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Modules / Tools / Capacity ramp planner

Capacity ramp planner

Plan a fab or line ramp month by month: tool install and qualification, wafer starts, cycle time, yield and the output that reaches customers.

Manufacturing, fab and supplyFree to useHow it worksSourcesWhere it helps

Fills the inputs below with typical figures. Replace any of them with your own.

Plan length

Month 1 is the first month of the ramp. 6 to 60 months.

Tool sets and capacity

A tool set is a block of tools that together give a capacity in wafer starts a month. Size it to the step you actually buy and qualify.

A fraction is allowed, for example 0.5 for one every second month.

0 keeps installing at the same pace to the end of the plan.

For an expansion. It runs at this rate from before month 1.

From install to the first productive month: hook-up, tool qualification and process release.

Output ramp of each tool set

A newly qualified tool set does not give its full rate at once. Its output climbs in a straight line over the ramp time.

Allows for downtime, setups and the limit of loading a tool set.

Demand

0 for no ceiling.

Cycle time

Days from wafer start to wafer out. Wafers started in a month leave that many days later.

About two thirds of the fall has happened after one time constant.

Yield

Each yield climbs from its starting value to its mature value. To fit the shape to your own data, use the yield learning curve.

Share of wafers that finish without being scrapped.

Share of die on a finished wafer that work.

Gross die per wafer. For packaging, use finished units per wafer.

Month demand is met
Month 11
Capacity covers demand from this month to the end of the plan
Peak work in process
63,370 wafers
By Little's law, in month 16
First wafers out
Month 7
First good die out
Month 7
Good die out over the plan
214,059,825
572,911 wafers out of 646,233 started
Capacity in the last month
25,500 wafer starts
6 tool sets installed; starts 24,000 a month
Months held back by capacity
10
28% of the plan

Check these

  • Starts are held back by capacity in 10 months of the plan.
Wafer starts, wafers out, demand and capacity by month
Line chart of Wafers a month against Month of the plan, 4 lines: Wafer starts, Wafers out, Demand, Capacity. The same numbers are in the table under the chart.010,00020,000102030Month of the planWafers a month
  • Wafer starts (solid line, circles)
  • Wafers out (dashed line, squares)
  • Demand (dotted line, triangles)
  • Capacity (dash-dot line, diamonds)
Show the data as a table
Wafer starts, wafers out, demand and capacity by month
Month of the planWafer startsWafers outDemandCapacity
1006,0000
2006,6000
3007,2600
41,00007,9901,000
52,36008,7802,360
64,08009,6604,080
76,17070910,6006,170
88,6102,13011,7008,610
911,4003,97012,90011,400
1013,6006,67014,10013,600
1115,6009,13015,60015,800
1217,10011,90017,10017,900
1318,80014,10018,80020,100
1420,70016,10020,70021,900
1522,80017,70022,80023,300
1624,00019,50024,00024,400
1724,00021,40024,00025,100
1824,00023,20024,00025,500
1924,00023,90024,00025,500
2024,00023,90024,00025,500
2124,00023,80024,00025,500
2224,00023,80024,00025,500
2324,00023,80024,00025,500
2424,00023,70024,00025,500
2524,00023,70024,00025,500
2624,00023,70024,00025,500
2724,00023,70024,00025,500
2824,00023,70024,00025,500
2924,00023,60024,00025,500
3024,00023,60024,00025,500
3124,00023,60024,00025,500
3224,00023,60024,00025,500
3324,00023,60024,00025,500
3424,00023,60024,00025,500
3524,00023,60024,00025,500
3624,00023,60024,00025,500
Work in process by month
Line chart of Wafers in process against Month of the plan, 2 lines: Little's law (starts rate x cycle time), Counted wafer by wafer. The same numbers are in the table under the chart.020,00040,00060,000102030Month of the planWafers in process
  • Little's law (starts rate x cycle time) (solid line, circles)
  • Counted wafer by wafer (dashed line, squares)
Show the data as a table
Work in process by month
Month of the planLittle's law (starts rate x cycle time)Counted wafer by wafer
100
200
300
43,2501,000
57,4603,360
612,6007,440
718,50012,900
825,30019,200
933,00026,500
1038,50033,200
1143,50039,300
1247,20044,100
1351,20048,300
1455,70052,500
1560,70057,100
1663,40061,100
1762,90063,100
1862,40063,400
1962,00062,900
2061,70062,400
2161,40062,000
2261,10061,700
2360,90061,400
2460,70061,100
2560,50060,900
2660,40060,700
2760,20060,500
2860,10060,400
2960,00060,200
3059,90060,100
3159,80060,000
3259,70059,900
3359,60059,800
3459,60059,700
3559,50059,600
3659,50059,600

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The ramp month by month
MonthTool sets installedNew tool sets productiveCapacity (wafer starts)Demand (wafer starts)Wafer startsCycle time (days)Wafers outLine yieldDie yieldGood die outCumulative good dieWork in process (Little)Work in process (counted)
11006,0000110090.0%30.0%0000
21006,6000106091.2%35.3%0000
31007,2600102092.3%40.0%0000
4111,0007,9861,00099.1093.1%44.2%003,2541,000
5122,3618,7852,36196.2093.9%47.9%007,4653,361
6134,0839,6634,08393.7094.5%51.3%0012,5757,444
7046,16710,6296,16791.570995.1%54.3%192,533192,53318,54512,865
8058,61111,6928,61189.62,13495.5%57.0%608,438800,97225,34619,242
90611,41712,86211,41787.93,97095.9%59.4%1,179,8861,980,85832,96126,519
100613,58314,14813,58386.46,67296.2%61.6%2,055,0874,035,94538,54133,168
110615,75015,56215,562859,12596.5%63.5%2,899,1856,935,13043,47439,273
120617,91717,11917,11983.811,93296.7%65.3%3,894,07310,829,20347,15944,056
130620,08318,83118,83182.814,13896.9%66.8%4,723,56215,552,76551,23148,298
140621,88920,71420,71481.916,06497.1%68.2%5,478,28721,031,05255,73052,465
150623,33322,78522,78581.117,67797.2%69.4%6,138,04127,169,09460,69757,069
160624,41724,00024,00080.419,45097.3%70.6%6,861,68734,030,78163,37061,088
170625,13924,00024,00079.721,40097.4%71.5%7,655,65441,686,43562,87263,127
180625,50024,00024,00079.223,17097.5%72.4%8,391,93050,078,36562,43463,370
190625,50024,00024,00078.723,91097.6%73.2%8,754,95358,833,31862,04662,872
200625,50024,00024,00078.323,86897.7%73.9%8,824,46267,657,78061,70562,434
210625,50024,00024,00077.923,83097.7%74.6%8,886,37976,544,16061,40362,046
220625,50024,00024,00077.523,79697.8%75.2%8,941,56985,485,72961,13761,705
230625,50024,00024,00077.223,76697.8%75.7%8,990,79294,476,52160,90261,403
240625,50024,00024,0007723,73997.8%76.1%9,034,718103,511,23960,69561,137
250625,50024,00024,00076.723,71597.9%76.5%9,073,935112,585,17460,51260,902
260625,50024,00024,00076.523,69397.9%76.9%9,108,965121,694,13860,35060,695
270625,50024,00024,00076.423,67497.9%77.2%9,140,267130,834,40560,20860,512
280625,50024,00024,00076.223,65797.9%77.5%9,168,249140,002,65460,08260,350
290625,50024,00024,00076.123,64197.9%77.8%9,193,271149,195,92659,97160,208
300625,50024,00024,00075.923,62897.9%78.0%9,215,654158,411,58059,87360,082
310625,50024,00024,00075.823,61697.9%78.2%9,235,682167,647,26259,78759,971
320625,50024,00024,00075.723,60598.0%78.4%9,253,606176,900,86759,71059,873
330625,50024,00024,00075.623,59598.0%78.6%9,269,651186,170,51859,64359,787
340625,50024,00024,00075.623,58798.0%78.7%9,284,017195,454,53659,58459,710
350625,50024,00024,00075.523,57998.0%78.9%9,296,883204,751,41959,53159,643
360625,50024,00024,00075.423,57398.0%79.0%9,308,407214,059,82559,48559,584
What if qualification takes a different time
CaseMonth demand is metFirst wafers outPeak work in process (wafers)Good die out over the plan
0 monthsMonth 6Month 463,370223,407,058
1 monthMonth 7Month 563,370220,927,443
2 monthsMonth 9Month 663,370217,952,186
3 months (your plan)Month 11Month 763,370214,059,825
4 monthsMonth 17Month 862,872207,789,582
6 monthsMonth 19Month 1062,046192,009,699
What if the cycle time is different
CaseMonth demand is metFirst wafers outPeak work in process (wafers)Good die out over the plan
−30%Month 11Month 644,359219,472,576
−15%Month 11Month 653,864216,774,714
Your cycle timeMonth 11Month 763,370214,059,825
+15%Month 11Month 772,875211,319,696
+30%Month 11Month 882,381208,498,406

How it works

A new line does not switch on. Tool sets arrive, are qualified, and then climb to full output while the process learns. This planner turns an install schedule, a qualification lag, an output ramp, a cycle time and yield curves into wafer starts, wafers out, good die out and work in process, month by month, and shows the month capacity first catches up with demand.

  1. Install and qualify the tool sets. A tool set is a block of tools that together give a capacity in wafer starts a month. Tool sets are installed on the schedule you enter (a steady pace, or a month by month list). Each one becomes productive after the qualification lag. An existing line, if you have one, is counted from month 1 at its full rate.first productive month of a tool set = install month + qualification lag
  2. Ramp the output of each tool set. A newly qualified tool set does not deliver its full rate at once. Its output rises in a straight line from the starting share to the mature share over the ramp time, counted from its own first productive month. Capacity in a month is the sum over every productive tool set.output share at age a = start share + (mature share − start share) x min(1, a / ramp months); capacity = existing line + sum of (tool sets x wafer starts a month per tool set x output share)
  3. Limit the starts by capacity and demand. A line starts what it has capacity for, up to what customers ask for. Demand is a level that grows by a monthly percentage (with an optional ceiling), or a list in which each figure holds until the next one. The month demand is met is the first month from which capacity covers demand in every later month.wafer starts = min(capacity, demand)
  4. Move the starts through the line. Wafers started in a month leave the line one cycle time later. Starts are spread evenly across their month, so the wafers leave over an interval one month long that is shifted by the cycle time, and it is shared between the output months it overlaps. If cycle time learning is on, the cycle time falls from its starting value towards its mature value, and the cycle time that applies is the one in the month the wafers were started.cycle time in months = cycle time in days / 30.4375; wafers leaving in month m = sum over start months s of starts(s) x overlap of [s − 1 + cycle time, s + cycle time) with [m − 1, m); cycle time learning: cycle time(s) = mature + (start − mature) x exp(−(s − 1) / time constant)
  5. Apply the yields. Line yield is the share of wafers that finish the flow without being scrapped. Die yield is the share of die on a finished wafer that work. Both are applied in the month the wafers leave, and each climbs from a starting value to a mature value with a time constant, the same shape the yield learning curve tool fits to data.yield(m) = mature − (mature − start) x exp(−(m − 1) / time constant); wafers out = wafers leaving x line yield; good die out = wafers out x die per wafer x die yield
  6. Count the work in process. Little's law says the average work in process in a stable line equals the rate wafers enter times the time they spend in it. The tool applies it each month to the month's starts rate. The table also shows the work in process counted wafer by wafer (starts in minus wafers out), which differs from Little's law while the line is still ramping.work in process (Little) = wafer starts a month / 30.4375 x cycle time in days; counted work in process = previous + starts − wafers leaving

Assumptions

  • The planner follows the bottleneck: one kind of tool set whose capacity limits the whole line. A real line has many tool types, and the scarcest one sets the pace.
  • Wafers of one month's starts all take the same cycle time; there is no spread of cycle times between lots and no queueing model.
  • Wafers that fail the line yield are scrapped as they leave the line; the work in process counts them until then.
  • Yields are applied by the month wafers leave, not the month they start. The learning curve is calendar based, so a change in the plan's start date does not shift it.
  • The existing line (if any) runs at its full rate before month 1 with the starting cycle time, so its work in process is full at the start.
  • All figures in the presets are editorial estimates for a typical case. Replace them with your own tool counts, qualification times, cycle times and yields.

Limits and warnings

  • Cycle time does not rise with load. In a real line, cycle time climbs steeply as utilisation approaches the limit; feed that in as a longer cycle time or a lower mature output share.
  • Product mix, rework loops, reticle and tool re-use, and tool-by-tool constraints are not modelled; use a full line simulation for those.
  • Fab building, cleanroom and utility readiness are assumed to be in place before tool installation; they add to the real schedule.
  • Demand is a wafer start demand. Convert a die demand to wafers with the yields before entering it.
  • Months are average months of 30.4375 days; a plan shorter than six months or longer than five years is outside what the tool is meant for.

Sources

The methods and default figures rest on these public sources. The wording here is our own; read the source for its full text.

Where it helps

The lifecycle stages this tool serves: 10 stages in 10 lifecycles.

Method notev1Formula, ranges, sources and limits

Plans a fab or line ramp month by month from tool installs, qualification lag, an output ramp, cycle time and yield curves: wafer starts, wafers out, good die out, the month demand is met and the work in process.

Formula

first productive month of a tool set = install month + qualification lag; output share at age a = start share + (mature share − start share) x min(1, a / ramp months); capacity = existing line + sum of (tool sets x wafer starts a month per tool set x output share); wafer starts = min(capacity, demand); cycle time in months = cycle time in days / 30.4375; wafers leaving in month m = sum over start months s of starts(s) x overlap of [s − 1 + cycle time, s + cycle time) with [m − 1, m); cycle time learning: cycle time(s) = mature + (start − mature) x exp(−(s − 1) / time constant); yield(m) = mature − (mature − start) x exp(−(m − 1) / time constant); wafers out = wafers leaving x line yield; good die out = wafers out x die per wafer x die yield; work in process (Little) = wafer starts a month / 30.4375 x cycle time in days; counted work in process = previous + starts − wafers leaving

Inputs
InputUnitRange it holds forComes from
Plan lengthmonths6 to 60Your figure
Tool set installs fromchoicelinear, rowsYour figure
First install monthmonth1 to 60Your figure
Tool sets installed each monthtool sets0 to 50Your figure
Tool sets to install in totaltool sets, 0 for no limit0 to 500Your figure
Capacity of a tool set at full ratewafer starts a month0 to 100000Your figure
Existing line already runningwafer starts a month0 to 500000Your figure
Qualification lagmonths0 to 24Your figure
Output of a newly qualified tool set%0 to 100Your figure
Output of a mature tool set%0 to 100Your figure
Months to reach the mature outputmonths0 to 48Your figure
Demand fromchoicelevel, rowsYour figure
Demand in month 1wafer starts a monthfrom 0Your figure
Demand growth% a month-20 to 50Your figure
Demand ceilingwafer starts a month, 0 for nonefrom 0Your figure
Cycle timedays1 to 365Your figure
Cycle time learningchoiceconstant, learningYour figure
Mature cycle timedays1 to 365Your figure
Cycle time learning time constantmonths0 to 60Your figure
Line yield at the start%0 to 100Your figure
Line yield when mature%0 to 100Your figure
Line yield time constantmonths0 to 60Your figure
Die yield at the start%0 to 100Your figure
Die yield when mature%0 to 100Your figure
Die yield time constantmonths0 to 60Your figure
Die (or units) per waferdiefrom 0Your figure

Outputs: Month demand is met (month); First month wafers come out (month); Peak work in process (Little's law) (wafers); Good die out over the plan (die).

Assumptions

  • The planner follows the bottleneck: one kind of tool set whose capacity limits the whole line. A real line has many tool types, and the scarcest one sets the pace.
  • Wafers of one month's starts all take the same cycle time; there is no spread of cycle times between lots and no queueing model.
  • Wafers that fail the line yield are scrapped as they leave the line; the work in process counts them until then.
  • Yields are applied by the month wafers leave, not the month they start. The learning curve is calendar based, so a change in the plan's start date does not shift it.
  • The existing line (if any) runs at its full rate before month 1 with the starting cycle time, so its work in process is full at the start.
  • All figures in the presets are editorial estimates for a typical case. Replace them with your own tool counts, qualification times, cycle times and yields.

Uncertainty: The arithmetic is exact; the result is as good as the install dates, qualification times, cycle times and yields entered. A real ramp slips more often than it runs early, so test the plan with a longer qualification lag and a longer cycle time.

Known limits

  • Cycle time does not rise with load. In a real line, cycle time climbs steeply as utilisation approaches the limit; feed that in as a longer cycle time or a lower mature output share.
  • Product mix, rework loops, reticle and tool re-use, and tool-by-tool constraints are not modelled; use a full line simulation for those.
  • Fab building, cleanroom and utility readiness are assumed to be in place before tool installation; they add to the real schedule.
  • Demand is a wafer start demand. Convert a die demand to wafers with the yields before entering it.
  • Months are average months of 30.4375 days; a plan shorter than six months or longer than five years is outside what the tool is meant for.

Where the method comes from

The Hub's own month by month ramp arithmetic, using Little's law for work in process and the usual exponential learning shape for yield and cycle time. Presets are editorial and sit near the scale of the capacity targets named in the sources. (Editorial)

Reference example, checked by test: Worked example in this method note and in the tool's unit test: two tool sets of 1,000 wafer starts a month installed in month 1, qualified after one month at full output, demand 1,500 a month, a cycle time of exactly one month, no yield loss in the line, 50% die yield and 100 die per wafer, over six months. Month demand is met 2; First month wafers come out 3; Peak work in process (Little's law) 1,500; Good die out over the plan 300,000.

Versions

  • v1 (2026-10-25): First version, built from the tool idea.

All models in the register

Terms on this page

Fab
The cleanroom facility where wafers are processed, together with its subfab utilities, chemical distribution and automation.
WSPM
The standard measure of fab capacity, counting wafers entering the line rather than good die leaving it.
Cycle time
The elapsed time a lot takes from wafer start to wafer out, including all queueing, not just processing.
Yield
The share of manufactured units that meet specification, counted at a given step: line yield through the fab, die yield at wafer sort, and assembly and final test yield after packaging.
Wafer
A thin, polished disc of single-crystal silicon on which hundreds or thousands of identical circuits are built at the same time.
Die
A single rectangular block of processed silicon cut from a finished wafer, carrying one complete circuit.
WIP
The total quantity of wafers currently released into the line but not yet completed, held at various process steps.
Line yield
The fraction of wafers started that emerge from the fab intact and eligible for test, lost to breakage, misprocessing, scrap and hold decisions rather than to die-level defects.
Die yield
The fraction of die on a wafer that pass electrical probe test, the headline yield number for a product.
Yield learning curve
The empirical trajectory of yield versus time or cumulative volume for a technology, typically steep early and flattening as random defect limits are approached.
Learning curve
The steady fall in unit cost as cumulative production grows, driven by yield improvement, cycle-time reduction and equipment productivity.
Utilisation
The fraction of available placeable core area consumed by cell and macro instances, typically quoted as a percentage.

The full glossary

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