The Weibull Distribution: A Handbook - Index of

9.3 WEIBULL plotting techniques 353
1.1) (b2/b1) c ≈ 1 or
1.2) (b2/b1) c ≫ 1
and whether in the case c2 > c1
2.1) b1 ≈ b2 or
2.2) b1 ≫ b2 or
2.3) b1 ≪ b2.
When c1 = c2, the curve C will have only one point of inflection called T , whereas curve
C has three points of inflection for c2 > c1. The two subcases to case 1 are detected as
follows: when the data points are scattered on either side of T , we have (b2/b1) c ≈ 1.
When (b2/b1) c ≫ 1, the data are scattered either mainly on one side or on both sides of T .
To discriminate between the three subclasses of case 2, we have to determine the point of
intersection I of the asymptote to the right hand side of C with the curve C. When most of
the data points are to the left (right) of I we can assume b1 ≪ b2 (b1 ≫ b2).
The reader is referred to the original paper of JIANG/MURTHY (1995) for a description of
the procedure in each of the five cases. Besides the disadvantage of all graphical procedures
in statistics, the graphical analysis of mixed WEIBULL distributions demands a large
sample size to clearly perceive the underlying model. Fig. 9/12 demonstrates the latter assertion
for the cases c1 = c2 (upper row) and c2 > c1 (lower row) with p = 0.4 in either
case. The smooth curve in each graph represents the WEIBULL probability plot of (9.35).
Figure 9/12: WEIBULL probability plots of mixed distributions
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