You run one shift on a segment of a vehicle final-assembly line: five stations in series with small buffer lanes between them. Every stoppage ripples up and down the line, every defect is either fixed at the station or travels on, and the shift has a production plan to meet.
Percent of rated speed. Faster cycles raise output — and the breakdown and defect rates.
Units each lane between stations can hold. More decouples stoppages, but adds work in process.
Each technician repairs one station; the bottleneck is served first, a second technician speeds up a repair.
Operators stop their station to fix a defect on the spot. It costs uptime — including stops for abnormalities that turn out to be nothing — but keeps defects from travelling on.
A team of three repairs units caught at end-of-line test for one hour, so they can ship.
| Availability | 100.0 % |
|---|---|
| Performance | 0.0 % |
| Quality rate | 100.0 % |
| Pace vs takt | 100 % |
| Throughput | 50.0 JPH |
| Units ahead (+) / behind (−) plan | 0 |
| Lead time through the line | 16 min |
| Units waiting in the repair bay | 0 |
| Labour hours per unit | 0.00 h |
| Stations down | 0 |
| Bottleneck idle (starved or blocked) | 0.0 % |
Plan: 50 units per hour for a four-hour half-shift. Station 3 is the line’s bottleneck and only one maintenance technician is on shift. Maintenance reports that a worn part on station 2 — right in front of the bottleneck — must be replaced at minute 35: a 40-minute job for one technician.
Plan: 52 units per hour for a four-hour half-shift, and ten units from the last shift are still waiting in the repair bay. Twenty minutes in, a fastening problem appears at station 4: about one unit in eight leaves it with a defect. End-of-line test catches most of them — not all.
The line has been running at 80 % speed for a plan of 47 units per hour. Twenty minutes into the half-shift, sales raises the plan to 56 units per hour — takt time drops from about 1.28 to 1.07 minutes, and the bottleneck cannot keep up at 80 %. No overtime is allowed.
Every relation the simulator uses, with its source. Constants marked as assumptions are illustrative calibrations.
OEE = A × P × Q; A = (T_plan − T_stop)/T_plan, P = CT_ideal · N_bn / (T_plan − T_stop), Q = N_first-pass / N_out; OEE = CT_ideal · N_good / T_plan when N_bn = N_out[1][2]The product equals ideal cycle time × good units ÷ planned time only while the bottleneck’s output equals the line’s output; units still between station 3 and the end of the line make a small difference.station i: cycle = c_i / v; moves on iff buffer_i < K (else blocked); starts iff buffer_{i−1} > 0 (else starved)[3][4]r_line ≤ r_b = v / max_i c_i; takt = available time / demand = 60 / plan [min/unit][5][7]σ_n(v) = ((1.05 − 0.85) / (1.05 − v))^n (σ = 1 at 85 %; σ_1: 2× at 95 %, 4× at 100 %; σ_2: 4× at 95 %, 16× at 100 %)Assumption: cycle times, failure and repair times, defect and false-stop rates, the speed-stress law and team sizes are illustrative values, not data from a real plant.P(fail in Δt) = 1 − exp(−λ_i · t_work), λ_i = σ_1(v) / MTBF_i; repair work ~ Erlang-3(mean MTTR_i), done at rate 1 + 0.6·(n−1), n ≤ 2[4][1]Assumption: cycle times, failure and repair times, defect and false-stop rates, the speed-stress law and team sizes are illustrative values, not data from a real plant.p_i = p0_i · σ_2(v) (+0.12 excursion at S4); andon: detect 90 %, stop 1.5 min, fix; false stops 0.3 % · σ_2(v) per unit and station; end-of-line test catches 70 %[7][1]Assumption: cycle times, failure and repair times, defect and false-stop rates, the speed-stress law and team sizes are illustrative values, not data from a real plant.lead time W = WIP / throughput (L = λW)[6][5]cycle c = 0.62/0.64/0.90/0.75/0.72 min at rated speed (S3 = bottleneck) · MTBF 120/100/200/110/150 min of work, MTTR 4/4/3/4/3 min at 85 % speed · S2 part replacement 40 technician-min · p0 = 0.15/0.15/0.2/0.2/0.05 % per unit · excursion contained after 3 andon pulls or 15 units caught at test · rework 4 min/unit, team of 3 for 1 h per call · 40 line operators · moving averages over 30 minAssumption: cycle times, failure and repair times, defect and false-stop rates, the speed-stress law and team sizes are illustrative values, not data from a real plant.Randomness: a seeded mulberry32 generator; distributions used — uniform, exponential (inverse CDF), normal (Box–Muller), Poisson (Knuth). The seed is shown and shareable.
Educational model — not for operational decisions. Real sites calibrate every constant to their own equipment and data.