The threshold parameter γ, provides an estimate of the earliest time a failure may occur. The threshold parameter locates the distribution along the time scale and has the same units of time, such as hours, miles, or cycles.
When γ = 0, the distribution starts at the origin.
When γ > 0, the distribution starts to the right of the origin. The period from 0 to γ is the failure-free operating period.
When γ < 0, the distribution starts to the left of the origin. For time-to-failure data, a negative γ indicates that failures occurred before the start of a test, such as during storage or transit.
When should I use a distribution with a threshold parameter?
Choose a distribution with a threshold parameter (3-parameter Weibull, 2-parameter exponential, 3-parameter lognormal, or 3-parameter loglogistic) to estimate the earliest time-to-failure. On a probability plot, the third parameter of the Weibull distribution is used when the data do not fall on a straight line, but fall concave down as the data decrease. The value of γ is that which plots the points in a straight line when subtracted from your data.
The threshold parameter is assumed fixed when calculating confidence intervals with the 3-parameter lognormal and 2-parameter exponential distributions.