Weibull and Reliability/Failure Time Analysis - Two- and three-parameter Weibull distribution
The Weibull distribution is bounded on the left side. If you look at the probability density function, you can see that the term x-θ must be greater than 0. In most cases, the location parameter θ (Theta) is known (usually 0): it identifies the smallest possible failure time. However, sometimes the probability of failure of an item is 0 (zero) for some time after a study begins, and in that case it may be necessary to estimate a location parameter that is greater than 0. The options available via the Weibull analysis and reliability/failure time analysis facilities (accessible from the Process Analysis Startup Panel) provide several methods for estimating the location parameter of the three-parameter Weibull distribution. In practice, Dodson (1994) recommends to look for downward or upward sloping tails on a probability plot, as well as large (>6) values for the shape parameter after fitting the two-parameter Weibull distribution, which may indicate a non-zero location parameter.