Line capacity, takt time and Little's law

A simulation answers what happens. Before you run one, the analytic line capacity tells you what can happen at best: the takt time, which station limits the line with and without losses, and how long parts wait for a given work in process. Analyze → Line capacity… calculates it from the open scenario with the same engine as the twinworks-line-capacity API and MCP tool.

1. Open the 3-station line

Open the 3-station line template: a saw, a mill and a deburring station with triangular cycle times and random arrivals. Choose Analyze → Line capacity….

The dialog reads the line from the source to the sink. Each machine becomes a station with the mean of its cycle-time distribution (saw 41.67 s, mill 48.67 s, deburr 37.67 s), its number of servers as Parallel, its MTBF/MTTR as Availability and its scrap as Quality. This template has no failures or scrap, so every OEE is 100 %.

2. Read the capacity

With the default 450 minutes, the Demand per period (good units) is pre-filled from the source's arrival rate (491 units, 65.5 per hour). The result:

• Effective throughput 74 per hour, theoretical 74 per hour.
• Bottleneck Mill, 48.7 s per good unit.
• Takt time 55 s at a demand of 65.5 per hour.
• The green line says the demand is covered: the line needs at least 88.5 % line OEE and reaches 100 %.

The Stations in flow order table shows the load at demand: saw 75.8 %, mill 88.5 %, deburr 68.5 %. An orange note warns that the mill is loaded to 89 %. Above about 85 %, small disturbances already make queues and lead times grow quickly. That is why the simulation of this line shows long waits in front of the mill.

3. Lead time from work in process

Enter 6 in Work in process (units). Lead time (Little’s law) becomes 4.9 min: six units in the line divided by 74 units per hour. The table Little’s law and benchmarks adds the Factory Physics reference cases for the same WIP:

The heading also shows the raw process time (2.1 min) and the critical WIP (2.63 units): with fewer units than that in the line, even a perfect line cannot keep the mill busy.

4. Compare with the simulation

Close the dialog, click Experiment in the toolbar and open Analyze → Line capacity… again. A note now shows the last simulation run: 65.7 good units per hour, average WIP 5.4, mean lead time 5 min next to the analytic 74 per hour.

Why less? The note at the bottom of the dialog says the source releases only about 65.5 units per hour. This line is not saturated: the arrivals, not the mill, limit the output, and the mill idles about 11 % of the time. The simulated numbers also obey Little's law: 5.4 units ÷ 65.7 per hour ≈ 4.9 minutes. Raise the arrival rate (a shorter interval on Raw parts) and the simulated throughput approaches the analytic 74 per hour minus what variability costs.

5. Losses move the bottleneck

Open the Line with failures & shifts template and the dialog again. Turning has an availability of 92.3 % (MTBF 7200 s, MTTR 600 s) and hobbing 90.9 %, so hobbing supports 102.3 good units per hour and stays the bottleneck. Notes below the tables explain what the analytic view leaves out: hobbing fails only while working, and grinding's planned maintenance is not part of the availability.

Good to know

• Demand, available time and WIP are remembered in this browser. They describe the order book, not the model.
• The calculator reads serial lines only. A model that splits the flow shows a note instead of results.
• Batch stations and manual station lists are available in the twinworks-line-capacity tool on the website and through the API.