The line can ship today's volume in two days. It takes 34.
Process route
Each card shows a process center's capacity in panels per day. The bar shows its utilization at today's 1,400 panels/day.
Capacity vs. demand
Panels per day. Line capacity is set by the slowest center.
Diagnosis
What the corrected model says about the as-is line.
What changed from the 2024 workbook
The original Excel model was rebuilt and checked against the case data. Seven fixes changed the answer: the bottleneck moves from Procoat to Internal Circuitize (by a 3% margin, which is why it "floats"), raw process time rises from 30.4 h to 33.9 h, and the "current TH" curve is replaced by the single observed point. The full list, with reasons, is in Guide › Corrections log.
Where the line sits against the laws of flow
For any WIP level, Factory Physics bounds throughput and cycle time. A line above the practical-worst-case (PWC) curve is "good"; below it is "bad". The as-is line falls in the bad zone on both measures.
Throughput vs. WIP
Panels per day, WIP on a log axis.
Cycle time vs. WIP
Days of 19.5 productive hours.
Read-out at panels of WIP
Simulated CONWIP points appear here after you run a sweep on the Line Simulation tab.
2024 workbook vs. corrected model
Same case data, different arithmetic.
Variability Lab
Change any station parameter or the variability settings and watch utilization, queue time and WIP respond. Your edits form the "Lab scenario" used by the Benchmark and Simulation tabs.
Where each panel spends its time
Hours per station: waiting to form a lot, queueing, processing, and fixed move/other-step time.
The hockey stick
Line cycle time as demand approaches capacity, for this scenario and the case data.
Station parameters and results
Edit the white fields. Results update immediately. The shaded row is the bottleneck.
V = (ca² + ce²)/2 is the variability term, U the utilization term of the Kingman/Sakasegawa formula, te the effective lot process time. CTq = V × U × te.
Station calculation, step by step
Every number in the table above, worked out with this scenario's values. Click a station name in the table to jump here.
Line Simulation
Run the line day by day. Compare push release (an MRP schedule that releases at the demand rate) with CONWIP (a fixed WIP cap: a new job starts only when one finishes).
WIP in the line
Panels on the floor at the end of each day, total and at the three most loaded centers.
Cycle-time distribution
Share of jobs by days from release to finish. The line marks the quoted lead time.
Stations: simulated vs. queueing model
Utilization and average panels waiting.
CONWIP sweep
Simulated throughput at seven WIP caps, against the best-case and PWC curves.
Press "Run CONWIP sweep" to fill this chart.
Path forward to 3,000 panels a day in two days
Start with the lever that costs nothing: stop flooding the floor. Then lift capacity cheapest-first, so every dollar goes to the station that is the constraint at that moment. All figures below are computed live by the corrected model.
Capacity by phase
Panels per day versus the 3,000 target.
Cycle time by phase
Days at today's 1,400/day and at the 3,000/day target (blank = target not reachable yet).
Management system to keep the gains
- Daily WIP cap meeting replaces the 4:00 throughput meeting. Track WIP, output and the bottleneck's queue, not just panels shipped.
- Quote lead times from the model. With CT under 3 days, the 20-day frozen zone covers real orders, so the line builds to orders instead of forecasts.
- Product families for setups. Group the 150+ part numbers by core blank and circuit density so SMED gains hold as the mix grows.
- Quality at the source. A scrapped finished board costs about $200 versus $2 at core blank. Add an optical gate before lamination of composites.
- Level the seasonal load. Build ahead in January–February against firm forecasts instead of vendoring capacity March–December.
KPI targets
Guide & Formulas
Quick start
- Overview: read the four headline numbers and the route. Red cards are the stations that hold the line back.
- Case Benchmark: slide the WIP read-out and compare best, practical-worst and worst cases with the observed line (the black dot).
- Variability Lab: pick a preset or edit a station, then watch the bottleneck, utilization and cycle time move.
- Line Simulation: run push vs. CONWIP on the same data and see the WIP trace and cycle-time spread.
- Path Forward: follow the phased plan; "Open in Lab" loads any phase so you can stress-test it.
Your Lab edits are saved in this browser only. Nothing is sent anywhere.
Using each tab
Case Benchmark
- "As-is data" draws the curves from the case table. "Lab scenario" uses your Lab edits; "Both" overlays them (scenario dashed).
- The black dot is the observed line: 47,600 panels WIP, 1,400 panels/day, 34 days. By Little's law these three must agree: 47,600 / 1,400 = 34 days.
- Use the log scale for cycle time; the worst case grows so fast that a linear axis hides the others.
Variability Lab
- Demand is the good-panel output per day. Above line capacity the model flags the line as unstable (utilization ≥ 1).
- SCV = squared coefficient of variation (variance ÷ mean²). 0 means no variability, 1 is exponential (random), above 1 is highly erratic.
- MTTF = 0 means the station has no failure data (the case lists none for optical test and sizing).
- Raising a lot size lifts capacity (fewer setups) but adds wait-to-batch and process time per panel. Try the "Team Plan 1" preset to see this trade-off.
Line Simulation
- Push: jobs of 60 panels are released at the chosen rate with release SCV from the Lab. If the rate exceeds capacity, WIP climbs without limit.
- CONWIP: the line holds a fixed number of jobs. The minimum cap is 480 panels so lots of 300 and 120 can always form.
- Starting WIP spreads extra panels across the stations at time zero, to watch a bloated line drain.
- Statistics exclude a warm-up of 10% of the run (at least 10 days). Change the seed to see run-to-run noise.
Notation
| Symbol | Meaning | Unit |
|---|---|---|
| m | machines (tools) at a station | – |
| rbase, E | base speed of one machine; efficiency (operator, quality and other detractors) | panels/h; – |
| mf, mr, A | mean time to failure, mean time to repair, availability | h; h; – |
| L, k | lot size; lot size in 60-panel jobs (k = L/60) | panels; jobs |
| ts, tnb | setup per lot; non-bottleneck (move + other steps) time | h |
| t0, te | natural time per job; effective time per lot | h |
| c0², cs², cr², ca², ce² | SCVs of process, setup, repair, arrivals, effective process time | – |
| rb, T0, W0 | bottleneck rate, raw process time, critical WIP | panels/h; h; panels |
| w, TH, CT, u | WIP, throughput, cycle time, utilization | panels; panels/h; h; – |
Capacity formulas
Efficiency slows the machine; failures are preemptive (they stop work mid-lot); setups happen once per lot.
Worked example, Internal Circuitize: t0 = 60/(94×0.95) = 0.672 h; A = 351/354 = 0.9915; te = 2×0.672/0.9915 + 0.75 = 2.105 h; capacity = 2×120/2.105 = 114.0 panels/h = 2,223 panels/day.
Best, worst and practical worst case
A line whose throughput sits below the PWC curve at its own WIP is in the "bad" region: its variability is worse than a balanced line of exponential stations. That is a management problem (release, priorities, rework), not a capacity problem.
Queueing network (Variability Lab)
Stations are solved in route order. Each passes its departure variability to the next.
Simulation model
- The unit of flow is a job of 60 panels. A station starts a lot when k jobs are waiting and a machine is free (first-in, first-out).
- Lot process time is gamma-distributed with mean k·t0 and SCV c0²/k. Setups are gamma with mean ts and SCV cs².
- Failures are operation-dependent: during p hours of work the number of failures is Poisson(p/mf), each adding a repair with mean mr and SCV cr². This gives exactly t0/A on average.
- After a lot finishes, each job waits tnb (move and other steps) and joins the next queue. With yield below 1 a job is scrapped with probability 1 − y.
- Validation: at 1,400 panels/day push, the simulation gives CT ≈ 2.0 days and WIP ≈ 2,800 panels, matching the queueing model within 3%. Saturated throughput is ≈ 2,240/day against a computed rb of 2,223.
Case data (as-is)
Large-panel line, 3 shifts = 19.5 productive hours/day. Output 1,400 panels/day, WIP 47,600, cycle time 34 days, 50% on-time delivery, target 3,000 panels/day.
Corrections log
What was changed from the 2024 workbooks and slides, and why.
| # | Original | Corrected | Why it matters |
|---|---|---|---|
| 1 | Station rate = m/(t0+ts/L)·A·E, so availability and efficiency also shrank setup time | te = k·t0/A + ts, with E inside t0 (Factory Physics convention) | Bottleneck is Internal Circuitize (2,223/day), not Procoat (2,158). Procoat is a close second at 2,288: the "floating bottleneck" in the case |
| 2 | Queueing sheet left efficiency out of te and divided utilization by E | E applied to process time, so queue and process times both reflect it | Cycle times were understated at slow stations |
| 3 | Single-machine departure formula cd² = u²ce² + (1−u²)ca² at multi-tool stations | Multi-machine linking equation with the 1/√m term | Drilling has 31 tools; the old form passed far too much variability downstream |
| 4 | Queueing model fed 2,000 panels/day ("estimated capacity") as the arrival rate | Arrival = actual demand 1,400/day (adjustable) | Capacity is not demand; using it inflated every queue |
| 5 | "Current TH = w/34/19.5" drawn as a curve across all WIP levels | One observed point (47,600; 1,400/day; 34 days) | Little's law ties CT, TH and WIP only at the observed state; the old curve fell below the worst case at low WIP |
| 6 | Bottleneck rate labelled "2,157.75 parts/hour"; T0 = 30.4 h without non-bottleneck time at every station | Units in panels/day; T0 = Σ(te + tnb) = 33.9 h = 1.74 days | Matches the case statement that real processing takes "less than two days" |
| 7 | MTTF = 1, MTTR = 0 placeholders; yields of 90–99% invented in one workbook | "No failure data" handled explicitly; yields default to 100% (the case gives none; efficiency already covers quality loss) and stay editable | Avoids silent assumptions that move the bottleneck |
| 8 | Report solution 6: MTTR = 0, t0 = 0.001; solution 5: raise release to 2,222/day | Path forward uses achievable kaizen steps ("double the good, halve the bad") and release control | Releasing more than rb only grows WIP and cycle time; zero repair time is not attainable |
| 9 | No wait-to-batch time where lots of 300 and 120 are formed from 60-panel moves | Wait-to-batch added at Lamination – Cores, both Circuitize steps and Lamination – Composites | Shows why bigger lots ("Team Plan 1") cost cycle time |
Assumptions & limits
- One standard panel type. Real boards differ in drilling time (the plant's "complexity factor"), which makes the bottleneck move with the mix.
- Shared resources with the small-panel line (lamination, copper plate) are treated as dedicated.
- The queueing model is an approximation; trust trends and rankings more than the second decimal. The simulation checks it.
- Neither model includes expediting, "put aside" WIP in the hallway, or rework loops. That gap is why the real line runs at 34 days while both models say about 2.
- Phase costs are qualitative (low / medium / high). Capital decisions need quotes and a cash-flow case.
Sources
- Station data and situation: HAL, Inc. teaching case, Large Panel Line (W. J. Hopp, Northwestern University, 1996, rev. 2001). Names in this lab are generalized.
- Method: W. J. Hopp & M. L. Spearman, Factory Physics, chapters 7–9 (basic factory dynamics, variability, queueing networks).
- Built from an NYU Tandon Production Science (MN-GY 7893) capstone by Joey Zhou and team, Prof. Shashikant Sathaye.