Reliability analysis of multicomponent stress-strength reliability from a bathtub-shaped distribution

Area of Science:

• Statistics
• Reliability Engineering
• Probability Theory

Background:

• Reliability analysis is crucial for system performance.
• Stress-strength models assess system integrity under load.
• Bathtub distributions and Type-II censoring are common in reliability studies.

Purpose of the Study:

• To develop inference methods for multicomponent stress-strength reliability (MSR).
• To establish maximum likelihood estimates (MLE) for MSR under specific conditions.
• To construct confidence intervals and hypothesis tests for MSR.

Main Methods:

• Utilizing bathtub-shaped distributions for strength and stress variables.
• Applying Type-II censored failure time data.
• Employing maximum likelihood estimation and delta method.
• Developing estimators based on pivotal quantities.
• Implementing likelihood ratio tests.

Main Results:

• Established MLE for MSR with common and unequal parameters.
• Constructed approximate and generalized confidence intervals for MSR.
• Provided likelihood ratio tests for parameter equivalence.
• Demonstrated methods with simulation studies and a real data example.

Conclusions:

• The proposed methods offer robust inference for MSR.
• The study contributes novel estimators and testing procedures.
• Findings are applicable to systems with bathtub-shaped failure rates.