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Inference under balanced joint progressive type-II censoring scheme.

Kundan Singh1, Chandrakant Lodhi2, Yogesh Mani Tripathi3

  • 1Brij Disa Centre for Data Science and Artificial Intelligence, Indian Institute of Management Ahmedabad, Ahmedabad, India.

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Summary

This study introduces new statistical methods for analyzing bathtub-shaped hazard rate data using joint progressive censoring. The research provides reliable parameter estimation and interval calculations for the Chen distribution.

Keywords:
62N0162N0262N05Balanced joint progressive censoringBeta-Dirichlet priorChen distributionimportance samplingmaximum likelihood estimation

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Area of Science:

  • Statistics
  • Reliability Engineering
  • Survival Analysis

Background:

  • Bathtub-shaped hazard rates model non-monotone failure patterns common in reliability and survival studies.
  • Joint progressive censoring schemes offer efficient data collection strategies in life testing experiments.
  • The Chen distribution is a flexible model for various lifetime data patterns.

Purpose of the Study:

  • To develop statistical inference procedures for populations with bathtub-shaped hazard rates under a balanced joint progressive type-II censoring scheme.
  • To estimate model parameters using both maximum likelihood and Bayesian approaches.
  • To assess the practical applicability and performance of the proposed methods.

Main Methods:

  • Utilizing a balanced joint progressive type-II censoring scheme.
  • Applying maximum likelihood estimation (MLE) to determine point and interval estimates.
  • Employing Bayesian estimation with importance sampling under general prior distributions.
  • Establishing the existence and uniqueness of MLEs.
  • Constructing asymptotic confidence intervals and bootstrap intervals.
  • Obtaining Bayesian estimates and highest posterior density (HPD) intervals.

Main Results:

  • The existence and uniqueness of maximum likelihood estimators were proven.
  • Asymptotic and bootstrap-based intervals were developed for parameter estimation.
  • Bayesian estimates and HPD intervals were derived using importance sampling.
  • Extensive Monte Carlo simulations demonstrated the performance of Bayesian estimators compared to classical ones.
  • A real-world data example validated the practical utility of the proposed methods.

Conclusions:

  • The developed methods provide effective tools for analyzing bathtub-shaped hazard rate data under joint progressive censoring.
  • Both maximum likelihood and Bayesian approaches yield reliable parameter estimates and confidence intervals.
  • The study confirms the practical applicability of the proposed statistical inference techniques in reliability and survival analysis.