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

B.1.1 Remarks 
To generate the example data used in 3.5.1, values of 
α
and 
β
were taken from an actual utility data set, and 
then daily SAIDI/day values were artificially generated using a log normal distribution with these values of 
α
and 
β
. The daily SAIDI values were then adjusted to illustrate all aspects of the calculation (e.g., a day in 
Table 2 was assigned a SAIDI value of zero, and a day in Table 3 was assigned a SAIDI value higher than 
the computed threshold). 
This annex provides a technical description and analysis of the 2.5β method of identifying MEDs in 
distribution reliability data. The 2.5β method is a statistical method based on the theory of probability and 
statistics. Fundamental concepts such as probability distribution and expected value are highlighted in 
italics when they are first used and provided with a short definition. An undergraduate probability and 
statistics textbook can be consulted for definitions that are more complete. 
B.2 2.5β method description 
See 3.5 of this guide for the detailed procedure for identifying MEDs. The short version is presented here. 
A threshold on daily SAIDI is computed once a year as follows: 
a) 
Assemble the five most recent years of historical values of SAIDI/day. If less than five years of 
data is available, use as much as is available. 
b) Discard any day in the data set that has a SAIDI/Day of zero. 
c) 
Find the natural logarithm of each value in the data set. 
d) Compute the average (α, or Alpha) and standard deviation (β or Beta) of the natural logarithms 
computed in step a). 
e) 
Compute the threshold T
MED
= exp(α + 2.5 * β). 
f) 
Any day in the next year with SAIDI > T
MED
is a MED. 
B.3 Random nature of distribution reliability 
The reliability of electric power distribution systems is a random process, that is, a process that produces 
random values of a specific random variable. A simple example of a random process is rolling a die. The 
random variable is the value on the top face of the die after a roll, which can have integer values between 
one and six. 
In electric power distribution system reliability, the random variables are the reliability indices defined in 
this guide. These are evaluated on a daily or yearly basis and take on values from zero to infinity.