Scale Parameter (Eta)(Eta)
Definition
The Weibull scale parameter (eta, also called characteristic life) that represents the time by which 63.2% of the population is expected to have failed. Eta defines the horizontal scale of the Weibull distribution and is always expressed in the same units as the failure time data (hours, cycles, km). At t = eta, the reliability R(t) = e^(-1) = 0.368, regardless of the shape parameter.
Context
Eta provides the life estimate that drives replacement planning. In Reliatic's Weibull module, eta is displayed with confidence intervals and is used to calculate B-life values for maintenance interval optimization. A large eta relative to the required operating period indicates ample design life; a small eta indicates the need for more frequent intervention.
Formula
At t = eta: R(eta) = e^(-1) = 0.368 (36.8% survival probability)
Examples
- Eta = 25,000 hours for a pump impeller means that 63.2% of impellers are expected to fail by 25,000 hours of operation.
- Comparing two bearing suppliers: Supplier A has eta = 15,000 hours, Supplier B has eta = 22,000 hours. Supplier B bearings have 47% longer characteristic life, justifying the price premium.
Applicable Standards
- IEC 61649:2008
Related Terms
A 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.
B-LifeThe time by which a specified percentage of a population is expected to have failed, derived from the Weibull distribution parameters. B10 life is the time by which 10% of the population has failed (90% survival); B50 is median life (50% survival); B90 is the time by which 90% have failed. B-life values are used to set preventive replacement intervals and warranty periods.
Mean Time To Failure(MTTF)The average time from the start of operation until the first failure of a non-repairable item, or the average time between replacement and next failure for items that are replaced rather than repaired. MTTF is technically correct for non-repairable components (bearings, seals, filters, lamps) while MTBF applies to repairable systems. In practice, the terms are often used interchangeably.
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.