The Weibull distribution is defined by three parameters: shape, scale, and threshold.
The shape describes the shape of the Weibull curve. A shape of 3 approximates a normal curve. A shape between 2 and 4 is still fairly normal. A low value for shape, say 1.25, gives a right-skewed curve. A high value for shape, say 10, gives a left-skewed curve.
The scale, or characteristic life, is the 63.2 percentile of the data. The scale defines the position of the Weibull curve relative to the threshold, analogous to the way the mean defines the position of a normal curve. A scale of 10, for example, says that 63.2% of the equipment will fail in the first 10 hours following the threshold time.
The threshold is a shift of the distribution away from 0. A negative threshold shifts the distribution to the left of 0, and a positive threshold shifts the distribution to the right of 0. All data must be greater than the threshold. The Weibull distribution in Minitab is the same as the 3-parameter Weibull but with a threshold of 0. For example, a Weibull(3,100) distribution is exactly the same as a 3pWeibull(3,100,50) except for the 3-parameter Weibull is shifted 50 units to the right of 0.
When you run Stat > Reliability/Survival > Distribution Analysis > Distribution ID Plot or Parametric Distribution Analysis, the Session window displays percentile estimates and associated confidence intervals. For example, if you are interested in seeing the B10 life, the time associated with the tenth percentile, look at the table in the Session window.
To view the Weibull probability density function, click on the link, Weibull Probability Density Function, below.
