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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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Mechanistic models are utilized in individual analysis using single-source data, but imperfections arise due to data collection errors, preventing perfect prediction of observed data. The mathematical equation involves known values (Xi), observed concentrations (Ci), measurement errors (εi), model parameters (ϕj), and the related function (ƒi) for i number of values. Different least-squares metrics quantify differences between predicted and observed values. The ordinary least...
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Survival models analyze the time until one or more events occur, such as death in biological organisms or failure in mechanical systems. These models are widely used across fields like medicine, biology, engineering, and public health to study time-to-event phenomena. To ensure accurate results, survival analysis relies on key assumptions and careful study design.
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Parametric survival analysis models survival data by assuming a specific probability distribution for the time until an event occurs. The Weibull and exponential distributions are two of the most commonly used methods in this context, due to their versatility and relatively straightforward application.
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Updated: Jun 18, 2025

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Data analysis with applications in physics and engineering using XLindley model with improved adaptive Type-II

Refah Alotaibi1, Mazen Nassar2,3, Ahmed Elshahhat4

  • 1Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia.

Heliyon
|August 5, 2024
PubMed
Summary
This summary is machine-generated.

This study introduces an improved adaptive Type-II progressive censoring strategy for lengthy trials. Bayesian estimation with likelihood functions is superior for parameter estimation, while Bayesian methods with spacings functions are best for reliability metrics.

Keywords:
Bayesian estimationLikelihood estimationProduct of spacings estimationReliability measuresXLindley distribution

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Area of Science:

  • Statistics
  • Reliability Engineering
  • Survival Analysis

Background:

  • Adaptive Type-II progressive censoring is crucial for efficient data collection in long-term trials.
  • The XLindley distribution is a flexible model for analyzing lifetime data.
  • Accurate parameter and reliability estimations are vital for practical applications.

Purpose of the Study:

  • To investigate classical and Bayesian estimation methods for the XLindley distribution under an improved adaptive Type-II progressive censoring scheme.
  • To compare the performance of different estimation techniques for model parameters and reliability metrics.
  • To identify the optimal progressive censoring strategy using optimality criteria.

Main Methods:

  • Employed two classical estimation methods (e.g., Maximum Likelihood Estimation) for point and interval estimations.
  • Utilized Bayesian estimation with a squared error loss function and Markov chain Monte Carlo (MCMC) techniques.
  • Generated Bayes point and credible intervals based on two posterior distribution forms.

Main Results:

  • Simulation studies indicated that Bayesian estimation using the likelihood function outperformed classical methods for parameter estimation.
  • For reliability metrics, Bayesian estimation with the spacings function demonstrated superior performance.
  • Real-world data analysis validated the proposed methods and aided in selecting an optimal censoring strategy.

Conclusions:

  • The Bayesian approach offers significant advantages for estimating parameters and reliability metrics of the XLindley distribution under adaptive Type-II progressive censoring.
  • The choice between likelihood and spacings functions in Bayesian estimation depends on whether parameters or reliability metrics are the primary focus.
  • The study provides practical guidance for implementing advanced censoring strategies and estimation techniques in reliability analysis.