The replenishment lead time is different from the standard time period (For example, weekly or monthly) used to collect demand data. We need a way to compute σm from σ1, where σ1 refers to the standard deviation of demand over the standard time period. For example, the lead time is three weeks and the standard time period is one week. Consider the lead time demands as the sum of three weekly random demands. Then if the weekly demands are independent, the variances of the sum equals to the sum of the variances:

(σm)^2=(σ1)^2+(σ1)^2+(σ1)^2=3(σ1)^2

So that: σm=3^(1/2)σ1

If L is the length of lead time, then general formula is:

σL=L^(1/2)σ1