EX 4.31

The accompanying observations are on lifetime (in hours) of power apparatus insulation when thermal and electrical stress acceleration were fixed at particular values (“On the Estimation of Life of Power Apparatus Insulation Under Combined Electrical and Thermal Stress,” IEEE Trans. on Electrical Insulation, 1985: 70-78). A Weibull probability plot necessitates first computing the 5th, 15th, … , and 95th percentiles of the standard extreme value distribution. The $\left(100p\right)$ th percentile $\eta \left(p\right)$ satisfies

$$p=F\left(\eta \left(p\right)\right)=1-e^{-e^{\eta \left(p\right)}}$$

from which $\eta \left(p\right)=\ln \left[-\ln \left(1-p\right)\right]$ .

Percentile	-2.97	-1.82	-1.25	-0.84	-0.51
( x )	282	501	741	851	1072
( \ln(x) )	5.64	6.22	6.61	6.75	6.98

Percentile	-0.23	0.05	0.33	0.64	1.10
( x )	1122	1202	1585	1905	2138
( \ln(x) )	7.02	7.09	7.37	7.55	7.67

The pairs $\left(-2.97,5.64\right),\left(-1.82,6.22\right),\dots ,\left(1.10,7.67\right)$ are plotted as points in Figure 4.38. The straightness of the plot argues strongly for using the Weibull distribution as a model for insulation life, a conclusion also reached by the author of the cited article.

Figure 4.38 A Weibull probability plot of the insulation lifetime data