The Weibull distribution can be used to model many different failure distributions.
Given a shape parameter (β) and characteristic life (η) the reliability can be determined at a specific point in time (t).
The two-parameter Weibull distribution probability density function, reliability function and hazard rate are given by:
Probability Density Function
The characteristic life (η) is the point where 63.2% percent of the population will have failed, regardless of the shape parameter (β).
The following shape parameter characteristics are noted:
β = 1.0 : Exponential distribution, constant failure rate
β = 3.5 : Normal distribution (approximation)
β < 1.0 : Decreasing failure (hazard) rate
β > 1.0 : Increasing failure (hazard) rate
The calculation inputs below show units of "hours," but any life metric (cycles, years, etc.) can be used as long as there is consistency among the three inputs.