Piecewise modelling and parameter estimation of repairable system failure rate

Area of Science:

• Reliability Engineering
• System Maintenance
• Statistical Modeling

Background:

• Lifetime failure data often exhibits a bathtub-shaped failure rate, with random failures dominating the life cycle.
• Single distribution models frequently yield significant errors when analyzing such data.
• Existing models struggle to accurately capture the duration of the random failure phase in repairable systems.

Purpose of the Study:

• To propose a novel bathtub-shaped reliability model for repairable systems using a piecewise intensity function.
• To develop and validate parameter estimation methods for the proposed model.
• To enhance the quantitative analysis of system reliability and identify critical failure points.

Main Methods:

• Development of a bathtub-shaped reliability model based on a piecewise intensity function.
• Parameter estimation utilizing the maximum likelihood method, two-stage Weibull process interval estimation, and the Artificial Bee Colony Algorithm.
• Application and validation of the model on a repairable Computer Numerical Control (CNC) system.

Main Results:

• The proposed model accurately fits bathtub-shaped failure rates and reflects the duration of the random failure phase.
• The parameter estimation methods provide feasible quantitative analysis.
• The critical point of the bathtub curve can be reliably estimated.
• Validation on a CNC system confirmed the model's effectiveness.

Conclusions:

• The developed bathtub-shaped reliability model and its estimation approach offer a significant improvement for analyzing repairable systems.
• The model provides a robust framework for understanding system degradation and predicting failure behavior.
• Accurate estimation of the bathtub curve's critical point enables proactive maintenance strategies and enhances system longevity.