Simplified Explanation of the Three-Beta Method

Prepared by Cheri Warren

After the winter power meeting in NYC, the working group elected to review the three sigma method and prepare a detailed explanation of the exact steps required to complete the analysis. The sub group of myself, Jim Bouford, Rich Christie, John McDaniel, Rodney Robinson, Dave Schepers, Charlie Williams, Hector Valtierra, and Joe Viglietta spent time working through the method and determined that a variation of the three sigma method is the approach that the group at large should apply of discussion at the Webex meeting during the week of March 1st. (please let me know if you have a preference of time/day that week).

The new method has been dubbed the “Three Beta Method”. Attached you will find a document that details the statistics of the three beta versus the three sigma methodology. In short, create a spreadsheet with the following characteristics:

  1. Using five years of data (or as many as you have up to five).
  2. Create columns of data with date, year, CMI per day, and SAIDI per Day. Also include the customers served.
  3. Order the SAIDI/Day from Highest to Lowest
  4. Calculate the natural log (LN function) of each value. Ln(SAIDI/day)
  5. Calculate the mean () (AVERAGE function) and standard deviation () (STDEV function) of the natural log values.
  6. Find the threshold by e( + 3) (EXP function).
  7. For the following year of data, segment the days above the threshold into the abnormal group.

A spreadsheet is attached that shows sample data and the calculations. In the examples, we have identified the days that would have been segmented into the abnormal group had this analysis been used. We are not recommending that you apply this approach looking back in time, but instead looking forward in time. This means that using five years of data, a threshold is established and used in the 6th year. Of you have less than five years of data, still try the methodology and let us know your thoughts.

Segmentation of extreme storms prior to analysis is deemed to be critical since if events such as the Montreal ice storm are included in the outlined statistics then the approach will become so skewed as to be unrepresentative of normal performance. Our attempt to mitigate this effect is the calculate 6 please see the spreadsheet. The concept is to establish a level beyond which a 25-year storm is considered to have occurred. It is not clear yet whether 6 is the correct level. For those of you that have had a 25-year storm, please test the level using your data.

Please apply this approach to your system, operating company and district levels. It is assumed that most will apply it at the company or operating system level for benchmarking, but may apply it at the district or region level for internal goals or public relations.

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Created February 19, 2002