Template:Weibull parameters probability plotting

Probability Plotting
One method of calculating the parameters of the Weibull distribution is by using probability plotting. To better illustrate this procedure, consider the following example from Kececioglu [20].

Example 1:

Probability Plotting for the Location Parameter, γ 

The third parameter of the Weibull distribution is utilized when the data do not fall on a straight line, but fall on either a concave up or down curve. The following statements can be made regarding the value of γ:


 * Case 1: If the curve for MR versus tj is concave down and the curve for MR versus (tj − t1) is concave up, then there exists a γ such that 0 &lt; γ &lt; t1, or γ has a positive value.


 * Case 2: If the curves for MR versus tj and MR versus (tj − t1) are both concave up, then there exists a negative γ which will straighten out the curve of MR versus tj.


 * Case 3: If neither one of the previous two cases prevails, then either reject the Weibull as one capable of representing the data, or proceed with the multiple population (mixed Weibull) analysis. To obtain the location parameter, γ:


 * Subtract the same arbitrary value, γ, from all the times to failure and replot the data.
 * If the initial curve is concave up, subtract a negative γ from each failure time.
 * If the initial curve is concave down, subtract a positive γ from each failure time.
 * Repeat until the data plots on an acceptable straight line.
 * The value of γ is the subtracted (positive or negative) value that places the points in an acceptable straight line.

The other two parameters are then obtained using the techniques previously described. Also, it is important to note that we used the term subtract a positive or negative gamma, where subtracting a negative gamma is equivalent to adding it. Note that when adjusting for gamma, the x-axis scale for the straight line becomes (t − γ).

Example 2: