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First Passage Time of a Lévy Degradation Model with Random Effects

Author

Listed:
  • Narayanaswamy Balakrishnan

    (McMaster University Hamilton)

  • Chengwei Qin

    (McMaster University Hamilton)

Abstract

This paper introduces the weighted-convolution Lévy degradation process motivated by a multiple-sensor system. To estimate the first passage time (FPT) of this degradation model, the method based on inverse Laplace transform and the saddlepoint approximation is proposed to obtain the certain percentile of the FPT distribution which is generally taken as an important index regarding product reliability. Although the likelihood function of such a process is usually intractable because of its complexity, the parameter estimation can be alternatively realized by the generalized method of moments (GMM). As an example, the degradation model is assumed as the weighted convolution of two differently parameterized gamma processes incorporating random effects and its efficiency and applicability are evaluated by simulations and empirical data analysis.

Suggested Citation

  • Narayanaswamy Balakrishnan & Chengwei Qin, 2019. "First Passage Time of a Lévy Degradation Model with Random Effects," Methodology and Computing in Applied Probability, Springer, vol. 21(1), pages 315-329, March.
    • Handle: RePEc:spr:metcap:v:21:y:2019:i:1:d:10.1007_s11009-018-9657-9
    DOI: 10.1007/s11009-018-9657-9
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    References listed on IDEAS

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