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A new gamma degradation process with random effect and state-dependent measurement error

Author

Listed:
  • Nicola Esposito
  • Agostino Mele
  • Bruno Castanier
  • Massimiliano Giorgio

Abstract

In this paper, a new gamma-based degradation process with random effect is proposed that allows to account for the presence of measurement error that depends in stochastic sense on the measured degradation level. This new model extends a perturbed gamma model recently suggested in the literature, by allowing for the presence of a unit to unit variability. As the original one, the extended model is not mathematically tractable. The main features of the proposed model are illustrated. Maximum likelihood estimation of its parameters from perturbed degradation measurements is addressed. The likelihood function is formulated. Hence, a new maximization procedure that combines a particle filter and an expectation-maximization algorithm is suggested that allows to overcome the numerical issues posed by its direct maximization. Moreover, a simple algorithm based on the same particle filter method is also described that allows to compute the cumulative distribution function of the remaining useful life and the conditional probability density function of the hidden degradation level, given the past noisy measurements. Finally, two numerical applications are developed where the model parameters are estimated from two sets of perturbed degradation measurements of carbon-film resistors and fuel cell membranes. In the first example the presence of random effect is statistically significant while in the second example it is not significant. In the applications, the presence of random effect is checked via appropriate statistical procedures. In both the examples, the influence of accounting for the presence of random effect on the estimates of the cumulative distribution function of the remaining useful life of the considered units is also discussed. Obtained results demonstrate the affordability of the proposed approach and the usefulness of the proposed model.

Suggested Citation

  • Nicola Esposito & Agostino Mele & Bruno Castanier & Massimiliano Giorgio, 2023. "A new gamma degradation process with random effect and state-dependent measurement error," Journal of Risk and Reliability, , vol. 237(5), pages 868-885, October.
  • Handle: RePEc:sae:risrel:v:237:y:2023:i:5:p:868-885
    DOI: 10.1177/1748006X211067299
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    References listed on IDEAS

    as
    1. Hao, Songhua & Yang, Jun & Berenguer, Christophe, 2019. "Degradation analysis based on an extended inverse Gaussian process model with skew-normal random effects and measurement errors," Reliability Engineering and System Safety, Elsevier, vol. 189(C), pages 261-270.
    2. Rensheng Zhou & Nagi Gebraeel & Nicoleta Serban, 2012. "Degradation modeling and monitoring of truncated degradation signals," IISE Transactions, Taylor & Francis Journals, vol. 44(9), pages 793-803.
    3. Giorgio, Massimiliano & Pulcini, Gianpaolo, 2018. "A new state-dependent degradation process and related model misidentification problems," European Journal of Operational Research, Elsevier, vol. 267(3), pages 1027-1038.
    4. Laurent Bordes & Christian Paroissin & Ali Salami, 2016. "Parametric inference in a perturbed gamma degradation process," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(9), pages 2730-2747, May.
    Full references (including those not matched with items on IDEAS)

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