Estimation of stress-strength reliability from unit-Burr Ⅲ distribution under records data

Area of Science:

• Statistics
• Reliability Engineering
• Probability Theory

Background:

• Stress-strength reliability (SSR) is a critical measure in engineering and science.
• Estimating SSR often relies on complete or censored data, with less focus on record values.
• Unit-Burr III distribution is a flexible model applicable in various reliability contexts.

Purpose of the Study:

• To develop a generalized inferential approach for estimating stress-strength reliability (SSR).
• To utilize upper record values from unit-Burr III distributions for SSR estimation.
• To provide methods for both common and unequal parameter cases between strength and stress variables.

Main Methods:

• Utilizing upper record values from unit-Burr III distributions.
• Constructing pivotal quantities for generalized point and interval estimations.
• Employing Monte Carlo simulations to assess method performance.
• Developing distinct estimation strategies for common and unequal parameter scenarios.

Main Results:

• Proposed generalized point and interval estimators for SSR based on upper record values.
• Demonstrated the effectiveness of the methods through extensive simulation studies.
• Validated the applicability of the proposed techniques for both identical and distinct parameter distributions.

Conclusions:

• The proposed generalized inferential approach effectively estimates stress-strength reliability using upper record values.
• The methods are robust for both common and unequal parameter distributions of strength and stress.
• The study provides a valuable tool for reliability analysis in scenarios involving record data.