Multicomponent Stress-Strength Model Based on Generalized Progressive Hybrid Censoring Scheme: A Statistical...

Area of Science:

• Reliability analysis
• Statistical inference
• Probability distributions

Background:

• The stress-strength (S-S) model is crucial in reliability analysis.
• Generalized progressive hybrid censoring (GPHC) is a common data collection scheme.
• Multicomponent stress-strength (MSS) models analyze systems with multiple stress and strength variables.

Purpose of the Study:

• To estimate reliability and parameters of the MSS model under GPHC.
• To compare different estimation methods including Maximum Likelihood Estimation (MLE) and Bayesian Estimation (BE).
• To evaluate the performance of various confidence intervals.

Main Methods:

• Assumed stress follows Chen distribution and strength follows Gompertz distribution.
• Employed Newton-Raphson method for MLE and constructed Asymptotic Confidence Intervals (ACI) and Exact Confidence Intervals (ECI).
• Utilized hybrid Markov Chain Monte Carlo (MCMC) for Bayesian Estimation (BE) and High Posterior Density Credible Intervals (HPDCI).

Main Results:

• Simulation studies compared MLE and BE using bias and Mean Squared Error (MSE).
• Interval estimates (ACI, ECI, HPDCI) were compared using Average Interval Length (AIL) and Coverage Probability (CP).
• Performance metrics indicated the effectiveness of the proposed estimation techniques.

Conclusions:

• The study provides robust statistical inference for MSS models under GPHC.
• Both MLE and BE methods offer valuable insights into system reliability.
• The findings contribute to the advancement of reliability engineering and statistical analysis.