4. Establishing specification limits for CAE results

In a statistical capability study of a CAE process, the specification limits are the fixed reference against which all variation is judged. Unlike manufacturing, where limits are often inherited from a drawing, CAE results frequently have no single authoritative specification. The analyst must construct defensible limits from three distinct sources: geometric tolerance allocation, design requirements expressed as performance constraints, and customer-driven targets. Getting this wrong invalidates every Cp, Cpk, and control chart that follows, because capability indices are only as meaningful as the limits they reference.

Why CAE Specification Limits Are Harder Than Manufacturing Limits

A machined bore has a nominal diameter and a tolerance band printed on the drawing. A CAE result — say, peak stress at a bracket fillet, or maximum deflection of a suspension arm — is a computed quantity that depends on mesh density, material model, boundary conditions, and load assumptions. The "specification" is therefore a derived quantity, and different stakeholders may hold different views of what it should be. Three failure modes recur:

• Borrowed limits. A limit is copied from a similar program without checking whether the load case, material, or safety factor still applies.
• Round-number limits. A limit is set to a convenient value (e.g., "stress below 200 MPa") that has no traceable basis in yield strength, safety factor, or customer requirement.
• Double-counted margins. A safety factor is applied to the load, then again to the allowable stress, then again in the acceptance criterion, producing a limit so conservative that the process appears incapable even when it is well controlled.

The remedy is to make the derivation of each limit explicit and traceable, so that the capability study can cite a documented source rather than an assumption.

Tolerance Allocation as a Source of Limits

When the CAE result is a dimensional or geometric quantity — for example, predicted springback angle, predicted gap at a flange, or predicted thermal expansion — the specification limit can be derived directly from the tolerance stack-up of the assembly. The standard approach is to allocate the assembly-level tolerance among contributing components, then convert the allocated tolerance into an allowable range for the CAE-predicted quantity.

Consider a simplified example. An assembly requires a final gap of 2.0 ± 0.5 mm. The gap is influenced by three contributors: part A thickness, part B thickness, and fixture location. Using worst-case (linear) allocation with equal weighting, each contributor receives ±0.5/3 ≈ ±0.167 mm. If the CAE model predicts the gap as a function of these three inputs, the allowable prediction error can be set so that the predicted gap plus its uncertainty band stays inside 2.0 ± 0.5 mm. In practice, a root-sum-square (RSS) allocation is often preferred when contributors are independent:

T_assembly = sqrt(T_A^2 + T_B^2 + T_fixture^2)
# With T_assembly = 0.5 mm and equal contributors:
T_each = 0.5 / sqrt(3) ≈ 0.289 mm

The choice between worst-case and RSS allocation is itself a design decision: worst-case is conservative and appropriate for safety-critical interfaces, while RSS is more realistic for high-volume assemblies with independent variation. Whichever is chosen, the CAE specification limit should be stated together with the allocation method, because a limit derived by RSS is not interchangeable with one derived by worst-case.

Design Requirements and Safety-Factor Discipline

For performance quantities such as stress, deflection, frequency, or fatigue life, the specification limit comes from design requirements. The most common form is an allowable stress derived from material yield or ultimate strength divided by a safety factor:

allowable_stress = yield_strength / safety_factor
# Example: yield = 355 MPa, safety factor = 1.5
allowable_stress = 355 / 1.5 ≈ 236.7 MPa

The critical discipline is to apply the safety factor exactly once and to document where. If the load case already includes a load factor of 1.3, and the material allowable already includes a factor of 1.5, then the acceptance criterion should be the computed stress compared directly to 236.7 MPa — not to 236.7/1.3. Double-counting margins is the single most common reason a CAE process looks incapable: the variation is real, but the limit is artificially tight.

For deflection or frequency requirements, the limit is usually a hard performance threshold (e.g., first natural frequency above 45 Hz to avoid resonance with a 40 Hz excitation, with a 12.5% margin). Here the margin is explicit and should be stated as part of the requirement, not buried in the acceptance criterion.

Customer-Driven Targets

Some limits originate outside the engineering organization: a customer specifies a maximum temperature rise, a maximum acoustic emission, or a minimum fatigue life in cycles. These targets are contractual and should be treated as fixed specification limits, but they still require interpretation. A customer target of "fatigue life ≥ 1×10⁶ cycles" must be paired with a defined load spectrum, a defined survival probability, and a defined analysis method; otherwise the CAE result cannot be compared to it consistently.

When a customer target is expressed as a capability requirement rather than a single value — for example, "Cpk ≥ 1.33 for the predicted life" — the specification limit must be established first, because Cpk is computed from the limit. The customer's capability requirement does not define the limit; it defines how tightly the process must cluster around it.

Reconciling the Three Sources

In practice, a single CAE result may be subject to a tolerance-derived limit, a design-requirement limit, and a customer target simultaneously. The governing limit is the tightest one that is technically valid, but the analyst should record all three and explain which governs. The SVG below shows how the three sources converge on a single specification band for a predicted gap result, and how the governing limit is selected.

Worked Example: Setting Limits for a Predicted Gap Result

Suppose a CAE process predicts the gap at a body-panel interface. The assembly drawing specifies 2.0 ± 0.5 mm. The design requirement adds that the gap must not exceed 2.6 mm to avoid contact with an adjacent component. The customer specifies a maximum visible gap of 2.4 mm for appearance. The three limits are 2.5 mm (tolerance), 2.6 mm (design), and 2.4 mm (customer). The governing upper limit is 2.4 mm, because it is the tightest and all three are technically valid. The lower limit is 1.5 mm from the tolerance band, since neither the design requirement nor the customer target constrains the lower side.

The analyst then computes capability against USL = 2.4 mm and LSL = 1.5 mm, and records in the study report: "USL governed by customer appearance target; LSL governed by assembly tolerance; design contact limit of 2.6 mm is non-governing but retained for reference." This traceability is what allows the capability result to survive a design review.

Practical Checklist for Limit Establishment

Once these limits are established and documented, the capability analysis has a stable foundation. The next step — computing Cp and Cpk against these limits and interpreting the result — depends entirely on the rigor applied here. A limit that cannot be traced to a tolerance allocation, a design requirement, or a customer target is not a specification; it is a guess, and any capability index built on it inherits that uncertainty.