Shape Parameter (Beta)(Beta)
Definition
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.
Context
Beta is the most diagnostic parameter in Weibull analysis because it reveals the nature of the failure process. In Reliatic's Weibull analysis module, beta is prominently displayed alongside the Weibull plot, with interpretation guidance. Beta values guide maintenance strategy: beta < 1 suggests quality issues, beta near 1 suggests random events, beta > 1 justifies time-based replacement.
Examples
- Beta = 3.5 for turbine blade failures indicates a strongly wear-out-dominated failure mode, supporting a preventive replacement strategy at a fixed interval.
- Beta = 0.6 for electronic control module failures indicates infant mortality, suggesting that burn-in testing or incoming quality inspection would be more effective than time-based replacement.
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.
Scale Parameter (Eta)(Eta)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.
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.
Hazard RateThe 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.
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.
Where this appears in Reliatic
This concept is used in the Reliability Analytics module.