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Dependent Competing Failure Processes in Reliability Systems.

Jewgeni H Dshalalow1, Hend Aljahani1, Ryan T White1

  • 1Department of Mathematical Science, College of Engineering and Science, Florida Institute of Technology, Melbourne, FL 32901, USA.

Entropy (Basel, Switzerland)
|June 26, 2024
PubMed
Summary
This summary is machine-generated.

This study models system reliability under three shock types: harmless, critical, and extreme. It provides a closed-form distribution for system failure, crucial for reliability engineering.

Keywords:
N-critical shocks systemclosed formcompeting failure processesdiscrete operational calculusextreme shocksfailure timefluctuation theorymultiple δ-shocksprefailure timerandom walkreliability function

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Area of Science:

  • Reliability Engineering
  • Stochastic Processes
  • System Dynamics

Background:

  • Complex systems face multiple failure modes from various shock types.
  • Understanding competing failure processes is vital for accurate reliability assessment.
  • Existing models may not capture the interplay of different shock magnitudes and timings.

Purpose of the Study:

  • To develop a comprehensive reliability model for systems subjected to three distinct shock types.
  • To derive a closed-form joint distribution for key system failure characteristics.
  • To analyze a modified system with restricted shock lag conditions.

Main Methods:

  • Modeling the system as a generalized random walk process.
  • Utilizing an advanced discrete operational calculus approach.
  • Employing Monte Carlo simulation for validation.

Main Results:

  • A closed-form joint distribution of time-to-failure, shock counts, and cumulative damage is obtained.
  • The system's reliability function is derived from the marginal distribution of failure time.
  • Analytical tractability of the derived formulas is demonstrated.

Conclusions:

  • The study provides a robust analytical framework for systems with competing failure shock processes.
  • The derived formulas offer precise predictions for system reliability and failure characteristics.
  • The model's validity is confirmed through simulation, enhancing its practical applicability.