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Model check
The science
Line model
Lots of 24 blocks are released as a Poisson stream at rate λ. Each of the 30 stations takes a fixed cycle time per lot (the datasheet cycle plus the conveyor travel time to the next station), has c parallel servers and a finite input buffer. A finished lot waits on its machine (blocking) when the next buffer is full. Failures arrive after exponential operating times with mean MTBF and last an exponential repair time with mean MTTR; a station is up a fraction A = MTBF/(MTBF + MTTR) of the time.
Bottleneck and Little's law
The line can never outrun its slowest station: capacity = mini ci Ai / ti. Above it the release rate only fills the entry buffer and lots are rejected. In steady state L = λ W (average lots in the system equals throughput times mean lead time), independent of the details. Station utilisation is ρ = λ t / c; queues grow sharply as ρ approaches 1.
Checks
(1) Saturate the line and compare the throughput with the bottleneck capacity. (2) At 40 lots/h compare L with λW from the measured lead times. (3) Compare the first station's measured utilisation with λt.
Simplifications
Fixed service times (no variability inside a cycle), failures only while a lot is being processed, no shift breaks, no rework loops and scrap simply lowers the finished block count. The machine data come from the 3D factory's process graph, but the exact figures of the 3D baseline run are not reproduced here.
What to try
- Raise the release rate to 85 lots/h and watch the entry buffer reject lots while the bottleneck outlined in orange saturates.
- Add a server at the bottleneck and see which station becomes the next one.
- Shrink the buffers and watch red blocking appear upstream.