Inference of progressively type-II censored competing risks data from Chen distribution with an application

Area of Science:

• Reliability Engineering
• Statistical Inference
• Survival Analysis

Background:

• The Chen distribution is a flexible model for lifetime data.
• Competing risks and progressive censoring are common in real-world reliability scenarios.
• Accurate parameter estimation is crucial for reliability assessment.

Purpose of the Study:

• To estimate unknown parameters of the Chen distribution under progressive Type-II censoring with competing failure causes.
• To compare frequentist and Bayesian estimation approaches.
• To evaluate the performance of different estimation and confidence interval methods.

Main Methods:

• Maximum Likelihood Estimation (MLE) using the Expectation-Maximization (EM) algorithm.
• Computation of the expected Fisher information matrix.
• Asymptotic and bootstrap confidence intervals (Bootstrap-p, Bootstrap-t).
• Bayesian estimation via Markov Chain Monte Carlo (MCMC) with various loss functions (squared error, LINEX, general entropy).

Main Results:

• The study provides point and interval estimates for Chen distribution parameters under complex censoring and competing risks.
• Performance evaluation through simulation demonstrates the effectiveness of the proposed methods.
• A real-life example illustrates the practical application of the developed techniques.

Conclusions:

• Both frequentist and Bayesian approaches offer viable methods for parameter estimation in this setting.
• The simulation study aids in selecting appropriate estimators and confidence intervals based on desired properties.
• The findings contribute to improved reliability analysis in the presence of progressive censoring and competing failure modes.