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Survival analysis is a statistical method used to analyze time-to-event data, often employed in fields such as medicine, engineering, and social sciences. One of the key challenges in survival analysis is dealing with incomplete data, a phenomenon known as "censoring." Censoring occurs when the event of interest (such as death, relapse, or system failure) has not occurred for some individuals by the end of the study period or is otherwise unobservable, and it might have many different...
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Bayesian and non-bayesian analysis for stress-strength model based on progressively first failure censoring with

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Summary

This study estimates reliability using Bayesian and non-Bayesian methods for progressively censored data. Both methods provide effective estimators for reliability (P[T < Q]) under Burr distributions, with MCMC for Bayesian approaches.

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Area of Science:

  • Statistics
  • Reliability Engineering
  • Probability Theory

Background:

  • Estimating reliability is crucial for system performance and safety.
  • Progressively first-failure censored data is common in reliability studies.
  • The Burr III and Burr XII distributions are frequently used to model stress-strength relationships.

Purpose of the Study:

  • To estimate the reliability parameter ϑ = P [T < Q] using both Bayesian and non-Bayesian approaches.
  • To compare the performance of different estimators under progressive censoring.
  • To apply the developed methods to real-world data.

Main Methods:

  • Maximum Likelihood Estimation (MLE) for non-Bayesian approach.
  • Bayesian estimation using non-informative and informative priors under different loss functions.
  • Construction of confidence and credible intervals using delta method, asymptotic normality, and Markov Chain Monte Carlo (MCMC) techniques.
  • Monte Carlo simulations for performance evaluation.

Main Results:

  • Both Bayesian and non-Bayesian estimators for ϑ were derived.
  • Confidence and credible intervals were constructed for the estimators.
  • Numerical analysis via Monte Carlo simulations demonstrated the effectiveness of the proposed estimators.
  • An application to real data was investigated for practical illustration.

Conclusions:

  • The study successfully developed and compared Bayesian and non-Bayesian methods for reliability estimation.
  • The proposed estimators are effective for progressively first-failure censored data from Burr distributions.
  • MCMC techniques are valuable for obtaining accurate Bayesian estimates and credible intervals.