In an earlier post, I talked about the Three Process Metrics that Matter; process inventory, throughput and cost. These three metrics are the cornerstone to understanding how a particular process is performing. But, sometimes it can be difficult to find the average inventory of a system. Taking periodic sampling is one way to do it. Simply count the units in the process at several intervals and take the average to get average inventory. There are a few problems with this method however. For one thing, it is time consuming. It can also lead to inaccuracies caused by natural ebbs and flows of a process. For instance, say you decide to take the sampling of a trouble ticketing system every morning. Because the night shift is lightly staffed, the system naturally has a higher volume of tickets than later in the day after the fully staffed shifts have worked down the list. In this case, your average inventory will be artificially high. You could randomize your sampling schedule to take samples at different times throughout the day, but this can start to get rather complex and laborious. A better way is to use Little’s Law to calculate the average inventory over time.
In 1954, John Little published a paper on queuing theory in which he postulated that the average number of units in a stable system is equal to the average arrival rate of new units multiplied by the average time to process a single unit. This is the algebraic expression of Little’s Law:
Or, putting it a bit more simply:
Inventory = Throughput * Time
While the original description refers to “arrival” rate (as in, the arrival of customers to a store), the formula works equally as well to use the “exit” rate (as in, the rate at which sales orders are completed). Therefore, if we know for instance that we completed 50 sales orders in 10 days, our rate is 5 orders per day (throughput). And, assume we know that the average amount of time to process a single order is 2 days, then we can solve for the average inventory in the system.
Inventory (L units) = Throughput (5 orders per day) * Time (2 days)
Average Inventory = 10
Rearrange the formula to find any one of the missing three variables.
Time = Inventory / Throughput
OR
Throughput = Inventory / Time
A couple points of caution when using Little’s Law. First, be sure to keep your units of measure the same. If you are measuring throughput in days and process time in hours, you will need to convert hours to a portion of a day (or vice versa). The other thing to be aware of is Little’s Law does not account for units already present in a system at the start of the testing interval or units that have not yet completed when the testing interval is stopped. Using a longer testing interval tends to decrease the mathematical effects of these two conditions. If you need to keep your testing intervals short, you may need to find a way to estimate the leading and lagging units.
Little’s Law can save a great deal of time and produce more consistent results when measuring process performance. Try it out next time your measuring a process and amaze your friends and coworkers.