化学工程
ToolFusion / Beam Dyeing Machine / Engineering Tools

Project Tool: Dye Uptake Uniformity Validation for Beam Dyeing Machine

Specification & Integration Verification

F6 Composition for Dye Uptake Uniformity Validation for Beam Dyeing Machine

● Not Golden Verified ● Project Trust Verified Runnable: 6 / 9 steps
VERIFIED SCOPE
○ Compute inner radial boundary CALCULATION Runnable
○ Compute middle radial boundary CALCULATION Runnable
○ Convert reflectance to K/S CALCULATION Partial
○ Compute RSD of K/S per zone CALCULATION Manual Workflow
○ Verify RSD compliance with textile quality threshold PASS / FAIL capable Runnable
○ Compute inter-zone bias penalty CALCULATION Partial
○ Compute intra-zone scatter penalty CALCULATION Runnable
○ Compute overall uniformity index CALCULATION Runnable
○ Verify overall uniformity index meets specification PASS / FAIL capable Runnable
⚠ This tool does not currently verify Reflectance_to_CIELAB_Conversion, Reflectance_to_KS_Conversion, Radial_Zone_Statistical_Summary.
PROJECT INPUTS

Runnable deterministic steps: 6 / 9. Enter the project conditions used by this verification workflow. Prefilled values (13/19 inputs) are demonstration inputs, not recommended design values.

01Step 1: Compute inner radial boundaryFormula
mm
To deterministically locate the 33% radial position from center for sampling grid definition.
02Step 2: Compute middle radial boundaryFormula
mm
To deterministically locate the 67% radial position from center for sampling grid definition.
03Step 3: Convert reflectance to K/SFormula
dimensionless
To transform instrument-measured reflectance into a linearized, concentration-proportional metric for statistical uni...
04Step 4: Compute RSD of K/S per zoneManual Workflow
1
To quantify intra-zone dye uptake variability for comparison against acceptance criterion (≤3%).
05Step 5: Verify RSD compliance with textile quality thresholdValidation Rule
To determine pass/fail status of radial zone uniformity per defined specification.
06Step 6: Compute inter-zone bias penaltyFormula
1
1
1
To quantify systematic radial gradient in dye uptake (e.g., center-to-edge depletion).
07Step 7: Compute intra-zone scatter penaltyFormula
%
%
%
To quantify average local variability across all zones, normalized by overall mean K/S.
08Step 8: Compute overall uniformity indexFormula
dimensionless
dimensionless
dimensionless
dimensionless
To synthesize bias and scatter penalties into a single pass/fail-relevant metric bounded between 0 (perfect) and 1 (u...
09Step 9: Verify overall uniformity index meets specificationValidation Rule
To confirm final cake-wide uniformity satisfies enterprise quality gate (U_index ≤ 0.07).

⚠ Runnable deterministic steps: 6 / 9. Steps marked "Input Required" or "Example Input Required" need user-provided engineering values before calculation.

Deterministic calculation · Results become stale when engineering inputs change.
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ENGINEERING EVIDENCE

Golden Coverage0 / 9
Project Trust11 / 11 PASS
RuntimeDeterministic
Components0 small tools, 9 steps

SCOPE & LIMITATIONS

NOT CURRENTLY VERIFIED
○ Reflectance_to_CIELAB_Conversion
○ Reflectance_to_KS_Conversion
○ Radial_Zone_Statistical_Summary
These capabilities are outside the current verified workflow.

HOW THIS VERIFICATION WORKS

  1. Step 1: Compute inner radial boundary — performs a deterministic calculation from the provided inputs. No acceptance criterion is applied; the result is CALCULATED only.
  2. Step 2: Compute middle radial boundary — performs a deterministic calculation from the provided inputs. No acceptance criterion is applied; the result is CALCULATED only.
  3. Step 3: Convert reflectance to K/S — performs a deterministic calculation from the provided inputs. No acceptance criterion is applied; the result is CALCULATED only.
  4. Step 4: Compute RSD of K/S per zone — engineering workflow step. Follow the documented method for manual execution.
  5. Step 5: Verify RSD compliance with textile quality threshold — compares engineering inputs against deterministic thresholds and produces a PASS or FAIL decision.
  6. Step 6: Compute inter-zone bias penalty — performs a deterministic calculation from the provided inputs. No acceptance criterion is applied; the result is CALCULATED only.
  7. Step 7: Compute intra-zone scatter penalty — performs a deterministic calculation from the provided inputs. No acceptance criterion is applied; the result is CALCULATED only.
  8. Step 8: Compute overall uniformity index — performs a deterministic calculation from the provided inputs. No acceptance criterion is applied; the result is CALCULATED only.
  9. Step 9: Verify overall uniformity index meets specification — compares engineering inputs against deterministic thresholds and produces a PASS or FAIL decision.

This tool coordinates 2 validation steps and 7 calculation steps. The overall engineering decision uses ALL_REQUIRED_VALIDATION_PASS aggregation: only validation steps contribute to the pass/fail outcome; calculation steps produce data only.

METHODS & EQUATIONS

All formulas are resolved from canonical runtime definitions and executed deterministically by the client-side engine.

Step 1: Compute inner radial boundary

Formula0.33 * outer_radius

Step 2: Compute middle radial boundary

Formula0.67 * outer_radius

Step 3: Convert reflectance to K/S

Formulapow((1-R_lambdamax),2)/(2*R_lambdamax)

Step 4: Compute RSD of K/S per zone

Manual Workflow
RSD (%) = 100 × [σ(K/S) / |μ(K/S)|], where σ is sample standard deviation and μ is sample mean

Step 5: Verify RSD compliance with textile quality threshold

Validation Rule
relative_standard_deviation <= 3 [customer_requirement:Textile_Quality_Spec_TQS-7.2]

Step 6: Compute inter-zone bias penalty

Formulamax(abs(mu_inner-mu_middle),abs(mu_middle-mu_outer),abs(mu_inner-mu_outer))/max(mu_inner,mu_middle,mu_outer)

Step 7: Compute intra-zone scatter penalty

Formula(RSD_inner+RSD_middle+RSD_outer)/300

Step 8: Compute overall uniformity index

Formulasqrt(pow(B,2)+pow(S,2))

Step 9: Verify overall uniformity index meets specification

Validation Rule
overall_uniformity_index <= 0.07 [customer_requirement:Textile_Quality_Spec_TQS-7.2]

UNDERSTANDING THE RESULTS

PASS
A proven validation criterion passed. The engineering input satisfies the deterministic threshold.
FAIL
A proven validation criterion failed. The engineering input does not satisfy the deterministic threshold.
CALCULATED
A deterministic calculation completed, but no acceptance criterion exists for this step. CALCULATED does NOT mean PASS.
RESULT NOT VALID
Runtime executed but engineering validity requirements were not met.
INCOMPLETE
Required inputs or workflow steps are incomplete.

The overall decision reflects only validation steps. Calculation steps produce numerical results without pass/fail claims.

WHEN TO USE THIS TOOL

  • When deterministic Beam Dyeing Machine engineering verification is needed for project-specific conditions.
  • For calculation of Compute inner radial boundary (Step 1).
  • For calculation of Compute middle radial boundary (Step 2).
  • For calculation of Convert reflectance to K/S (Step 3).
  • For calculation of Compute RSD of K/S per zone (Step 4).
  • For validation of Verify RSD compliance with textile quality threshold (Step 5).
  • For calculation of Compute inter-zone bias penalty (Step 6).
  • For calculation of Compute intra-zone scatter penalty (Step 7).
  • For calculation of Compute overall uniformity index (Step 8).
  • For validation of Verify overall uniformity index meets specification (Step 9).
  • For deterministic pre-checks before formal engineering review or submission.

When NOT to use this tool: This tool does not replace laboratory testing, formal engineering analysis by a licensed professional, or code-compliance certification. It performs deterministic threshold comparison and calculation only.

ENGINEERING FAQ

What does this verification tool check?

This tool performs 9 deterministic engineering steps: (1) Compute inner radial boundary, (2) Compute middle radial boundary, (3) Convert reflectance to K/S, (4) Compute RSD of K/S per zone, (5) Verify RSD compliance with textile quality threshold, (6) Compute inter-zone bias penalty, (7) Compute intra-zone scatter penalty, (8) Compute overall uniformity index, (9) Verify overall uniformity index meets specification.

What does a PASS result mean?

A PASS result means the validation step's deterministic threshold comparison was satisfied. It does not constitute laboratory certification or code compliance.

What does a CALCULATED result mean?

A CALCULATED result means the deterministic calculation completed, but no acceptance criterion is applied to this step. CALCULATED does NOT mean PASS.

What is not currently verified by this workflow?

Capabilities not currently verified include: Reflectance_to_CIELAB_Conversion, Reflectance_to_KS_Conversion, Radial_Zone_Statistical_Summary.

How many steps are golden verified?

0 out of 9 steps have been verified with deterministic golden test cases.

COMPONENT TOOLS

This workflow currently contains no bound executable Small Tools. Steps are defined by engineering methods and reference materials.

CalculationWorkflow StepRadial zone boundary radius calculation for beam dyeing fabric cake
CalculationWorkflow StepRadial zone boundary radius calculation for beam dyeing fabric cake
CalculationWorkflow StepReflectance-to-K_S conversion at dominant dye absorption wavelength
CalculationWorkflow StepRadial zone relative standard deviation (RSD) of K/S values
ValidationWorkflow StepRadial zone relative standard deviation (RSD) of K/S values
CalculationWorkflow StepOverall cake-wide dye uptake uniformity index
CalculationWorkflow StepOverall cake-wide dye uptake uniformity index
CalculationWorkflow StepOverall cake-wide dye uptake uniformity index
ValidationWorkflow StepOverall cake-wide dye uptake uniformity index