Hazard Rate Calculator

Visualize instantaneous failure rate h(t) using Weibull parameters with high-performance ECharts rendering.

Weibull Parameters

Hazard Rate Function h(t)

Failure Rate h(t)Time (t)00.00050.0010.00150.0020.002505001,0001,5002,000

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Hazard Rate Theory

The instantaneous failure rate h(t) describes the conditional probability of failure in the next instant, given survival up to time t.

Infant Mortality

The failure rate is high initially but decreases over time. This indicates early-life failures due to manufacturing defects, installation errors, or material flaws.

β<1\beta < 1

Random Failures

The failure rate is constant. The asset does not "age" in a reliability sense; a component that has survived 10 years is just as likely to fail in the next hour as a brand new component.

β=1\beta = 1

Wear-Out

The failure rate increases over time. This indicates components degrading due to fatigue, friction, corrosion, or simple aging. Preventive maintenance is highly effective here.

β>1\beta > 1

Frequently Asked Questions

Also known as the conditional failure rate, it is the instantaneous rate of failure at time t. This is related to the hazard profiles in the standard Bathtub Curve model, given that the component has survived up to time t.
While the average failure rate measures failures over a calendar window, the hazard rate changes dynamically with component age (e.g., rising as wear-out occurs).

Relevant Glossary

Availability

The probability that a system is operating satisfactorily at any point in time. It is a function of reliability (MTBF) and maintainability (MTTR).

B10 Life

The time at which 10% of a population is expected to fail (or 90% reliability). Commonly used for bearings and warranty analysis.

Failure Rate (λ)

The frequency with which an engineered system or component fails, expressed in failures per unit of time. It is the inverse of MTBF (for constant failure rate systems).

MTBC

Mean Time Between Crashes. Typically used in software reliability equivalent to MTBF for hardware.

MTBF

Mean Time Between Failures. The average expected time between repairable failures of a system during normal operation.

MTTR

Mean Time To Repair. The average time required to troubleshoot and repair a failed component and return it to service.

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