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Multi-component Reliability Inference in Modified Weibull Extension Distribution and Progressive Censoring Scheme.

Akram Kohansal1, Carlos J Pérez-González2, Arturo J Fernández2

  • 1Department of Statistics, Imam Khomeini International University, Qazvin, Iran.

Bulletin of the Malaysian Mathematical Sciences Society
|January 23, 2023
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Summary

This study estimates the reliability of multi-component systems using the modified Weibull extension distribution and progressive censoring. It compares classical and Bayesian estimation methods for improved system reliability analysis.

Keywords:
Bayes estimationClassical estimationMulti-component reliabilityProgressive censored

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Area of Science:

  • Statistics
  • Reliability Engineering
  • Statistical Modeling

Background:

  • Assessing the reliability of multi-component systems is crucial in engineering.
  • Non-identical component strengths and progressive censoring present significant statistical challenges.
  • The modified Weibull extension distribution offers a flexible model for complex reliability data.

Purpose of the Study:

  • To statistically infer the reliability of a multi-component stress-strength system with non-identical components.
  • To estimate the reliability parameter using both classical and Bayesian approaches under progressive censoring.
  • To compare the performance of various estimation techniques.

Main Methods:

  • Utilized the modified Weibull extension distribution for component strength modeling.
  • Employed progressive censoring for sample data acquisition.
  • Derived maximum likelihood estimation (MLE), uniformly minimum variance unbiased estimation (UMVUE), and Bayesian estimations (approximate and exact).
  • Constructed asymptotic confidence intervals and highest posterior density (HPD) intervals.

Main Results:

  • Developed and compared point and interval estimates for the system reliability parameter.
  • Evaluated the performance of different estimators using Monte Carlo simulations.
  • Assessed estimators based on mean squared error (MSE) and coverage probabilities.

Conclusions:

  • The study provides a comprehensive framework for reliability inference in complex systems.
  • Demonstrated the applicability of the proposed model and estimation techniques using a real-world data example.
  • Offers valuable insights for practitioners in reliability engineering and statistical analysis.