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Threshold from Standard Deviation

Threshold from Standard Deviation. Rich Christie University of Washington Distribution Design Working Group Webex Meeting October 26, 2001. Concept. Set threshold R* as the mean (average) plus a multiple of standard deviation Days with reliability r i > R* are Major Event Days.

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Threshold from Standard Deviation

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  1. Threshold from Standard Deviation Rich Christie University of Washington Distribution Design Working Group Webex Meeting October 26, 2001 Threshold from Standard Deviation

  2. Concept • Set threshold R* as the mean (average) plus a multiple of standard deviation • Days with reliability ri > R* are Major Event Days R* = μ + n·σ Threshold from Standard Deviation

  3. Normal (Gaussian) Distribution • If daily reliability has a normal (Gaussian) probability distribution • Equivalent to frequency criteria • Area under pdf above R* (= p) is constant as mean and standard deviation vary • p converts to MED frequency f Threshold from Standard Deviation

  4. Normal (Gaussian) Distribution μ = 1 σ = 1 n = 1 R* = 2 Areas [= p(x>R*)] the same μ = 1 σ = 2 n = 1 R* = 3 Threshold from Standard Deviation

  5. Normal (Gaussian) Distribution With μ = 0, σ = 1 Threshold from Standard Deviation

  6. Normal (Gaussian) Distribution p and f are independent of μ and σ • But daily reliability does NOT have a normal distribution Threshold from Standard Deviation

  7. Log-Normal Distribution • For Log-Normal Distribution • Most daily reliability data seems to be log-normal • Probability p and frequency f (MEDs/year) vary with mean μ and standard deviation σ, for same multiple n. • Effect due to skew (kurtosis) of distribution Threshold from Standard Deviation

  8. Log-Normal Distribution μ = 1 σ = 1 n = 1 R* = 2 Areas [= p(x>R*)] differ μ = 1 σ = 2 n = 1 R* = 3 Threshold from Standard Deviation

  9. Log-Normal Distribution MEDs/year decrease as mean μ decreases (Improving average reliability means fewer MEDs) Threshold from Standard Deviation

  10. Log-Normal Distribution MEDs/year increase as standard deviation σ decreases (Larger utilities have inherently lower standard deviation and thus would get higher MEDs/year.) Threshold from Standard Deviation

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