Ieee std 1366-2012 (Revision of ieee std 1366-2003) ieee guide for Electric Power Distribution Reliability Indices

ln(SAIDI/day)
Days
Figure B.4—Histogram of the natural logs of three years of daily SAIDI data from 
anonymous utility two supplied by the Distribution System Design Working Group
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IEEE Std 1366-2012 
IEEE Guide for Electric Power Distribution Reliability Indices 
Copyright © 2012 IEEE. All rights reserved. 
28
A consequence of the log-normality of daily reliability data is that the three sigma conditions no longer 
hold. In particular, the probability of exceeding a given threshold is no longer independent of the values of 
the average and standard deviation of the distribution. This means that using a method such as three sigma 
would result in significantly different numbers of MEDs for utilities with different average values of 
reliability, or with different standard deviation values. This seems inequitable. 
Fortunately, the logarithms of log-normal data have a Gaussian distribution. If the average of the 
logarithms of the data is called α, or Alpha, and the standard deviation of the logarithms of the data is 
called β, or Beta, then α and β are the mean and standard deviation of a Gaussian distribution, and a 
threshold on the log of the data can be set that is independent of the values of α and β. Eq. (B.4) and Eq. 
(B.5) show these concepts mathematically. 
(
)
β
α
k
T
MED
+
=
ln
(B.4) 
(
)
β
α
k
T
MED
+
=
exp
(B.5) 
The probability of exceeding T
MED
is a function of k, just as it was a function of n in the Gaussian example. 
Table B.2 gives these probabilities as well as the expected number of MEDs for various values of k.