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SPECIAL FORMULA FOR SPC

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SPECIAL FORMULA FOR SPC

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  1. Forecasting Formulas Symbolsn Total number of periods, or number of data points.A Actual demand for the period (Y).F Forecast demand for the period (Y). Y Dependent variable, or actual demand (Y = Actual, Y = Forecast).e Error.T Trend factor.

  2. C Cyclical factor.S Seasonal factor.Y Forecast dependent variable.a Y intercept.b Slope of the line. Alpha. The desired response rate, or smoothing constant.

  3. (P) Probability.P Mean proportion of a large sample.Sigma standard deviation of the population.x Independent variable. y Dependent variable data point.

  4. tMean of the error for a time interval.tError for a single time period. ZValue from normal distribution (i.e. number of standard deviation from the expected distribution).SStandard deviation of the errors.

  5. R2 Coefficient of determination (The percentage of exploised, eliminated and removed variances).Z MAD Mean absolute deviation. I Index. mu  population mead.

  6.  Sx = (X-X)2/(n-1) Sample standard deviation of X.  x = (X- )2/N Population standard deviation of X.  Syx = (Yt-Yt)2/(n-r)Standard deviation of estimate  standard deviation of forecast errors. (n = number of observations, r = smoothing) or regression (2) (a & b) indicators).

  7. Syx = S Standard deviation of estimate  standard deviation of the Errors.t = At - FtForecast error for period t = actual demand for period t less the (should be ~ ND (0,low) forecast demand for period t.Ft = Ft-1 +  (At-1 – Ft-1) The exponentially smoothed forecast for period t = the exponentially smoothed forecast for the prior period + the smoothing constant times (the actual for the prior period less the forecast for the prior period).

  8. Yt = a + bt Forecast: Simple Linear Trend.Yt = a + bt + ct2 Forecast: Quadratic Trend.Yt = T CI SI I Decomposition model: Forecast value = Trend times cyclical indicators times seasonal indicator times irregular indicator.Yt = T SI Simple Decomposition model: Forecast value = Trend times seasonal indicator.

  9. 2 x+y = 2 x +2 yStandard deviation squared for x + y = the standard deviation of x + the standard deviation of y. x+y = x +yPopulation mean for x + y = the mean of x + the mean of y. et - 0 TS =  Tracking signal = the totalMAD of errors/MAD.

  10. t - 0Z =  Z – value for Serrors = the mean of the errors for a time interval over the standard deviation of the errors.  APE MAPE =  n

  11. MAD = 0.8SeMean absolute deviation = 0.8 times the standard deviation of the forecast errors.S = MAD (1.25)Standard deviation of the forecast errors = mean absolute deviation times 1.25.t = 0  Z SConfidence interval for errors = times standard deviation of the forecast errors.

  12. A - FAPE= |A Absolute value of actual less forecast divided by actual.Syx 2 R2 = 1 -  sy 2The coefficient of se2 determination = 1 -  sy2

  13. s y 2 - s 2R2 =  The coefficient of s y 2 determination.

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