Specification interval
Outer permitted density region.
Unit Converters
Density Tolerance Calculator
Evaluate one corrected density result against asymmetric specifications using a declared point-value guard. The measurement temperature is checked separately because density is condition dependent.
Conditioned density conformity
Apply a guarded point decision only after temperature comparability passes
Build asymmetric density specifications, contract them by an explicit gU guard, retain the measurement interval as evidence, and route any temperature mismatch to Review.
Final decision—
Numerical decision—
Deviation from nominal—
Lower acceptance—
Upper acceptance—
Temperature difference—
Apply a guarded point decision only after temperature comparability passes ledgerUnrounded values drive calculations and decisions
| Boundary or check | Value | Role | Decision effect |
|---|
How to use
Apply a guarded point decision only after temperature comparability passes
Build asymmetric density specifications, contract them by an explicit gU guard, retain the measurement interval as evidence, and route any temperature mismatch to Review.
- Copy nominal density and asymmetric limits from the current specification.
- Enter the corrected unrounded measurement in the same density unit.
- Enter expanded uncertainty as an absolute half-width and use the approved guard multiplier.
- Enter specified and measured temperatures plus the permitted difference.
- Archive numerical and final decisions separately when temperature forces Review.
Guarded conformity quantities
Guarded acceptance
Specification contracted inward by gU.
Measurement interval
Measured value ± expanded uncertainty, retained as evidence.
Numerical decision
Point comparison before condition gating.
Temperature gate
Validity check for the conditioned density measurand.
Result interpretation
Read numerical verdict and condition gate separately
Accept requires both the unrounded point inside guarded acceptance and a matched temperature condition. Reject means the numerical point lies outside specification only when temperature matches. A temperature mismatch produces final Review regardless of whether the separate numerical screen says Accept or Reject.
Calculation method
Apply asymmetric limits and an uncertainty guard
Calculate asymmetric limits around nominal, form guard width gU, reject a collapsed acceptance interval, compare the measured point once with acceptance and specification, then apply the entered temperature allowance as a separate condition gate. Do not add the displayed ±U interval as a second hidden guard.
Evidence checks
Specification, guard, and temperature checks
Decision-rule authority
The quality plan or contract must authorize the guard multiplier and three-state rule; the calculator does not choose them.
Temperature conditioning
Density changes with temperature, so a point at the wrong condition is not the specified measurand without a valid correction.
Uncertainty interpretation
Expanded uncertainty is not a correction and its coverage statement must be retained.
Asymmetric limits
Lower and upper percentages are calculated independently; do not replace them with a symmetric average.
Boundary equality
Unrounded equality at an acceptance limit is accepted under this declared inclusive rule.
Review ownership
Assign who investigates Review outcomes and whether retesting, conditioning, or corrected reporting is allowed.
Risk limitation
This guard-band screen does not calculate producer or consumer risk probabilities.
Visual explanation
Guarded density corridor with uncertainty evidence and temperature gate
The outer band shows specifications, the inner band shows point acceptance, and the blue measurement interval remains separate. A temperature badge overrides the final color to Review when the condition fails.
Detailed calculation process
Acceptance corridor and condition gate
LSL = ρn(1−tL); USL = ρn(1+tU); AL = LSL+gU; AU = USL−gU; numerical point decision; |Tm−Ts| > ΔTmax ⇒ final Review
| Symbol | Meaning | Required unit |
|---|---|---|
| ρn | nominal density | selected unit |
| ρm | corrected measured density | selected unit |
| tL,tU | asymmetric tolerances | fraction |
| U | expanded uncertainty half-width | selected unit |
| g | guard multiplier | dimensionless |
| ΔTmax | allowed temperature difference | °C |
- Waiting for current inputs.
- Waiting for current inputs.
- Waiting for current inputs.
- Waiting for current inputs.
- Waiting for current inputs.
- Waiting for current inputs.
Reconciliation:Waiting for current inputs.
Defaults and assumptions
Point result, uncertainty, and test temperature
Defaults are a demonstration around 850 kg/m³ with asymmetric limits, a one-unit expanded uncertainty, and a narrow temperature allowance. They authorize no real release decision.
| Check | Current value A | Current value B | Decision role |
|---|
Decision analysis
Use the verdict as a documented decision rule
Use final Accept, Reject, or Review only under the declared rule. Preserve numerical decision separately so a condition hold does not erase evidence that the point itself was outside specification.
Treat the final decision as the output of both a numerical rule and a condition-validity rule. First verify that nominal density, asymmetric tolerances, uncertainty, and guard multiplier belong to the same specification revision. Then confirm that measured temperature is a corrected observation with adequate resolution and that the allowed difference is authorized by the product or method. If temperature fails, retain the numerical Accept or Reject as diagnostic evidence but route the workflow to Review; do not publish a conclusive conformity statement for the wrong conditioned measurand. Review may require reconditioning, retesting, or applying a validated temperature correction, with authority defined outside this calculator. When temperature passes, inspect how close the unrounded point lies to guarded acceptance and specification limits. The displayed measurement interval documents uncertainty but does not create a second hidden guard. Record coverage factor and uncertainty basis so another reviewer can reproduce gU. For high-consequence decisions, a fixed guard may be insufficient; the governing system may require explicit consumer or producer risk, one-sided limits, or Bayesian prior information. This page implements only the declared three-state point rule.
Evidence and data lineage
Retain specification, uncertainty, and condition
Retain specification revision, nominal basis, corrected result, unit, temperature records, uncertainty report and coverage, guard authority, acceptance limits, numerical decision, and final decision.
Limits and exclusions
What this guarded decision does not certify
The page does not correct density to reference temperature, estimate decision risk, combine uncertainty components, evaluate process capability, or replace a required standard-specific rule.
Reliable sources
References for Apply a guarded point decision only after temperature comparability passes
Conformity-assessment terms
Worked cases
Density release decisions
Conditioned product release
The density point is acceptable but the sample is two degrees warm, so final status remains Review until conditioning or valid correction.
Outside-spec point
The numerical screen is Reject; a simultaneous temperature mismatch still preserves Reject as numerical evidence while final workflow status is Review.
Important note
Apply a guarded point decision only after temperature comparability passes: scope before action
Never force a conclusive verdict from a measurement made at the wrong condition. Review is a deliberate decision state, not a calculation failure.
Apply a guarded point decision only after temperature comparability passes FAQ
Why are numerical and final decisions separate?
Temperature can invalidate comparability without erasing the point-value evidence.
Is uncertainty applied twice?
No. U forms gU; the displayed interval is supporting evidence.
What does guard factor zero do?
Acceptance limits coincide with specifications.
Can tolerances be asymmetric?
Yes. Lower and upper percentages are independent.
Why must temperature match?
The specification defines density at a condition, not as a condition-free constant.
Can the page correct temperature automatically?
No. That requires a validated material-specific expansion model.
What if the guard collapses the interval?
The inputs are rejected as an invalid decision rule.
Does equality pass?
Equality at an inclusive guarded limit is accepted when temperature matches.
Can uncertainty be entered as percent?
Convert it to an absolute half-width in the density unit first.
Does Reject always become final Reject?
Only when the temperature condition passes.
Who owns Review?
The governing quality procedure must define escalation and retest authority.
Does Accept prove process capability?
No. It evaluates one measurement under one rule.
Can I use standard deviation as U?
Not without the required uncertainty evaluation and coverage factor.
Was shared PDF logic changed?
No. This batch uses its own collector while reusing the existing report engine.