Stress-strength reliability estimation involving paired observation with ties using bivariate exponentiated...

Area of Science:

• Statistics
• Reliability Engineering
• Probability Theory

Background:

• Component reliability is crucial in engineering, influenced by stress and strength.
• Paired observations with ties present unique analytical challenges in reliability studies.
• Existing models may not adequately address continuous data with tied scores.

Purpose of the Study:

• To develop statistical methods for estimating stress-strength reliability with paired, tied data.
• To introduce and analyze a bivariate extension of the exponentiated half-logistic distribution.
• To compare the performance of maximum likelihood and Bayesian estimation techniques.

Main Methods:

• Utilizing a bivariate exponentiated half-logistic distribution for stress-strength modeling.
• Deriving maximum likelihood estimates (MLE) and interval estimates for reliability.
• Applying Bayesian estimation under a squared error loss function using importance sampling.
• Conducting simulation studies to assess estimation accuracy.

Main Results:

• An expression for stress-strength reliability using the proposed bivariate distribution was obtained.
• Both MLE and Bayes estimates were developed and their performance evaluated.
• The developed methods demonstrated usefulness in analyzing real-life data with tied scores.

Conclusions:

• The bivariate exponentiated half-logistic distribution effectively models stress-strength reliability with tied data.
• The proposed maximum likelihood and Bayesian methods provide reliable estimates for practical applications.
• The study offers a valuable tool for analyzing complex reliability data in engineering and science.