Inference for depending competing risks from Marshall-Olikin bivariate Kies distribution under generalized...

Area of Science:

• Statistics
• Reliability Engineering
• Survival Analysis

Background:

• Competing risk models are essential for understanding systems with multiple failure modes.
• Dependent failure times complicate standard analysis, necessitating advanced statistical approaches.
• Generalized progressive hybrid censoring introduces challenges in parameter estimation.

Purpose of the Study:

• To develop and evaluate classical and Bayesian inference methods for a competing risk model with dependent failure causes.
• To investigate the Marshall-Olikin bivariate Kies distribution within this framework.
• To explore estimation under generalized progressive hybrid censoring and restricted parameter spaces.

Main Methods:

• Maximum Likelihood Estimation (MLE) for unknown parameters.
• Construction of approximate confidence intervals using the observed Fisher information matrix.
• Bayesian estimation utilizing a Gamma-Dirichlet prior distribution.
• Development of estimators under a priori order information on competing risk parameters.

Main Results:

• Established existence and uniqueness for maximum likelihood estimators.
• Developed approximate confidence intervals for model parameters.
• Derived Bayesian estimators under a flexible prior.
• Provided classical and Bayesian estimates for the restricted parameter case.
• Demonstrated the performance of proposed estimators through simulations and a real data example.

Conclusions:

• The proposed classical and Bayesian methods provide effective tools for analyzing competing risks with dependent failures under generalized progressive hybrid censoring.
• The study validates the applicability of the Marshall-Olikin bivariate Kies distribution in complex reliability scenarios.
• Simulation and real-data analyses confirm the practical utility and behavior of the developed estimators.