Specification limits
Outer allowable interval around nominal.
Unit Converters
Concentration Tolerance Calculator
Produce an Accept, Review, or Reject point decision while keeping analytical recovery suitability distinct from specification conformance.
Conformity with method gate
Guard concentration limits and keep recovery validity separate
Evaluate one measured concentration against asymmetric specification limits with an explicit gU guard. An independent recovery window can hold the final decision for review when the analytical method is not valid for this result.
Final verdict—
Numerical point verdict—
Deviation from nominal—
Guarded acceptance interval—
Method recovery—
Applied guard width—
Concentration decision-rule ledgerUnrounded values drive calculations and decisions
| Boundary or gate | Value | Role | Decision meaning |
|---|
How to use
Guard concentration limits and keep recovery validity separate
Evaluate one measured concentration against asymmetric specification limits with an explicit gU guard. An independent recovery window can hold the final decision for review when the analytical method is not valid for this result.
- Enter nominal and measured values on one concentration basis.
- Enter authorized lower and upper percentage tolerances.
- Enter expanded uncertainty and the intended guard multiplier.
- Enter observed recovery and its approved range.
- Read numerical and final verdicts separately.
Specification limits, guard bands, recovery, and uncertainty
Guard band
gU moved inward from each specification limit.
Accept
Point lies inside the guarded interval and recovery gate is valid.
Review
Point lies in a guard band or method recovery is outside its window.
Reject
Point lies beyond an outer specification limit when the method gate is valid.
Result interpretation
Read numerical conformance and method validity separately
The numerical point verdict answers where the measured value lies. The final verdict also asks whether method recovery is acceptable. A failed recovery gate produces Review; it does not silently correct the concentration or transform a reject into acceptance.
Calculation method
Apply the guarded interval before the recovery gate
Calculate asymmetric limits from nominal. Multiply expanded uncertainty U by guard factor g and shrink both sides to form the acceptance interval. Apply the three-state point rule, then apply the recovery window as an independent validity gate.
Evidence controls
Control the specification and uncertainty decision rule
Decision-rule authority
Confirm specification revision, uncertainty basis, coverage, guard multiplier, and boundary convention before use.
Same concentration basis
Nominal and measured values must refer to the same analyte, denominator, dilution state, and unit.
Recovery relevance
Use recovery from an appropriate spike, reference material, or control for the same method and matrix.
Point versus interval rule
This calculator uses a point with guarded limits; it does not require the entire uncertainty interval inside specification.
Boundary equality
Equality at guarded acceptance limits is accepted; equality at outer limits remains inside the review or rejection logic as calculated.
Uncertainty components
Expanded uncertainty should already reflect justified method components and coverage.
High-consequence decisions
Risk-based or probabilistic rules may be required instead of a fixed guard.
Visual explanation
Guarded specification corridor with recovery validity gate
The pale corridor is specification; the inner green corridor is guarded acceptance. The measured marker shows numerical position, while the recovery annotation controls whether that numerical result is decision-valid.
Detailed calculation process
Recalculate Guard concentration limits and keep recovery validity separate from current inputs
LSL = nominal(1 − tlower); USL = nominal(1 + tupper); acceptance = [LSL + gU, USL − gU]
| Symbol | Meaning | Required unit |
|---|---|---|
| nominal | target concentration | declared concentration unit |
| tlower, tupper | asymmetric tolerances | fraction or % |
| U | expanded measurement uncertainty | same unit as concentration |
| g | guard multiplier | dimensionless |
| LSL, USL | outer specification limits | concentration unit |
| recovery | method-control recovery | % |
- 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
Guard concentration limits and keep recovery validity separate starting assumptions
Defaults illustrate a nominal 100 with −5%/+8% tolerances, U = 1.2, g = 1, and an approved 90–110% recovery window. They are not universal compliance limits.
| Check | Current value A | Current value B | Decision role |
|---|
Decision analysis
Act on Accept, Reject, and Review without hiding uncertainty
Use Accept, Review, or Reject only under the declared rule and recovery evidence. A Review should route to an authorized action such as reconditioning, reanalysis, investigation, or risk review.
Confirm whether uncertainty is expanded or standard; multiplying the wrong quantity by g changes the guard. Do not apply recovery twice by correcting the measured value and also using the recovery gate unless the method explicitly requires both. A recovery outside range may indicate matrix effects, preparation loss, contamination, calibration trouble, or an unsuitable control. Investigate cause rather than treating Review as a softer Reject. Record the unrounded distances to both outer and guarded limits for boundary cases.
Verification workflow
Validate the concentration conformity evidence chain
Freeze the governing decision rule
Record the specification owner, revision, nominal basis, asymmetric limits, boundary equality convention, uncertainty definition, guard multiplier, and recovery window before seeing the sample result. A legal, contractual, internal process, and laboratory control rule can differ even when their numeric limits look similar. Verify whether the rule applies to an individual result, a reportable mean, or a lot statistic. Do not choose g after calculating which value would produce acceptance.
Validate the uncertainty input
Determine whether the entered quantity is expanded uncertainty U, standard uncertainty u, or an interval from another method. Record coverage factor or probability and the concentration level to which it applies. If uncertainty changes with concentration, use the value relevant to the measured result. Confirm units after dilution restoration and do not combine relative and absolute uncertainty without conversion. Shared calibration and preparation components may be correlated and require a controlled uncertainty budget upstream.
Interpret recovery as method evidence
Use a control that is relevant to analyte, matrix, preparation, concentration, and batch. A spike may monitor extraction plus matrix effects, while a neat standard can monitor only calibration response. Confirm whether the approved range is inclusive and whether recovery is corrected for native analyte. An out-of-range recovery creates a method-validity hold here; the authorized laboratory procedure determines rerun, dilution, alternate method, investigation, or qualification.
Investigate every Review state
A point in the guard band has different implications from a centered point with failed recovery, even though both show Review. Preserve the numerical point verdict and gate state separately. Examine unrounded distances to specification and acceptance boundaries, source uncertainty, calibration, dilution, sample homogeneity, and control results. Do not describe Review as “almost pass” or “automatic fail.” Route it to the named decision authority with enough evidence to choose the next action.
Document the final conformity statement
A valid report identifies the measured quantity, result and unit, uncertainty and coverage, specification, decision rule, recovery-control result, boundary convention, and final authorized disposition. The calculator’s PDF provides the arithmetic trail but does not sign the conformity statement. If a repeat result is obtained, preserve the original and state whether the procedure permits replacement, averaging, or selection. Audit that no one applied recovery or dilution twice between the instrument, LIMS, calculator, and certificate.
Evidence and data lineage
Records required for Guard concentration limits and keep recovery validity separate
Retain specification version, nominal basis, uncertainty budget and coverage, guard rule, boundary convention, method, matrix, recovery control identity, acceptance window, raw result, dilution, analyst, and final disposition authority.
Limits and exclusions
Boundaries of Guard concentration limits and keep recovery validity separate
The page does not select a legal decision rule, estimate consumer or producer risk, correct recovery, calculate uncertainty, handle one-sided limits, or override method-control procedures.
Reference framework
Authority for Guard concentration limits and keep recovery validity separate
JCGM 106 addresses conformity assessment with measurement uncertainty and explains that decision rules control the balance of incorrect-acceptance and incorrect-rejection risk. The GUM provides the broader uncertainty framework, and the International Vocabulary of Metrology distinguishes measurement result, uncertainty, and metrological traceability. This calculator implements one transparent fixed-guard, three-state point rule rather than claiming universal compliance. The applicable specification, contract, regulation, laboratory procedure, and recovery-control method remain authoritative. Record the source and revision of each limit and the meaning of U and g; otherwise a correct calculation can still produce an unauthorized conformity statement.
Guard concentration limits and keep recovery validity separate terminology
LSLLower specification limit.
USLUpper specification limit.
Guard bandZone between specification and guarded acceptance boundary.
Expanded uncertaintyStandard uncertainty multiplied by a coverage factor.
Recovery controlKnown addition or material used to monitor analytical bias.
ConformityFulfilment of specified requirements under a stated rule.
ReviewIndeterminate or invalid-for-decision state requiring authority.
Decision riskChance of incorrect acceptance or rejection.
Worked decision cases
Guard concentration limits and keep recovery validity separate decisions in practice
Release result near upper limit
A point inside specification but outside guarded acceptance is routed to Review.
Good point, poor recovery
The numerical result may be centered, yet final verdict remains Review because method validity failed.
Important note
Before relying on Guard concentration limits and keep recovery validity separate
Never use the recovery gate as a hidden correction or let a numerical Accept override invalid analytical performance.
Guard concentration limits and keep recovery validity separate FAQ
Why are there two verdicts?
The point verdict describes concentration position; the final verdict also includes recovery validity.
Does uncertainty get added to the measured value?
Not in this rule. gU is applied to specification limits.
Why asymmetric tolerances?
Some concentration requirements permit different low and high deviations.
Can the guarded interval disappear?
Yes. Excessive uncertainty or guard width makes acceptance impossible, and the calculator rejects that setup.
Does Review mean failure?
No. It means the declared rule cannot support a direct acceptance or rejection.
Can recovery correct the result?
Only if the governing method authorizes a correction. This calculator treats recovery as a gate.
What if recovery is exactly at a boundary?
The inclusive window treats it as valid.
Can U be zero?
Yes only when zero is genuinely the authorized input; it should not be used to hide missing uncertainty.
Is g always one?
No. It must come from the chosen decision rule.
Can I use legal limits?
Only after confirming the legal text, units, basis, and mandated decision rule.