Reliability inference for multi-component stress-strength systems with heterogeneous Lomax-distributed components...

Area of Science:

• Reliability Engineering
• Statistical Inference
• Probability Distributions

Background:

• The m-component stress-strength parameter is crucial for system reliability assessment.
• Progressive first failure (PFF) censoring is a practical data collection scheme in reliability studies.
• The Lomax distribution is frequently used to model lifetime data due to its flexibility.

Purpose of the Study:

• To estimate the m-component stress-strength parameter under PFF censoring.
• To compare the performance of classical and Bayesian estimation methods.
• To analyze real-world datasets using the developed methodologies.

Main Methods:

• Maximum Likelihood Estimation (MLE) for parameter estimation.
• Bayesian estimation utilizing Markov Chain Monte Carlo (MCMC) and Lindley's approximation.
• Derivation of asymptotic confidence intervals and Highest Posterior Density (HPD) credible intervals.
• Uniformly Minimum Variance Unbiased Estimator (UMVUE) considered for known parameters.
• Monte Carlo simulation for performance evaluation.
• Real data analysis for practical illustration.

Main Results:

• Performance comparison of MLE and Bayesian methods under different scenarios.
• Evaluation of interval estimation techniques (confidence and credible intervals).
• Demonstration of the applicability of the methods on real-world stress-strength data.

Conclusions:

• The study provides a comprehensive framework for stress-strength reliability estimation under PFF censoring.
• Both classical and Bayesian approaches offer viable estimation strategies, with performance varying by scenario.
• The findings are applicable to engineering systems where component failures follow Lomax distribution and data is PFF censored.