Hazard Rate
Definition
The instantaneous rate of failure at time t, given that the item has survived to time t. Hazard rate (also called the instantaneous failure rate or hazard function) describes how the risk of failure changes over the item's life. Unlike failure rate (which is an average), hazard rate is a time-dependent function that captures the changing nature of failure risk as equipment ages.
Context
Hazard rate is the theoretical foundation for the bathtub curve. In Weibull analysis, the hazard rate function reveals whether equipment is in the infant mortality phase (decreasing hazard rate), the useful life phase (constant hazard rate), or the wear-out phase (increasing hazard rate). This determines the appropriate maintenance strategy.
Formula
h(t) = (beta/eta) * (t/eta)^(beta-1) for Weibull; h(t) = f(t)/R(t) in general
Examples
- A component with Weibull beta=2.5 has a hazard rate that increases with time: h(t) = (2.5/10000) * (t/10000)^1.5, meaning the risk of failure accelerates as the equipment ages.
- The hazard rate at t=5000 hours for a component with beta=2.0, eta=10000 is h(5000) = (2/10000)*(5000/10000)^1 = 0.0001/hour, corresponding to a 10-hour instantaneous failure rate.
Applicable Standards
- IEC 61649:2008
- IEC 60300-3-1
Related Terms
The average number of failures per unit of time for a population of items, typically expressed as failures per hour, per year, or per million hours. Failure rate (lambda) is the reciprocal of MTBF for constant-failure-rate systems. It is a statistical average measure, distinct from the instantaneous hazard rate, and is most accurate when the failure rate is approximately constant (beta near 1).
Bathtub CurveA graph of the hazard rate versus time that describes the typical life cycle of a population of items, characterized by three distinct phases: (1) Infant Mortality — a decreasing failure rate period caused by manufacturing defects, installation errors, or design weaknesses; (2) Useful Life — a period of approximately constant, low failure rate representing random failures; (3) Wear-Out — an increasing failure rate period caused by age-related degradation mechanisms.
Weibull DistributionA continuous probability distribution widely used in reliability engineering to model the time-to-failure of components and systems. The two-parameter Weibull distribution is defined by the shape parameter (beta) and scale parameter (eta). Its versatility lies in its ability to model increasing, constant, or decreasing failure rates depending on the shape parameter value, making it suitable for all phases of the bathtub curve.
Shape Parameter (Beta)(Beta)The Weibull shape parameter (beta, also written as b or k) that determines the form of the failure distribution and the nature of the failure rate over time. Beta < 1 indicates decreasing failure rate (infant mortality); beta = 1 indicates constant failure rate (random failures, equivalent to exponential distribution); beta > 1 indicates increasing failure rate (wear-out). The value of beta reveals the physics of the dominant failure mechanism.
ReliabilityThe probability that an item will perform its required function under stated conditions for a specified period of time. Reliability is a quantitative measure expressed as a probability (0 to 1) or percentage. It is a function of the failure rate and time: for constant failure rate systems, R(t) = e^(-lambda*t). Higher reliability means lower probability of failure over the same period.
Where this appears in Reliatic
This concept is used in the Reliability Analytics module.