Statistical inference for a competing failure model based on the Wiener process and Weibull distribution.

Area of Science:

• Reliability Engineering
• Statistical Modeling
• Risk Analysis

Background:

• Competing failure models are increasingly vital in practice, encompassing both degradation phenomena and sudden failures.
• Accurate statistical modeling is crucial for understanding system reliability under complex failure modes.

Purpose of the Study:

• To propose and investigate the generalized pivotal quantity method for modeling competing failures involving degradation and sudden failures.
• To derive point and interval estimations for model parameters and reliability functions.

Main Methods:

• Modeling degradation failure using a Wiener process and sudden failure using a Weibull distribution.
• Employing maximum likelihood estimation for Wiener process parameters ($ \mu $, $ \sigma^2 $).
• Deriving inverse estimation for Weibull parameters ($ \eta $, $ \beta $) and constructing generalized pivotal quantities.

Main Results:

• Exact confidence intervals were obtained for $ \mu $, $ \sigma^2 $, and $ \beta $.
• Generalized confidence intervals were derived for $ \eta $, reliability function, $ p $th percentile of lifetime, and mean time to failure.
• Simulation studies confirmed the effectiveness of the proposed generalized confidence intervals in terms of coverage percentage.

Conclusions:

• The generalized pivotal quantity method effectively models competing failures with both degradation and sudden failure modes.
• The derived confidence intervals provide reliable estimates for critical reliability metrics.
• The proposed method offers a practical approach for reliability analysis in complex systems.