The thing is that with a fat-tailed distribution the concept of an average is meaningless until you have at least 2,000 data points (10,000 data points ideally). Consequently, anything that depends on an average such as Little´s Law cannot be used until this amount of data is analyzed. The ability to calculate or forecast a reliable average for less than 100 data points is vital for everyday planning, and this is only possible with a thin tail.
In the case of a fat-tailed lead time just a few high-value data points may skew the mean upward and may dramatically affect the accuracy of a forecast. Trimming the tail on your lead time distribution is the first step to predictability and the ability to forecast reliably.
“The risk is always in the tail”. Fat-tailed distributions require a different approach to managing risk. The length of the fat tail indicates the possible impact of delay and directly affects customer satisfaction. Even with small probabilities of a 2%- 3% percent (which means a long lead time happens only occasionally), a fat-tail lead time represents long painful delays that may damage customer trust. Therefore, 99 good experiences could be destroyed with 1 painful bad experience.
For example, one item has a mode of ten (the most commonly occurring lead time in the data set), a median of twenty (the 50th percentile), and a mean of thirty (the arithmetic average).
A customer asks: “When will my request be ready?” and he is told, “We usually process items in fifteen to twenty days.” If then he waits 155 days — or ten times longer than he has been told to expect, which may happen with fat-tailed processes, he will be burned by this one bad experience and no longer trust the service delivery. Consequently, every future request he makes will have a deadline attached to it and penalties for failure to deliver.