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The Relationship Between Cycle Time and Variability

Cycle time increases with variability. For example, suppose that you have a single machine that can process four lots per hour (one at a time). If each lot takes exactly 15 minutes to process, and lots arrive exactly every 15 minutes, then the lots will experience no queue delay. The cycle time through this step for each lot will be 15 minutes of pure process time, and the machine will operate with 100% utilization. However, in a real fab, neither the interarrival times nor the processing times will be exactly the same from lot to lot.

Variability in Processing Times

All sorts of things contribute to variability in processing time in a fab. Different recipes are processed on the same machine, and have different process times. Setups increase process time (from the lot’ perspective), as do equipment failures. When rework lots come through, they typically have fewer wafers than regular lots, and so have lower processing times. Similarly, yield loss reduces the number of wafers per lot, and can reduce process time per lot. Operators don’t always remove lots from the machine immediately upon completion, increasing the effective process time. 

Suppose that in the example above the processing time averages 15 minutes, but can range from 10 minutes to 20 minutes for each individual lot. Also suppose that the first lot takes 20 minutes. When the second lot arrives 15 minutes after the first, it will have to wait for five minutes. This means that the average queue time of the first two lots has increased from zero to 2.5 minutes. And things will just keep getting worse over time. Once you have any lots that wait, you can never again have zero wait time, because the best case for a lot is that its waiting time is zero. You never have any negatives to cancel out the positive delay. 

Now suppose that the first lot only took 10 minutes to process. This means that the machine will be idle for five minutes, until the second lot arrives. This is a problem, because this machine is supposed to be operating at 100% utilization. Those five minutes of idle time can never be recovered. For a good illustration of this, we recommend that you read The Goal by Eli Goldratt and Jeff Cox. 

Variability in Arrival Times

Even more of a problem in wafer fabs than variability in process times is variability in time between arrivals. The primary culprit here is batch processing. Suppose that in our example, the step before the example machine takes place on a batch tool with a batch size of four lots, and a processing time of one hour per batch. Instead of arriving at our machine once every 15 minutes, lots arrive instead in a batch of four every hour. Since the example machine can only process one lot at a time, the other three lots will have to wait while the first lot is processed. Then lots three and four will wait while the second is processed, and so on. The average queue delay for this batch (assuming that the machine is idle when it arrives) is [0 + 15 + 2*(15) + 3(15)]/4 = 22.5 minutes.

Other factors also contribute to variability in lot arrival times, including rework, transfer batching, and operator delays. The net result is that when a system has variability, the cycle time increases. How much the cycle time increases depends in part on the utilization of the system. In the example below, we have a single machine, loaded to 60%, 75%, and 90% utilization. The process time is constant, but the interarrival times vary. As the chart shows, the more variability there is in the arrival process (as shown on the X-axis), the higher the cycle times will be (as shown on the Y-axis). The higher the overall utilization of the system, the worse the effect is. 

The above chart was generated using a simple queueing formula for the queue delay for a single machine. Simulation can also be used to do what-if analysis of the impact of variability on cycle time. The bottom line is that any system system with variability will experience some queueing - the higher the utilization of the system, the worse the effect. See the discussion on cycle time and capacity for more details.