The Weibull Distribution data trend
Embed Weibull Distribution data trends into your test data
Key Developer Profile: Llyr Jones
Llyr Jones is a Developer and Mathematical Analyst for Grid-Tools. He is a Maths graduate from St Andrews University and is currently specializing in data trend analysis for Datamaker™.
Notes from Llyr on the Weibull Distribution data trend
This is a family of 2-parameter distributions which are used to model many different phenomena. They are characterised by two positive parameters: a scale parameter λ and a shape parameter k. The Weibull distribution can be thought of as a generalisation of the exponential distribution (when k = 1 it represents an exponential distribution with intensity (1 / λ)) and the Rayleigh distribution (when k = 2).
The primary usage of this distribution is in reliability modeling, where there are sound mechanical grounds behind its usage. In fact, it is suitable for modeling any phenomenon which involves a ‘time to failure’ and the failure rate is proportional to a power of time – in this case the parameter k describes how the failure rate changes over time, as follows:
- k < 1 implies that the failure rate decreases over time.
- k = 1 implies that the failure rate is constant over time.
- k > 1 implies that the failure rate increases over time – this is particularly useful for modeling the reliability of an ageing component.
The Weibull distribution has the following probability density function (when x ≥ 0):
In addition to reliability modeling, the Weibull distribution arises in the following contexts:
- Materials science – when modeling the distribution of strengths of materials, the parameter k is called the Weibull modulus
- Medicine – used to model age-related cerebral atrophy
- Economics – modeling ageing asset failure patterns
- Modeling the annual variability of wind speed
