the Wald CIs and bootstrap‐p CIs by simulation. The simulation results show that the proposed GCIs and GPIs are superior to the Wald CIs and the bootstrap‐p CIs in terms of the coverage probability. Finally, two examples are used to illustrate the proposed procedures.

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Exponential Dispersion Process for Degradation Analysis

Cited by 46 publications

References 43 publications

Generalized exponential‐dispersion process model for degradation analysis under nonlinear condition

Generalized exponential‐dispersion process model for degradation analysis under nonlinear condition

Durability and Reliability Estimation of Flax Fiber Reinforced Composites Using Tweedie Exponential Dispersion Degradation Process

Interval estimation for inverse Gaussian distribution

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