Multi-component Reliability Inference in Modified Weibull Extension Distribution and Progressive Censoring Scheme.

Area of Science:

• Statistics
• Reliability Engineering
• Statistical Modeling

Background:

• Assessing the reliability of multi-component systems is crucial in engineering.
• Non-identical component strengths and progressive censoring present significant statistical challenges.
• The modified Weibull extension distribution offers a flexible model for complex reliability data.

Purpose of the Study:

• To statistically infer the reliability of a multi-component stress-strength system with non-identical components.
• To estimate the reliability parameter using both classical and Bayesian approaches under progressive censoring.
• To compare the performance of various estimation techniques.

Main Methods:

• Utilized the modified Weibull extension distribution for component strength modeling.
• Employed progressive censoring for sample data acquisition.
• Derived maximum likelihood estimation (MLE), uniformly minimum variance unbiased estimation (UMVUE), and Bayesian estimations (approximate and exact).
• Constructed asymptotic confidence intervals and highest posterior density (HPD) intervals.

Main Results:

• Developed and compared point and interval estimates for the system reliability parameter.
• Evaluated the performance of different estimators using Monte Carlo simulations.
• Assessed estimators based on mean squared error (MSE) and coverage probabilities.

Conclusions:

• The study provides a comprehensive framework for reliability inference in complex systems.
• Demonstrated the applicability of the proposed model and estimation techniques using a real-world data example.
• Offers valuable insights for practitioners in reliability engineering and statistical analysis.