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The Wiener Process with a Random Non-Monotone Hazard Rate-Based Drift

Author

Listed:
  • Luis Alberto Rodríguez-Picón

    (Department of Industrial Engineering and Manufacturing, Institute of Engineering and Technology, Universidad Autónoma de Ciudad Juárez, Ciudad Juárez, Chihuahua 32310, Mexico)

  • Luis Carlos Méndez-González

    (Department of Industrial Engineering and Manufacturing, Institute of Engineering and Technology, Universidad Autónoma de Ciudad Juárez, Ciudad Juárez, Chihuahua 32310, Mexico)

  • Luis Asunción Pérez-Domínguez

    (Department of Industrial Engineering and Manufacturing, Institute of Engineering and Technology, Universidad Autónoma de Ciudad Juárez, Ciudad Juárez, Chihuahua 32310, Mexico)

  • Héctor Eduardo Tovanche-Picón

    (Department of Industrial Engineering and Manufacturing, Institute of Engineering and Technology, Universidad Autónoma de Ciudad Juárez, Ciudad Juárez, Chihuahua 32310, Mexico)

Abstract

Several variations of stochastic processes have been studied in the literature to obtain reliability estimations of products and systems from degradation data. As the degradation trajectories may have different degradation rates, it is necessary to consider alternatives to characterize their individual behavior. Some stochastic processes have a constant drift parameter, which defines the mean rate of the degradation process. However, for some cases, the mean rate must not be considered as constant, which means that the rate varies in the different stages of the degradation process. This poses an opportunity to study alternative strategies that allow to model this variation in the drift. For this, we consider the Hjorth rate, which is a failure rate that can define different shapes depending on the values of its parameters. In this paper, the integration of this hazard rate with the Wiener process is studied to individually identify the degradation rate of multiple degradation trajectories. Random effects are considered in the model to estimate a parameter of the Hjorth rate for every degradation trajectory, which allows us to identify the type of rate. The reliability functions of the proposed model is obtained through numerical integration as the function results in a complex form. The proposed model is illustrated in two case studies based on a crack propagation and infrared LED datasets. It is found that the proposed approach has better performance for the reliability estimation of products based on information criteria.

Suggested Citation

  • Luis Alberto Rodríguez-Picón & Luis Carlos Méndez-González & Luis Asunción Pérez-Domínguez & Héctor Eduardo Tovanche-Picón, 2024. "The Wiener Process with a Random Non-Monotone Hazard Rate-Based Drift," Mathematics, MDPI, vol. 12(17), pages 1-15, August.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:17:p:2613-:d:1462842
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    References listed on IDEAS

    as
    1. Massimiliano Giorgio & Fabio Postiglione & Gianpaolo Pulcini, 2020. "Bayesian estimation and prediction for the transformed Wiener degradation process," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 36(4), pages 660-678, July.
    2. Peihua Jiang, 2022. "Statistical Inference of Wiener Constant-Stress Accelerated Degradation Model with Random Effects," Mathematics, MDPI, vol. 10(16), pages 1-18, August.
    3. Zhou, Shirong & Tang, Yincai & Xu, Ancha, 2021. "A generalized Wiener process with dependent degradation rate and volatility and time-varying mean-to-variance ratio," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
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