Decision rule and specific risk

Apply a decision rule to one measured value: simple acceptance, a guard band w = r × U (w = U is the common rule), or a guard band set for a target risk. Shows the acceptance limits, the probability the true value is outside tolerance, and wording you can paste onto a certificate that names the rule.

Conformity · decision rule

v0.1.0 · ILAC G8 · JCGM 106

Measured valueLower limit (blank for none)Upper limit (blank for none)Unit (for the wording)Expanded uncertainty UCoverage factor kDecision ruleMultiplier r (1 gives w = U)

Result, per the rule chosenConformsRule: guarded acceptance, w = 1 × U. Acceptance limits -9.6 to 9.6; w = 0.4.

Specific false-accept risk0.62 %Probability the true value is outside tolerance, for this reading (normal, u = U/k)

Wording for the certificate

Conforms to the specification (−10 to 10 mV) per decision rule: guarded acceptance, w = 1 × U; guard band w = 0.4 mV, acceptance limits −9.6 to 9.6 mV. Measured value 9.5 mV, expanded uncertainty U = 0.4 mV (k = 2). Specific probability of false accept: 0.62 % (probability for this measured value, normal distribution, JCGM 106:2012).

AL = TL + w, AU = TU − w, w = r·U · P(out) = Φ((TL − y)/u) + Φ((y − TU)/u), u = U/kShow full precision

How this is calculated

Equation: AL = TL + w, AU = TU − w, w = r·U; P(out) = Φ((TL − y)/u) + Φ((y − TU)/u), u = U/k; conforms per the rule when AL ≤ y ≤ AU
Source: Decision rules and guard bands as described in ILAC G8:09/2019 (§1.7 guard band; §4.1–4.2 simple and guarded acceptance; §5.2 Table 1, w = r·U) and ASME B89.7.3.1; specific risk from a measured value with a normal distribution as in JCGM 106:2012 (cite the documents, do not reproduce them).
Valid range: k from 1 to 4; r from 0 to 10; target specific risk 0.0001 to 0.5. Normal distribution assumed.
Rounding: Risks shown as percentages to 2 significant figures; limits and guard bands to 6. The decision is made at full precision.
Version: v0.1.0 · changelog

Calculated value, not a certified result. Accredited laboratories must validate any software they use (ISO/IEC 17025 clause 7.11).

Test vectors for this tool

The reference cases this calculator is tested against on every change. Use them to check your own software. All test vectors · Download JSON

ID	Inputs	Expected	Tolerance	Source
CONF-01	reading = 10, lower = -10, upper = 10, U = 1, k = 2	0.5 probability	± 1e-15	Exact: Φ(0) = 1/2 by the symmetry of the normal distribution
CONF-02	reading = 9, lower = -10, upper = 10, U = 1, k = 2	0.02275013194817921 probability	± 1e-14	Closed-form standard normal value; checked with mpmath 1.4.1 at 30 significant digits: Φ(−2) = erfc(√2)/2 = 0.022750131948179207
CONF-03	reading = 0, lower = -1.959963984540054, upper = 1.959963984540054, U = 2, k = 2	0.05 probability	± 1e-14	Closed-form standard normal value; checked with mpmath 1.4.1 at 30 significant digits: Φ⁻¹(0.975) = 1.959963984540054
CONF-04	reading = 8, upper = 10, U = 2, k = 1	0.15865525393145705 probability	± 1e-14	Closed-form standard normal value; checked with mpmath 1.4.1 at 30 significant digits: Φ(−1) = erfc(1/√2)/2 = 0.15865525393145705
CONF-05	reading = -1, lower = 0, upper = 100, U = 2, k = 2	0.8413447460685429 probability	± 1e-14	Closed-form standard normal value; checked with mpmath 1.4.1 at 30 significant digits: Φ(1) = 1 − Φ(−1) = 0.8413447460685429
CONF-06	U = 2, k = 2, targetRisk = 0.025, lower = -100, upper = 100	1.959963984540054 same as U	± 1e-12	Closed-form standard normal value; checked with mpmath 1.4.1 at 30 significant digits: Φ⁻¹(0.975) = 1.959963984540054
CONF-07	U = 0.4, k = 2, targetRisk = 0.025, upper = 10	0.3919927969080108 same as U	± 1e-12	Closed-form standard normal value; checked with mpmath 1.4.1 at 30 significant digits: 0.2 × Φ⁻¹(0.975) = 0.3919927969080108
CONF-08	reading = 9.5, lower = -10, upper = 10, U = 0.4, k = 2, rule = guard-band, multiplier = 1	9.6 same as reading	± 1e-12	Definition of the guarded acceptance limit AU = TU − w with w = r·U (ILAC G8:09/2019 §1.7, §5.2; ASME B89.7.3.1)
CONF-09	reading = 9.5, lower = -10, upper = 10, U = 0.4, k = 2, rule = guard-band, multiplier = 1	conforms per rule	exact	Binary guarded acceptance: conforms when AL ≤ y ≤ AU (ILAC G8:09/2019 §4.2.2; ASME B89.7.3.1)
CONF-10	reading = 9.7, lower = -10, upper = 10, U = 0.4, k = 2, rule = guard-band, multiplier = 1	does-not-conform per rule	exact	Binary guarded acceptance: conforms when AL ≤ y ≤ AU (ILAC G8:09/2019 §4.2.2; ASME B89.7.3.1)
CONF-11	reading = 10, lower = -10, upper = 10, U = 1, k = 2, rule = simple	conforms per rule	exact	Simple acceptance: acceptance limits equal the tolerance limits (w = 0)
CONF-12	reading = 0, lower = -1, upper = 1, U = 1, k = 5	OutOfRangeError	exact	Metrology Bench rule: refuse rather than extrapolate (coverage factor accepted from 1 to 4)
CONF-13	reading = -5.47, upper = -5.4, U = 0.05, k = 1	0.08 probability	± 0.005	JCGM 106:2012 (BIPM, https://www.bipm.org/documents/20126/2071204/JCGM_106_2012_E.pdf), 7.3.3 Example 1 (Zener diode), p. 15 (PDF p. 24): printed pc = 0.92 (2 decimals), so P(out) = 0.08 ± 0.005. Repeated in UKAS LAB 48 Edition 5 (July 2024), Decision rules and statements of conformity, Example 7, p. 23.
CONF-14	reading = 509.7, lower = 490, U = 8.6, k = 1	0.01 probability	± 0.005	JCGM 106:2012 (BIPM, https://www.bipm.org/documents/20126/2071204/JCGM_106_2012_E.pdf), 7.3.3 Example 2 (container bursting strength), p. 15 (PDF p. 24): printed pc = 0.99, so P(out) = 0.01 ± 0.005. Repeated in UKAS LAB 48 Edition 5 (July 2024), Decision rules and statements of conformity, Example 6, p. 21.
CONF-15	reading = 13.6, lower = 12.5, upper = 16.3, U = 1.8, k = 1	0.34 probability	± 0.005	JCGM 106:2012 (BIPM, https://www.bipm.org/documents/20126/2071204/JCGM_106_2012_E.pdf), 7.4 Example (SAE 40 motor oil viscosity), p. 16 (PDF p. 25): printed pc = 0.66, so P(out) = 0.34 ± 0.005. Repeated in UKAS LAB 48 Edition 5 (July 2024), Decision rules and statements of conformity, Example 12, p. 29 (PFA = 34 %).
CONF-16	U = 0.5, k = 2, targetRisk = 0.05, lower = 0, upper = 1	0.45 same as U	± 0.005	JCGM 106:2012 (BIPM, https://www.bipm.org/documents/20126/2071204/JCGM_106_2012_E.pdf), 7.7.5 (Figure 7), p. 19 (PDF p. 28): with Cm = 1 (um = T/4) pc ≥ 95 % only for 0.45 ≤ ỹ ≤ 0.55, i.e. guard band 0.45 T on each side (2 decimals, read from the figure).
CONF-17	U = 1.2755, k = 1, targetRisk = 0.001, lower = -10, upper = 10	3.9416 same as U	± 0.00005	NASA-HDBK-8739.19-4 (Baseline 2010-07-13, revalidated 2018-03-01, standards.nasa.gov), 5.5 Table 5-4 (confidence level guardband limits), p. 65 (PDF p. 85): max allowable risk 0.10 %, printed ±guardband limit 6.0584 mV; expected w = 10 − 6.0584.
CONF-18	U = 1.2755, k = 1, targetRisk = 0.005, lower = -10, upper = 10	3.2855 same as U	± 0.00005	NASA-HDBK-8739.19-4 (Baseline 2010-07-13, revalidated 2018-03-01, standards.nasa.gov), 5.5 Table 5-4 (confidence level guardband limits), p. 65 (PDF p. 85): max allowable risk 0.50 %, printed ±guardband limit 6.7145 mV; expected w = 10 − 6.7145.
CONF-19	U = 1.2755, k = 1, targetRisk = 0.01, lower = -10, upper = 10	2.9673 same as U	± 0.00005	NASA-HDBK-8739.19-4 (Baseline 2010-07-13, revalidated 2018-03-01, standards.nasa.gov), 5.5 Table 5-4 (confidence level guardband limits), p. 65 (PDF p. 85): max allowable risk 1.00 %, printed ±guardband limit 7.0327 mV; expected w = 10 − 7.0327.
CONF-20	U = 1.2755, k = 1, targetRisk = 0.02, lower = -10, upper = 10	2.6196 same as U	± 0.00005	NASA-HDBK-8739.19-4 (Baseline 2010-07-13, revalidated 2018-03-01, standards.nasa.gov), 5.5 Table 5-4 (confidence level guardband limits), p. 65 (PDF p. 85): max allowable risk 2.00 %, printed ±guardband limit 7.3804 mV; expected w = 10 − 7.3804.
CONF-21	U = 1.2755, k = 1, targetRisk = 0.03, lower = -10, upper = 10	2.399 same as U	± 0.00005	NASA-HDBK-8739.19-4 (Baseline 2010-07-13, revalidated 2018-03-01, standards.nasa.gov), 5.5 Table 5-4 (confidence level guardband limits), p. 65 (PDF p. 85): max allowable risk 3.00 %, printed ±guardband limit 7.6010 mV; expected w = 10 − 7.6010.
CONF-22	U = 1.2755, k = 1, targetRisk = 0.04, lower = -10, upper = 10	2.233 same as U	± 0.00005	NASA-HDBK-8739.19-4 (Baseline 2010-07-13, revalidated 2018-03-01, standards.nasa.gov), 5.5 Table 5-4 (confidence level guardband limits), p. 65 (PDF p. 85): max allowable risk 4.00 %, printed ±guardband limit 7.7670 mV; expected w = 10 − 7.7670.
CONF-23	U = 1.2755, k = 1, targetRisk = 0.05, lower = -10, upper = 10	2.098 same as U	± 0.00005	NASA-HDBK-8739.19-4 (Baseline 2010-07-13, revalidated 2018-03-01, standards.nasa.gov), 5.5 Table 5-4 (confidence level guardband limits), p. 65 (PDF p. 85): max allowable risk 5.00 %, printed ±guardband limit 7.9020 mV; expected w = 10 − 7.9020.

Put this calculator on your site

Free for labs, schools and anyone else. Paste this into your page.

<iframe src="https://metrologybench.com/embed/conformity" title="Decision rule and specific risk · Metrology Bench" width="100%" height="850" style="border:0;max-width:640px" loading="lazy"></iframe>

Preview the embed

Ask your AI

Connect metrology-toolbox-mcp and your assistant runs this exact calculation, with the source in the answer.

Set it up