Conformance probability & false-acceptance risk calculator
Enter a measured value, your tolerance limits, and the measurement uncertainty to get the probability that the item is truly in tolerance, plus the specific risk of a false accept or false reject for that one result, following JCGM 106:2012. Everything runs in your browser.
Your numbers
Your best estimate of the measurand, same units as the limits.
Result
Conformance probability, in plain terms
The measurement distribution
When you report a measured value y with a standard uncertainty u, you are saying the true value is somewhere around y, with a spread of u. JCGM 106:2012 models that belief as a normal probability distribution centered on y with standard deviation u. If you only have an expanded uncertainty U at coverage factor k (commonly k = 2 for roughly 95%), the standard uncertainty is simply u = U / k.
Conformance probability
The conformance probability is the share of that distribution that lies inside the tolerance. For a two-sided tolerance with a lower limit (LSL) and upper limit (USL), it is the area between them: p_c = Φ((USL − y)/u) − Φ((LSL − y)/u), where Φ is the standard normal cumulative distribution. For a one-sided upper limit it is Φ((USL − y)/u); for a one-sided lower limit it is Φ((y − LSL)/u). A conformance probability of 0.98 means a 98% chance the item is genuinely within spec.
Specific risk of a wrong decision
Your decision follows from where the measured value falls. If y is inside the tolerance you accept, and the specific risk of a false acceptance is 1 − p_c: the probability the true value was actually outside the limits. If y is outside the tolerance you reject, and the specific risk of a false rejection is p_c: the probability the item was really in tolerance. Both numbers come from this single result and its uncertainty, with no assumption about your process.
That last part matters. This is the specific risk for one reported result. The global (or average) risk, the long-run false-accept rate over many items, is a different quantity: it needs a prior distribution describing the population entering inspection. That is a separate analysis under JCGM 106, and this tool does not invent a process distribution to estimate it.
Common questions
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What is conformance probability?
Conformance probability is the probability that the true value of a measured quantity lies inside the tolerance, given one reported result and its measurement uncertainty. It is the area of the measurement probability distribution (a normal curve centered on the measured value, with standard deviation equal to the standard uncertainty) that falls between the specification limits. A conformance probability of 0.98 means there is a 98% chance the item is genuinely in tolerance.
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What is the specific risk of false acceptance?
When you accept an item because the measured value is inside the tolerance, the specific risk of false acceptance is the probability that the true value is actually outside the tolerance, equal to one minus the conformance probability. It is computed from this single result and its uncertainty alone. If instead you reject because the measured value is outside the tolerance, the specific risk of false rejection equals the conformance probability: the chance the item was really in tolerance after all.
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How is this different from a guard band?
A guard band is a fixed decision rule applied before you measure: you shrink the acceptance limit by some amount (often the expanded uncertainty) so that passing items are comfortably inside tolerance. This calculator does the opposite direction of analysis: it takes a result you already have and reports the actual probability of conformance and the risk attached to the accept or reject decision for that one result. Use the guard band calculator to set the rule; use this to quantify the risk of an individual measurement.
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What is the difference between specific and global risk?
The specific risk is the risk attached to one particular reported result, computed only from that result and its uncertainty. It needs no assumption about how your process is distributed, which is why it is reported here. The global (or average) risk is the long-run false-accept or false-reject rate over many items, and it requires a prior probability distribution describing the population of items entering inspection. JCGM 106:2012 covers both; this tool computes the specific risk and deliberately does not invent a process distribution to estimate the global risk.
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Do I use standard or expanded uncertainty?
The model uses the standard uncertainty u (the standard deviation of the measurement distribution). If you only have an expanded uncertainty U, divide by the coverage factor: u = U / k, with k = 2 being the usual choice for an approximate 95% interval. The calculator accepts either: enter a standard uncertainty directly, or enter U with its k and it converts for you.
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Does ISO/IEC 17025 require this analysis?
ISO/IEC 17025:2017 clause 7.8.6 requires that, when a statement of conformity to a specification is reported, the laboratory documents the decision rule it applies and accounts for the level of risk associated with it. Conformance probability and specific risk are the standard quantitative way to express that risk for an individual result, following JCGM 106:2012 and ILAC-G8:2019. The decision rule and acceptable risk level remain your laboratory’s policy.
This calculator computes the specific (per-result) conformance probability and decision risk for one measured value, assuming a normal measurement distribution per JCGM 106:2012. It does not assess the global (average) risk over many items, which requires a prior process distribution, and it does not set your laboratory’s acceptable-risk policy or replace JCGM 106:2012, ISO/IEC 17025:2017, or ILAC-G8:2019. Confirm the normality assumption fits your measurement and review any conformity decision against your own quality system before you use it.
Carry the risk with the result
Axiospec keeps every calibration, uncertainty, and conformity decision in one tamper-evident ledger built for ISO/IEC 17025. See it on real calibration data, no signup.