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Combining Generalized Renewal Processes with Non-Extensive Entropy-Based q-Distributions for Reliability

Isis Didier Lins1,2, Márcio Das Chagas Moura1,2, Enrique López Droguett1,3,4

  • 1Center for Risk Analysis and Environmental Modeling-CEERMA, Universidade Federal de Pernambuco, Recife PE 50740-550, Brazil.

Entropy (Basel, Switzerland)
|December 3, 2020
PubMed
Summary
This summary is machine-generated.

This study introduces new Generalized Renewal Process (GRP) models using q-Exponential and q-Weibull distributions for enhanced repairable system reliability analysis. These novel models offer improved data fitting, especially for extreme values and complex failure patterns.

Keywords:
generalized renewal processparticle swarm optimizationq-Exponential distributionq-Weibull distributionreliability analysis

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Area of Science:

  • Reliability Engineering
  • Statistical Modeling
  • Non-extensive Statistical Mechanics

Background:

  • The Generalized Renewal Process (GRP) is a key probabilistic model for repairable systems, often combined with the Weibull distribution.
  • Existing models may have limitations in capturing complex failure intensity behaviors and handling extreme data values.

Purpose of the Study:

  • To develop novel GRP models utilizing Tsallis' non-extensive entropy-based q-Exponential and q-Weibull distributions.
  • To enhance the modeling capabilities for repairable systems, particularly for data with extreme values and diverse failure patterns.
  • To provide advanced alternatives to the traditional Weibull-GRP model.

Main Methods:

  • Development of Generalized Renewal Process (GRP) models incorporating q-Exponential and q-Weibull probability distributions.
  • Parameter estimation using the maximum likelihood method.
  • Optimization via a particle swarm algorithm and validation through Monte Carlo simulations.

Main Results:

  • The q-Exponential-GRP serves as an alternative to the Weibull-GRP, adept at handling extreme values due to its power-law behavior.
  • The q-Weibull-GRP generalizes existing models, capable of fitting decreasing, constant, increasing, bathtub-shaped, and unimodal failure intensity functions.
  • Application to complex system reliability data demonstrated the efficacy of the proposed models.

Conclusions:

  • The integration of q-distributions with GRP offers a powerful and flexible framework for analyzing repairable systems.
  • These novel models provide superior performance in fitting diverse and complex reliability data compared to traditional methods.
  • The developed q-distribution-based GRP models are promising for advanced reliability analysis of complex systems.