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 (x).
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. This is true regardless of the shape parameter (β) chosen.
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. Because the minimum time step for chart generation is 1.0, if small single digit numbers are entered for η, the charts will appear choppy (regardless of the "time step division" input selected). If charts are desired, say for η = 2 years, values entered should be it terms of hours, not years, in order to generate smooth charts. Note, inputs of 2*8760 to represent two years time, in terms of hours, is a valid input for items #2 and #3 below.