A new age‐ and state‐dependent degradation process with possibly negative increments

Giorgio, Massimiliano; Pulcini, Gianpaolo

doi:10.1002/qre.2525

Cited by 13 publications

(6 citation statements)

References 15 publications

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“…From Giorgio and Pulcini, 20 the conditional pdf and Cdf of the RUL under the proposed WP (1) with bathtub shaped degradation rate function, given the degradation level w t at the current time t, are respectively given by:…”

Section: Remaining Useful Life and Reliabilitymentioning

confidence: 99%

A new Wiener process with bathtub‐shaped degradation rate in the presence of random effects

Giorgio

Piscopo

Pulcini³

2023

Appl Stoch Models Bus & Ind

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This paper proposes a new time scaled Wiener process with random effects that has been specially designed to allow the description of non‐monotonic degradation phenomena with bathtub shaped degradation rate, here intended as derivative of the mean function. Two different parameterizations of the proposed Wiener process are suggested, and the main features of the process are illustrated and discussed. The maximum likelihood estimation of its parameters is addressed. A failure threshold model is adopted to formulate and estimate the probability distribution function of the remaining useful life, which constitutes the core prognostic tool in condition‐based maintenance. As a motivating example, the proposed model is applied to a set of real degradation data of metal‐oxide‐semiconductor field‐effect transistors, where, as a result of preliminary analyses, some of the process parameters are assumed to be random in order to describe the considerable heterogeneity observed between the degradation paths of different units. Obtained results demonstrate the affordability and utility of the proposed model, especially for the estimation of unit‐specific features performed on the basis of degradation data collected in the early phase of the life of a unit belonging to the considered heterogeneous population.

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Section: Remaining Useful Life and Reliabilitymentioning

confidence: 99%

A new Wiener process with bathtub‐shaped degradation rate in the presence of random effects

Giorgio

Piscopo

Pulcini³

2023

Appl Stoch Models Bus & Ind

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“…Giorgio et al 34 also discussed a transformed gamma degradation process model with unit-to-unit variability. Similarly, Giorgio and Pulcini 35 proposed a transformed Wiener process degradation model, Peng et al 36 In this study, an improved ED process model considering the correlation between degradation increment and degradation state is established. The motivation to explore the improved ED process model comes from two papers, that is, Fan et al 29 and Guo et al 30 These two papers studied the improved gamma process model and improved IG process model, respectively, which are special cases of the improved ED process model proposed in this paper.…”

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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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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“…When the detected degradation path exceeds the failure threshold, the product will be declared to be a failure. In this situation, the commonly used degradation models include the regression model, 8,9 Wiener process, 10,11 gamma process, [12][13][14] inverse Gaussian (IG) process, [15][16][17] exponential dispersion (ED) process, [18][19][20] and so on. The latter considers that the observed degradation data can only partially represent the potential state of the product, and assumes that the observed degradation data is randomly correlated with the potential state.…”

Section: Introductionmentioning

confidence: 99%

Remaining useful life evaluation for accelerated Wiener degradation process model with mixed random effects and measurement errors

Duan

Wang

Wei

et al. 2023

Quality & Reliability Eng

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This paper evaluates the remaining useful life (RUL) for the accelerated Wiener process with mixed random effects and measurement errors. In the discussed model, the random effects are included in both the drift and diffusion parameters of the Wiener process to model the heterogeneity among different degradation paths of products. The measurement errors are introduced to describe the inaccuracy during the measurement process. The effect of the accelerated stress level is included in the drift parameter. The expectation-maximization (EM) algorithm is applied to obtain the estimation of the model parameters. The expressions of the probability density functions (PDFs) and cumulative distribution functions (CDFs) of the lifetime and RUL distributions of products under the normal usage stress level are derived theoretically. Finally, an example of stress relaxation data is used to illustrate the effectiveness of the developed model and method.

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A new age‐ and state‐dependent degradation process with possibly negative increments

Cited by 13 publications

References 15 publications

A new Wiener process with bathtub‐shaped degradation rate in the presence of random effects

A new Wiener process with bathtub‐shaped degradation rate in the presence of random effects

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

Remaining useful life evaluation for accelerated Wiener degradation process model with mixed random effects and measurement errors

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