Lead time demand for simple exponential smoothing: An adjustment factor for the standard deviation

A new simple formula is found to correct the underestimation of the standard deviation for total lead time demand when using simple exponential smoothing. The traditional formula for the standard deviation of lead time demand is to multiply the standard deviation for the one-period-ahead forecast error (estimated by using the residuals) by the square root of the number of periods in the lead time. It has been shown by others that the traditional formula significantly underestimates variation in the lead time demand when the mean of the process is somewhat changing and simple exponential smoothing is appropriate. This new formula allows one to see readily the significant size of the underestimation of the traditional formula and can easily be implemented in practice. The formula is derived by using a state-space model for simple exponential smoothing.