Trade-Off Curves

Map cost against the design variable: weight, tolerance, power — know where the next saving lives.

Time45 min
FormatSmall group
StageEvaluate

Trade-Off Curves: what it is and why it works

A trade-off curve plots cost against one design variable, such as tolerance, weight, power, surface finish or design pressure, over the range the requirement discussion is considering. Each point comes from a quote or a cost model at that level of the variable. The shape of the curve then speaks for itself: along the flat part, tightening the requirement costs little; past the knee, each extra increment of performance costs disproportionately more. The method turns requirement negotiations from opinion into evidence, because everyone can see what the last increment of performance actually buys.

Trade-off curves work because most cost-performance relationships are strongly nonlinear, and people underestimate how steep the far end is. A tolerance that forces an extra grinding or honing operation, a weight target that forces titanium or a power density that forces liquid cooling all create step changes that are invisible in a single-point estimate. The curve is most useful when requirements are still negotiable, early in concept work alongside QFD Lite and Kano Value, which clarify what customers actually value. It also sets up the Cost Window by showing the cost range the design can realistically live in, and it should be refreshed whenever volume or technology shifts the curve.

What you need

The design variable under discussion and the range being considered
Cost data at four or more levels of the variable, from quotes or should-cost models
The functional or customer reason behind the requested level
Production volume and process assumptions behind the cost points

What you get

A cost-versus-variable chart with the knee identified
The process or technology step that causes each jump
A recommended requirement level with its cost and its functional justification
Documented assumptions and a trigger for re-checking the curve

When to use it

When requirements are negotiated without knowing what they cost.

How to do it, step by step

Pick the design variable under negotiation: weight, tolerance, power, finish.
Collect cost data for several levels of the variable from quotes or models.
Plot cost against the variable and find the knee of the curve.
Present the curve in requirement discussions instead of opinions.
Re-check the curve when volumes or technologies change.

Worked example: Bore tolerance on a hydraulic valve body

Illustrative scenario — figures are realistic but not from a real company.

A hydraulics manufacturer was developing a directional valve body machined from ductile iron, planned at 8,000 units a year. The design team wanted a spool bore tolerance of +/-0.00025 in; manufacturing argued it was excessive. The debate had lasted three meetings.

The cost engineer built a should-cost model for four tolerance levels: +/-0.002, +/-0.001, +/-0.0005 and +/-0.00025 in.
Unit costs came out at $42, $48, $71 and $118. The jump at +/-0.0005 in came from adding a honing operation; the jump at +/-0.00025 in came from honing plus 100% air-gauge inspection and selective fitting of spools.
Engineering reviewed leakage test data and found that +/-0.0005 in met the internal leakage requirement with margin when combined with a tighter spool diameter tolerance.
The curve and the leakage data were shown together at the next requirements review.

Result. The team set the bore at +/-0.0005 in, saving about $47 per unit, or roughly $376,000 a year at plan volume, with no loss of function. The knee was not where either side had argued: the tightest level was unnecessary, but the loosest would have failed the leakage requirement.

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Common pitfalls and how to avoid them

Plotting only two points, which makes every curve look linear.Cost at least four levels spanning the range, and include the level where a new process step becomes necessary.
Mixing cost points built on different volumes or suppliers.Hold volume, supplier and process assumptions constant along the curve and state them on the chart.
Choosing the cheapest point without checking function.Overlay the functional requirement or test data on the curve so the chosen level is both affordable and sufficient.
Treating the curve as permanent.Re-check when volumes, technology or suppliers change, since new processes move the knee.

Frequently asked questions

How do you find the knee of a cost curve?

Plot cost against the variable and look for where the slope changes sharply, typically where a new operation, material or technology becomes necessary. Numerically, compare the marginal cost per increment of performance between adjacent points; the knee is where that marginal cost jumps. It is usually explained by a physical step, so ask what process change occurs there.

Why do tight tolerances cost so much?

Beyond a certain level, a tolerance cannot be held by the base process and needs extra operations such as grinding, honing or lapping, slower feeds, more inspection, higher scrap or selective assembly. Each of these adds a step change in cost. That is why the tolerance-cost relationship is strongly nonlinear rather than proportional.

What is the difference between a trade-off curve and a Pugh matrix?

A Pugh matrix compares several discrete concepts against a baseline across multiple criteria, usually with plus, minus or same scores. A trade-off curve examines one continuous variable in depth and quantifies how cost changes along it. They are complementary: use Pugh to choose a concept, then trade-off curves to set the key parameters within it.

Origin

Trade-off curves in engineering design — systems engineering practice; Pugh concept selection context.

Related methods

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