to measure and communicate reliability, utility stakeholders often use reliability indices as a good measure of utility system health. Just as many complex systems have their own level of health measurements, reliability indices let everyone know if the utility system is getting better or worse over time. reliability indices help power engineers and other operations personnel see and show the interconnected nature of the many independent system components that make up an electric distribution system. to quantify the level of system reliability, power engineers have adopted and invented many reliability indices. a commonly used index for power distribution systems is system average interruption Duration index (saiDi), which indicates the total interruption duration for the average customer during a predefined period. the formula to calculate the index is SAIDI = Sum of all Customer Interuption Durations . Total Number of Customers Served the numerator can be thought of as the total number of outage minutes experienced by all customers for a predefined period, which is typically one year. saiDi is commonly given in minutes and, generally speaking, represents the average outage minutes experienced for a customer connected to the utility's system. Daily and monthly saiDi values may be used for a more detailed and timely analysis of system reliability. it should be noted that some utilities do not have enough outages to calculate a saiDi for every day in the year. a high saiDi value indicates poor system reliability. although saiDi, together with many other reliability indices, can be used to describe customer experience, it does not offer many actionable insights into the daily operations of utilities. this is because the saiDi calculation is significantly impacted by severe weather conditions that take out large numbers of customers for an extended period of time. let's consider two power companies, P1 and P2, each serving 1 million customers. P1 had 50,000 customers who experienced 300 6-min interruptions within one year. the annual saiDi value of P1 can be calculated as 6 # 300 # 50,000/1,000,000 = 90 min . P2 was hit by a major hurricane that caused a systemwide outage of 90 min, while no other interruptions occurred during the year. the annual saiDi value of P2 would be 90 # 1 # 1,000,000/1,000,000 = 90 min. although both companies share exactly the same saiDi value, the potential and strategy for them to improve their reliability can be quite different. P1 can improve its daily operations to reduce the number of interruptions and the duration of each interruption. on the other hand, the major hurricane that hit P2 could be a rare event that is out of anyone's control. if P2 chose to do exactly the same practice as before but did not experience another major hurricane in the next year, its saiDi value would be very small, indicating a very good reliability. if P2 chose to improve its storm 44 ieee power & energy magazine restoration practice, the duration of the interruption caused by a similar hurricane could be shortened. The Beta Method from IEEE Standard 1366 to study major events separately from daily operations and to reveal trends in daily operations that can be hidden by the statistical effect of major events, the ieee Working Group on Distribution reliability included the section "major event Day classification" in ieee standard 1366, IEEE Guide for Electric Power Distribution Reliability Indices. according to this standard, the daily saiDi value is assumed to follow a log-normal distribution. after taking the natural logarithm transformation of the daily saiDi values, the days falling beyond the 2.5 standard deviations to the right of the mean are classified as major event days. the mean and standard deviation are denoted by a and b, respectively. this method is also known as the Beta method, the 2.5 b method, or ieee 2.5 Beta. to appeal to a broad audience, the Beta method keeps its simplicity by avoiding any predictive modeling effort in the saiDi reporting process other than taking the logarithm transformation and calculating the mean and standard deviation. the Beta method is better at "revealing trends in daily operations that would be hidden by the large statistical effect of major events" than the original all-inclusive saiDi calculation. however, due to the exclusion of weather information, it is unable to answer some important and frequently asked what-if questions, such as "What would be the saiDi values if the weather this year was the same as last year?" consequently, the Beta method has limited capability to reveal trends in reliability, including any improvement or degradation that could be hidden by weather conditions not classified as major events. moreover, the assumption that daily saiDi always follows the lognormal distribution is yet to be verified. have utility operations been improving over the last few years? the power industry has been trying to answer this question since the late 20th century. While ieee standard 1366 has made great progress by bringing a simple tool to the reporting process, there is still a long way to go. in this article, we will demonstrate a predictive modeling approach that can provide a probabilistic view of reliability indices to help further reveal a utility's reliability trend. the case study is based on a small local distribution company (lDc) in the united states. Descriptive Outage and Reliability Analytics the lDc serves approximately 30,000 customers. the case study uses nine years of outage information collected from this lDc. interruptions occurred in 1,964 of the 3,288 days covered by the data set. after taking the log transformation on the daily saiDi values, we obtain the mean (a) of these nine years of log transformed daily saiDi values as −2.80 with a standard deviation (b) 1.88. Note that the unit of the may/june 2018

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