E-Bayesian and H-Bayesian Inferences for a Simple Step-Stress Model with Competing Failure Model under Progressively...

Area of Science:

• Reliability Engineering
• Statistical Inference
• Accelerated Life Testing

Background:

• Competing failure modes are common in real-world systems.
• Progressive Type-II censoring is an efficient data collection method.
• Step-stress testing is used to accelerate failures and study product reliability.

Purpose of the Study:

• To statistically analyze a step-stress accelerated competing failure model.
• To derive and compare various parameter estimation methods.
• To evaluate the performance of different estimation techniques.

Main Methods:

• Utilized a simple step-stress accelerated competing failure model.
• Assumed exponential distribution for unit lifetimes under stress.
• Employed the cumulative exposure model to link stress levels.
• Derived Maximum Likelihood, Bayesian, Expected Bayesian, and Hierarchical Bayesian estimations.
• Conducted Monte Carlo simulations for analysis.

Main Results:

• Derived parameter estimations using Maximum Likelihood, Bayesian, Expected Bayesian, and Hierarchical Bayesian approaches.
• Evaluated confidence intervals and credible intervals using average length and coverage probability.
• Demonstrated superior performance of Expected Bayesian and Hierarchical Bayesian estimations.
• Numerical studies confirmed better average estimates and mean squared errors for these methods.

Conclusions:

• Expected Bayesian and Hierarchical Bayesian methods offer improved accuracy and efficiency in parameter estimation for this model.
• The study provides a robust framework for statistical inference in accelerated life testing with competing risks.
• Illustrates practical application through a numerical example.