Failure Rate Modeling & The Bathtub Curve
Probabilistic Analysis of the Asset Lifecycle
The Hazard Function, often referred to as the failure rate , is a fundamental metric in reliability engineering. It represents the instantaneous probability of failure at time , given that the component has survived until that time. For most physical assets, this function follows the iconic "Bathtub Curve".
Phase I: Infant Mortality
Early-life failures caused by manufacturing defects or installation errors. Characterized by a decreasing failure rate.
Phase II: Useful Life
Failure occurs randomly due to unpredictable external stresses. Characterized by a constant failure rate (Exponential distribution).
Phase III: Wear-out
Failures caused by physical fatigue, corrosion, or material degradation. Characterized by an increasing failure rate.
Interactive Bathtub Modeler
Adjust the parameters below to witness how different failure distributions affect the overall reliability profile of your system over time.
Model Parameters
Adjust the failure rates to simulate different asset types (e.g., Electronics vs. Mechanical parts).
Instantaneous Failure Rate λ(t)
Reliability Function R(t)
The Weibull Connection
Reliability engineers often use the Weibull Distribution to model these phases numerically. By adjusting the shape parameter ( or ):
- : Models Phase I (Decreasing failure rate).
- : Models Phase II (Constant failure rate - memoryless property).
- : Models Phase III (Increasing failure rate).