Why is it better to have a thin tail?

As we already explained in the article “Five Things You Need to Know about Lead Time“, lead time probability function is a curve that shows the distribution of actual data for the lead time from a Kanban system. And it can be either “thin-tailed” or “fat-tailed”.

“Fat-tailed” of “thin-tailed” lead time

“Fat-tailed” lead time distribution has a long visible tail which means a poorly predictable and risky process where planning is difficult. Meanwhile, the “thin-tailed” lead time curve has a short tail and reflects the process that is reliable, predictable and has shorter delays with lower impact.

A fat, long tail affects your planning because you can't use simple forecasting equations (such as Little’s Law and the use of regression to the mean) with a fat-tailed curve. After all, these equations use the mean value (the arithmetic average), and the concept of an average is meaningless for fat tails.

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, you can't use anything that depends on an average such as Little´s Law until you analize this amount of data. 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 screw 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 we may tell him, “We usually process items in fifteen to twenty days.” If then he waits 155 days — or ten times longer than we told him 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.  

Explore more about lead time sitributions in KMM+ on Kanban+  

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