Overview
Lead time is a common variable that is assumed to be stochastic.
Stochastic Lead Time
Generally, it is assumed that lead times are distributed normally.
If the period over which demand is measured (for instance, demand per day) is small relative to the lead time, then the total demand over the lead time is
{% Total \, Demand = \sum_1^n Demand_i %}
If the demand is assumed to be normal, then the
sum is normal.
In this case,
the mean is given by
{% \mu = mean_{lead \: time} \times mean_{demand}%}
and the variance is
{% \sigma^2 = mean_{lead \: time} \times variance_{demand} + variance_{lead\:time}\times mean_{demand}^2%}