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On multicomponent stress-strength reliability for progressively censored logistic exponential model.

Amulya Kumar Mahto1, Kumar Abhishek2, Yogesh Mani Tripathi2

  • 1Mehta Family School of Data Science and Artificial Intelligence, Indian Institute of Technology Guwahati, Assam 781039, India.

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Summary

This study estimates the reliability of multicomponent stress-strength (MSS) models using progressively censored data. It introduces new methods for logistic exponential distributions, offering improved reliability assessment for complex products.

Keywords:
62F1062F1562N02Bayes estimationCredible intervalsLindley approximationMaximum likelihood estimationProgressive censoring scheme

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Area of Science:

  • Engineering
  • Statistics
  • Reliability Engineering

Background:

  • Modern technological advancements result in complex, multi-component products.
  • Assessing the reliability of these products before market launch is challenging.
  • Reliability estimation is crucial for product quality and consumer safety.

Purpose of the Study:

  • To develop and evaluate methods for reliability estimation in multicomponent stress-strength (MSS) models.
  • To apply these methods to progressively censored data using logistic exponential distributions.
  • To compare classical and Bayesian estimation techniques for MSS reliability.

Main Methods:

  • Utilizing classical and Bayesian estimation procedures.
  • Modeling component failures with logistic exponential distributions.
  • Employing progressively censored data for reliability analysis.
  • Deriving maximum likelihood estimators and constructing asymptotic intervals.
  • Applying Lindley approximation and Markov chain Monte Carlo (MCMC) for Bayesian inference.

Main Results:

  • Point and interval estimators for MSS reliability were derived under different scenarios (known/unknown common shape parameter).
  • Bayesian credible intervals were constructed using Lindley approximation and MCMC methods.
  • A simulation study demonstrated the performance of the proposed estimators.
  • The methods were illustrated using a real-world dataset.

Conclusions:

  • The study provides robust methods for reliability estimation in MSS models with logistic exponential distributions.
  • Both classical and Bayesian approaches offer valuable insights into product reliability.
  • The findings are applicable to manufacturers needing to assess complex product reliability.