Measurement Thinking, Traceability & Uncertainty

01 / 10

Agreeing readings can share the same bias

Sixteen readings agree beautifully. Why can the inferred transmitter power still be wrong by more than a decibel?

The sensor sits at the far end of a cable. Repeating its indication tests how consistently the same setup reports the same state; it does not move the sensor to the DUT output. A missing cable correction moves every inferred value together. The narrow spread survives.

SYN-SPREAD-01 · illustrative three-reading sketch, not the supplied 16-repeat dataset · scroll within this table if needed
Repeat	L-SENSOR indication	With +1.200 dB cable only	With +0.050 dB sensor residual too
1	18.000 dBm	19.200 dBm	19.250 dBm
2	18.050 dBm	19.250 dBm	19.300 dBm
3	18.100 dBm	19.300 dBm	19.350 dBm
Full spread	0.100 dB	0.100 dB	0.100 dB

Think about itWould another thousand readings remove the missing 1.200 dB cable correction?

Answer

No. More independent readings can narrow uncertainty in the mean of the indication. Every reading still contains the same uncorrected plane translation. The correction changes the location of the estimate; repeating it addresses only particular sources of spread.

Precision describes agreement under stated conditions. It does not establish closeness to the intended quantity. An indication is what the system reports; a measurement result includes the value assigned to the measurand with the information needed to interpret it, including uncertainty. Keep those roles distinct before interpreting extra decimal places. [VIM]

Common misconceptionA stable last digit proves an accurate measurement.

A stable common bias can leave the display quiet. The relevant failure is the inference from L-SENSOR to R1-TX, not necessarily the sensor’s repeatability.

Engineering decision → record update

Preserve SYN-IND-01 as the supplied indication evidence. Create a derived R1-TX result with its correction chain; do not overwrite the sensor record or claim that repeats tested the cable.

02 / 10

Start with the decision and measurand

Before choosing a sensor, what decision does “measure the TX power” need to resolve?

Start from an internal engineering requirement: the node’s on-time mean conducted output at R1-TX must be at most 19.700 dBm. This is a local, synthetic limit for TX-PWR-A. It is not a regulatory threshold, a peak limit, or a statement about the entire product population.

The measurand is the quantity we intend to estimate. Its definition includes the relevant state and conditions; connecting an instrument can change the quantity actually observed. Our declared matched 50 Ω loading is part of this definition, not a universal property of RF power. VIM 2.3.

REQ-TX-PWR-A-v1 · freeze the decision before the observation
Decision ingredient	Local definition
Quantity / plane	Mean conducted power during the settled on-time gate, at component port R1-TX.
DUT state	One fictional board: SYN-HW-A1 / SYN-FW-1.0; 3.300 V supply, 25 °C lab, fixed cable and telemetry-TX-A mode.
Limit / rule	Inclusive upper limit L=19.700 dBm; default interval containment with explicitly chosen k=2.
Eligible inference	Only this synthetic configuration and definition. Not PEP, duty-period mean, antenna power or production yield.
Evidence before closure	Loading, calibration chain, corrections, repeatability population and model validity must all be supplied.

A method must resolve the difference between competing hypotheses: excessive DUT output, a wrong plane translation, or shared setup error. A sensor with excellent short-term repeatability can still be unsuitable if its calibration or loading evidence cannot support the needed interval. Recall the distinction between requirements, margins and uncertainty in Path 05.

Engineering decision → record update

Record the limit, statistic, specimen and rule first. A later change to power mode or gate creates a named variant; it does not silently alter the earlier requirement.

03 / 10

Write the complete measurement definition

Do two labs measure the same quantity if one averages dBm and the other averages watts?

Follow the energy and the processing. The DUT sends the portfolio’s generic QPSK waveform at 2.450 GHz: 10 ksymbol/s, RRC roll-off 0.35, 256-symbol bursts. TX-PWR-A explicitly changes the output-power case. A local 21.6 ms gate runs from 2.0 to 23.6 ms inside each 25.6 ms burst. The sensor power path spans ±100 kHz about the carrier; capturing the relevant power and excluding settling are supplied model assumptions, not measured validations.

Power falls toward the sensor; the correction back to R1-TX is positive. No R2 antenna-feed, S0 radiated or R3 receiver-decision quantity is inferred. A real protection element would need its own characterized loss and uncertainty.

The sensor first averages RF watts within the gate, then expresses that result in dBm. This is different from averaging instantaneous logarithmic levels. Across the 16 repeats, the supplied s describes the variability of that log-domain indication under a small-error additive model. It is not the modulation’s peak-to-average power ratio or a distribution of production units.

$\begin{aligned}L_{\text{power mean}}&=10\log_{10}\left(\frac{\frac1N\sum_iP_i}{1\,\mathrm{mW}}\right)\\L_{\text{log mean}}&=\frac1N\sum_i10\log_{10}\left(\frac{P_i}{1\,\mathrm{mW}}\right)\end{aligned}$ Pᵢ are equal-duration power observations in watts; N is their count. The 1 mW reference belongs inside the logarithm.

Separate two-state averaging example · equal times, same power plane
Method	Calculation	Answer
Arithmetic mean of dBm	(0 + 10)/2	5.000 dBm → 3.162278 mW (geometric mean power)
Logarithm of mean power	10 log₁₀[(1 + 10)/2]	7.403626895 dBm → 5.500 mW (arithmetic mean power)

Reference-plane transformations need equally careful bookkeeping: calibration at L-SENSOR does not put the calibrated plane at R1-TX. Include each cable, adapter, attenuation and termination once. Internal sensor compensation already included in the indication is separate from the external +0.050 dB residual correction. Path 03’s plane and normalization contract supplies the network context.

Engineering decision → record update

Add waveform/version, gate, frequency response, loading, thermal state, and averaging domain to the record. If either lab used a different definition, reconcile that difference before comparing uncertainty bars.

04 / 10

Separate correction, calibration, and uncertainty

If the cable correction is known, why does uncertainty remain?

A correction compensates an estimated systematic effect. It can be positive, negative or zero. Its uncertainty expresses imperfect knowledge of that compensation; it is not an extra correction to add to the indication. The realized measurement error is a difference from a reference quantity value, often unknown in the actual DUT measurement. Assigning u=0.150 dB does not mean the realized error was +0.150 dB. [VIM]

$y = 18.050 + 1.200 + 0.050 + 0 = 19.300 \mathrm{dBm}$ Additive teaching model in dB; each residual correction estimate is zero, with nonzero uncertainty where supplied.

Different operations, different evidence
Operation	What it supplies	Local example
Correction	An applied compensation with an uncertainty.	Translate to R1-TX with +1.200 dB cable loss.
Calibration	A relation between reference values and indications, with uncertainties, used to obtain a result.	SYN-CERT-01 supplies a residual correction and U=0.300 dB at k=2.
Verification	Evidence against an already specified requirement.	Check a reference reading against the fictional ±0.400 dB check criterion, including uncertainty.
Adjustment	An operation that changes the system’s indications.	Changing gain/offset; the resulting state usually needs recalibration. No adjustment is performed here.

Calibration and adjustment are not synonyms; verification answers a separate requirement question. Calibration, verification, and adjustment have different VIM definitions.

Schematic metrological chain · all IDs fictional, not actual calibration evidence
Link	Required information	Budget treatment
SYN-SI-01 → SYN-TRANSFER-01	Reference realization, date, method, conditions and uncertainty.	Part of the aggregate sensor calibration contribution.
SYN-TRANSFER-01 → SYN-SENSOR-A	Calibration values, uncertainty, coverage basis, operating conditions.	SYN-CERT-01 aggregate u=0.150 dB; do not add its parent uncertainty again.
SYN-SENSOR-A → M08-01-DERIVED-A	Applicable sensor correction, cable calibration, loading, gate and acquisition.	The result contains U-CAL once plus the other nonduplicated contributions.

Metrological traceability belongs to a result linked to a stated reference by a documented calibration chain, with uncertainty carried through each link. A sticker, serial number, or “NIST traceable” label alone cannot establish it; neither does traceability guarantee the uncertainty is small enough for the decision. VIM 2.41.

Engineering decision → record update

Keep SYN-CERT-01 and SYN-CABLE-01 as parents of M08-01-DERIVED-A. An absent or stale link produces “inspect”; it is not repaired by selecting a larger k.

05 / 10

Identify what varies and what stays shared

What did the 16 repeats actually vary—and which influences stayed common to every reading?

Short-term repeatability describes precision with the procedure, operator, system, conditions and location held fixed over a short period. Reproducibility deliberately changes conditions such as systems, operators and locations. Day-to-day work in the same laboratory can instead probe intermediate precision; list what changed rather than calling every new run “reproducibility.” VIM 2.20, 2.24.

A variation plan distinguishes independent scatter from shared influence
Experiment	Allowed to change	Still unresolved
16 short repeats	Individual acquisition scatter; n=16, supplied s=.120 dB.	Same calibration, cable connection and thermal state.
Reconnect comparison	Cable seating, torque and route under a stated procedure.	A shared reference calibration may still bias every connection.
Different days / operators	Declared environmental and operator conditions.	Distinguish drift from mode/configuration changes; preserve sequence.
Other laboratory / system	Location, system and operator under a common measurand definition.	Independence of references, matching and processing must be checked.

An influence quantity changes the relation between indication and the quantity we want, even when it is not the desired output. Cable temperature can alter loss; reconnecting can alter mismatch. Those mechanisms suggest different discriminating measurements. Repeating without reconnecting cannot estimate the reconnect contribution.

$\begin{aligned}u_{\text{repeat mean}}&=\frac{0.120}{\sqrt{16}}=0.030\,\mathrm{dB}\\u_{\text{shared calibration}}&=0.150\,\mathrm{dB},\quad\text{not }\frac{0.150}{\sqrt{16}}\end{aligned}$ Independent log-reading fluctuations shrink in a mean; a common calibration offset is not independently sampled on every repeat.

Common misconceptionEvery uncertainty term falls as 1/√n.

Only a mean of appropriately independent observations earns that reduction. Reusing the same reference or cable does not give 16 independent calibrations. Averaging correlated readings requires their covariance.

Engineering decision → record update

Record an acquisition sequence and an influence map. Request a controlled reconnect/thermal comparison if that mechanism could decide the result; more unchanged readings cannot answer it.

06 / 10

Convert the evidence into standard uncertainty

Which numbers can be combined: a ±bound, a sample standard deviation, or a certificate’s expanded uncertainty?

First put them on the same basis. A standard uncertainty u has the scale of a standard deviation. Type A describes statistical evaluation from observations; Type B uses other relevant knowledge. These labels classify evaluation methods, not “random” versus “systematic” causes. A statistical calibration study can estimate a systematic effect. [GUM] [NIST-B]

$\begin{aligned}\bar{x} &= \frac{\sum x_{j}}{n}\qquad s^{2} = \frac{\sum (x_{j} - \bar{x})^{2}}{n-1} \\ u(\bar{x}) &= \frac{s}{\sqrt{n}}\end{aligned}$ For n independent repeated observations xⱼ in one declared additive unit: x̄ is the mean; s is the sample standard deviation. n−1 is the associated degrees of freedom.

Independent three-reading example · additive units (au), separate from RF power
Evidence	Mean	Sample s	Standard u of mean
9.9, 10.0, 10.1 au	10.0 au	0.1 au	0.057735026919 au
Only one reading	A value can be reported	Not estimable from one reading	Unknown; separate Type B evidence is another option

The sample-mean expression follows from independent observations; it does not turn an unknown variance into zero when n=1. [NIST-A]

Convert supplied evidence to standard uncertainty, with a reason · scroll within this table if needed
Representation	Conversion	Worked standard u	When justified
Rectangular ±a	a/√3	a=.100 dB → .057735026919 dB	Equal plausibility across the supplied interval.
Symmetric triangular ±a	a/√6	a=.100 dB → .040824829046 dB	Greater plausibility near zero under a supported triangular model.
Rounding step q	q/√12	q=.010 dB → .002886751346 dB	Rounding interval ±q/2, rectangular assumption.
Expanded certificate U, k	U/k	.300/2 → .150 dB	Read the certificate factor and conditions; do not guess a missing k.
Independent repeats s, n	s/√n	.120/√16 → .030 dB	The repeated population and independence support a mean uncertainty.
Supplied standard u	Use u directly	.060 dB → .060 dB	Already a standard uncertainty, not a tolerance.

The mismatch term’s ±0.100 dB rectangular bound is supplied only for this fixture. Real RF mismatch depends on complex reflections, source/load conditions and phase; a VSWR value alone does not justify this distribution. Likewise, U-RES is included only because the supplied repeat scatter is assumed not to contain quantization. If a real s already includes that effect, adding a separate rounding term can count it twice.

Go deeperWhere do √3, √6 and √12 come from?

For a symmetric rectangle on [−a,a], integrate x²/(2a): variance a²/3. For a symmetric triangular density (a−|x|)/a², the corresponding integral is a²/6. Substitute a=q/2 into a²/3 to get q²/12. These are distribution variances, not generic safety factors.

Engineering decision → record update

Store the original supplied representation beside u. Reject a missing n or k, document the distribution assumption, and resolve shared or duplicated evidence before forming the budget.

07 / 10

Propagate the actual measurement model

Can an unchanged indication become inconclusive when the reference evidence is better understood?

The uncertainty follows the measurement equation. In this additive dB model, each power correction has sensitivity +1. A paired difference has +1 for its first input and −1 for its second. Correlation therefore changes the variance with a sign determined by the equation; it is not always a penalty.

$\begin{aligned}u_c^2&=\sum_i(c_i u_i)^2+2\sum_{i<j}c_i c_j\rho_{ij}u_i u_j\\U&=ku_c\end{aligned}$ cᵢ=∂f/∂xᵢ evaluated at the estimates; uᵢ is standard uncertainty; ρᵢⱼ is dimensionless; u(xᵢ,xⱼ)=ρᵢⱼuᵢuⱼ is covariance. All inputs must share the equation’s declared units.

This is the first-order propagation law. For the supplied additive coordinate it is exact as a variance identity; the physical applicability of that coordinate and the input evidence remains an assumption. [NIST-A] [GUM]

Independent analytical sign checks · standard uncertainties
Equation / condition	Variance	Standard uncertainty
Sum, .3 and .4 dB, ρ=0	.09+.16=.25 dB²	0.500 dB
Sum, same u, ρ=+1	.09+.16+.24=.49 dB²	0.700 dB
Sum, same u, ρ=−1	.09+.16−.24=.01 dB²	0.100 dB
Difference, equal .3 au, shared ρ=+1	.09+.09−.18=0 au²	0 au for this shared term only

Think about itKeep y=19.300 dBm. Set only ρ(U-CAL,U-CABLE)=+0.5. Does the default interval still fit under 19.700 dBm?

Answer

The covariance adds 2×.150×.060×.5=.009 dB². U increases from .360416425819 to .407308237088 dB. Its upper endpoint is 19.707308237088 dBm, so the interval straddles the inclusive limit. The decision becomes inconclusive; the indication and corrections are unchanged.

TX-PWR-A · independently checked covariance comparison · scroll within this table if needed
Evidence hypothesis	Variance (dB²)	U at k=2 (dB)	Upper endpoint (dBm)	Containment
Independent	0.032475	0.360416425819	19.660416425819	Supported below limit
Only CAL / CABLE ρ=.5	0.041475	0.407308237088	19.707308237088	Inconclusive

Checking every ρ lies in [−1,+1] is insufficient. Three off-diagonal values +.9, +.9, −.9 imply eigenvalues −.8, 1.9, 1.9: that correlation matrix is impossible and must be rejected. Perfectly shared errors can instead produce a valid singular matrix; zero eigenvalues are allowed. The builder uses a dimensionless −10⁻¹² eigenvalue threshold and does not hide an invalid matrix by adding numerical jitter.

Common misconceptionA correlated budget has a unique percentage owned by each source.

Covariance belongs to pairs. Assigning it to one source is arbitrary. Compare a practical intervention by reducing one u and recomputing the whole model with the declared correlations; show ties and any loss of cancellation.

Engineering decision → record update

Preserve M08-01-DERIVED-A and add M08-01-DERIVED-CORR with the same raw parent. Record the reason for the shared reference assumption and request independent calibration evidence if that is the decision-changing gap.

08 / 10

Check coverage and nonlinear transformations

Does k=2 mean exactly 95%, and does converting the answer to mW preserve a symmetric error bar?

Multiplying by k sets the interval’s width. Coverage also depends on the distribution and how well its standard uncertainty is established. For an exactly normal output with known standard deviation, ±2σ covers about 95.45%; it is not exactly 95%. A mean estimated from a small normal sample has a Student-t coverage issue. The supplied repeat term has 15 degrees of freedom; the fictional certificate gives k but no real experimental degrees of freedom. [NIST-K]

The canonical output is approximately normal under its declared normal calibration/cable/repeat terms and smaller independent bounded terms. With additionally treated-as-exact Type B scales, the effective degrees of freedom are large; that supports approximate coverage for this teaching case, not universal 95% coverage or a physical certificate. One-sided probability statements and central two-sided intervals are different claims.

Think about itThe baseline interval is symmetric in dBm. Will its endpoints be equally far from 85.113803820238 mW?

Answer

No. Exact monotonic conversion gives 78.335452675538 to 92.478684341760 mW. The lower distance is about 6.77835 mW and the upper distance about 7.36488 mW. Keep both endpoints; do not force a symmetric mW bar.

$\begin{aligned}p &= 10^{\frac{y}{10}}\qquad u_{\mathrm{linearized}}(p) = (\frac{\ln 10}{10}) p u(y) \\ [p_{\mathrm{low}},p_{\mathrm{high}}] &= [10^{\frac{y-U}{10}},10^{\frac{y+U}{10}}]\end{aligned}$ p is in mW; y is in dBm. The derivative is local; mapping interval endpoints uses the exact monotonic function.

Exact baseline conversion · R1-TX, same chosen interval · scroll within this table if needed
Representation	Estimate	Lower	Upper
dBm	19.3	18.939583574181	19.660416425819
mW	85.113803820238	78.335452675538	92.47868434176

A deliberately nonlinear counterexample

In the separate LOG-NORMAL-3 mathematical variant, y is normally distributed with mean 0 dBm and standard deviation 3 dB. With a=ln(10)/10, p=exp(ay) mW is lognormal. Completing the square in the Gaussian integral gives E[exp(ty)]=exp(tμ+t²σ²/2). Therefore the transformed mean depends on σ, not just μ.

$\begin{aligned}\operatorname{median}(p)&=\exp (a\mu) \\ E[p]&=\exp (a\mu +\frac{a^{2}\sigma ^{2}}{2}) \\ \operatorname{Var}(p)&=[\exp (a^{2}\sigma ^{2})-1] \exp (2a\mu +a^{2}\sigma ^{2})\end{aligned}$ μ and σ are the normal log-level mean and standard deviation; a=ln(10)/10. This is a mathematical distribution fixture, not an RF sensor calibration.

LOG-NORMAL-3 · exact analytic moments versus first-order approximation
Statistic	Exact	First order
Median	1 mW	f(E[y]) = 1 mW
Mean	1.269452131623 mW	1 mW
Standard deviation	0.992699160054 mW	0.690775527898 mW

The 2026 GUM amendment addresses significant nonlinearity in both the estimate and uncertainty. GUM-6 also cautions against general uncertainty calculations in logarithmic quantities. Our frozen dB budget is deliberately restricted to already-expressed small-error terms; an actual nonlinear RF mismatch or detector model needs its own statistically consistent treatment in appropriate linear variables. [GUM-AMD] [GUM-6]

The builder cross-checks declared distributions with fixed Halton samples, using the same source dimensions at 4,096 and 16,384 points. It reports a sample mean, standard deviation, median and central 95% quantiles, distinct from the chosen k·u interval. Correlated normal inputs use a PSD factorization. Correlated mixed distributions are left unavailable unless a defensible joint model is supplied; their valid first-order covariance budget still stands. [DIST]

Engineering decision → record update

Attach the coverage qualification and transformation method to the record. Keep f(E[y]) separate from E[f(y)], preserve exact endpoints, and withhold unsupported distribution or first-order inferences.

09 / 10

Declare a decision rule before seeing the answer

What does the team mean by “pass”—a nominal screen, an interval statement, or an acceptance policy?

Agree before seeing the answer. A nominal screen ignores uncertainty. Interval containment asks where the entire chosen interval lies relative to the allowed set. A fixed guard band deliberately narrows acceptance, independent of the current U. Each answers a different question. None of them turns missing calibration or plane evidence into an eligible result.

p08-m01-decision-rules-v1 · inclusive upper-limit rule definitions
Rule	Condition	Outcome
Nominal screen	y ≤ L / y > L	Clears / fails nominal screen; uncertainty ignored.
Interval containment	y+U ≤ L	Supported below limit under this interval.
Interval containment	y−U > L	Supported above limit under this interval.
Interval containment	Otherwise	Inconclusive. Lower endpoint equal to L still intersects the allowed set.
Fixed guard band	y ≤ L−g, g ≥ 0	Accepted by this rule; otherwise not accepted. g is not automatically U.
Evidence gate	Calibration, loading, plane or model evidence missing	Inspect; show eligible arithmetic, do not accept the measurement.

Equality and overlap truth table · local units, L=10, k·u=U · scroll within this table if needed
Rule / allowed set	y / U / g	Outcome
Upper containment (≤10)	y=9, U=1	Supported below: upper endpoint equals 10.
Upper containment (≤10)	y=11, U=1	Inconclusive: lower endpoint equals 10.
Upper containment (≤10)	y=11.001, U=1	Supported above: lower endpoint is greater than 10.
Lower containment (≥0)	y=1, U=1	Supported above: lower endpoint equals 0.
Lower containment (≥0)	y=−1, U=1	Inconclusive: upper endpoint equals 0.
Two-sided containment [0,10]	y=5, U=5	Supported inside; both endpoints equal limits.
Two-sided containment [0,10]	y=−1, U=1	Inconclusive: touching is not disjoint.
Fixed upper guard (L=10)	y=9.6, g=.4	Accepted inclusively, independently of U.
Any otherwise accepted rule	Calibration unknown	Inspect, not a measurement acceptance.

For a lower limit L, containment requires y−U≥L; support below that limit requires y+U<L. For two inclusive limits [L,H], support inside requires y−U≥L and y+U≤H; support outside requires y+U<L or y−U>H. Every other interval overlaps the boundary and remains inconclusive.

The canonical y=19.300 dBm clears the nominal screen, fits the independent expanded interval below 19.700 dBm, and lies exactly on the fixed g=.400 dB acceptance boundary. Adding ρ=.5 changes interval containment to inconclusive while leaving those other two decisions unchanged. That is a reason to declare the rule, not to choose whichever one gives the preferred result.

Common misconceptionNot accepted proves the DUT is above its specification.

A result can miss a guarded acceptance threshold while remaining below the specification. Conversely, a nominal clearance can have an uncertainty interval extending beyond the limit. State which rule produced the outcome and what it leaves unresolved.

Guard bands affect acceptance behavior, but consumer/producer risk needs a defensible measurement/process distribution as well as the rule. A k selector or fixed g alone does not calculate risk. These local engineering rules are informative; formal conformity routes remain with specialists and Path 09. [RULE]

Engineering decision → record update

Freeze p08-m01-decision-rules-v1 in the derived record. If correlation makes the result inconclusive, improve the evidence or measurement; do not retroactively replace the rule to close the item.

10 / 10

Audit and improve the measurement record

Would you buy another hour of repeats, or improve the calibration evidence?

The complete independent budget has variance 0.032475 dB² and U=0.360416425819 dB at k=2. Halving the calibration standard uncertainty from .150 to .075 dB reduces U to .249799919936 dB. Doubling only n from 16 to 32 gives .357910603363 dB. The shared terms stayed shared; the intervention acts only where its evidence supports a reduction.

Independent intervention comparison · same y=19.300 dBm and R1-TX definition
Intervention	Expanded U (dB)	Reduction in U (dB)
Baseline	0.360416425819	—
Half calibration u	0.249799919936	0.110616505883
Double repeat count	0.357910603363	0.002505822455

Choose the largest credible improvement, not simply the largest row. Correlation evidence itself may be the first thing to resolve. In the Path 06.6 gain-comparison example, shared errors can cancel in a difference. Here the CAL/CABLE covariance increases a sum. Carry the equation and reference planes into that judgment.

One decision · Define, compare, improve

Uncertainty & Decision-Rule Builder

Does the complete evidence support the internal power limit? Compare one deliberate change at a time. Every value here is synthetic; a smaller uncertainty is useful only when its supporting evidence is credible.

Predict the independent interval decision, then inspect the committed endpoints.
Load the correlated certificate/cable preset. Identify the new covariance term and explain the decision change.
Reset; compare halving U-CAL with increasing the repeat count. Keep shared influences intact.
Switch the diagram to mW. Explain why the interval is asymmetric while the decision stays unchanged.

Load a complete example

ScenarioChoose, then load. Each preset restores all inputs, correlations and evidence metadata.

Measurement equationChanging equation loads its complete defining example, including units and source rows.

1 · Indication and signed corrections

Power indication (dBm)Default TX-PWR-A: 18.050 dBm. Range −100…+40; step 0.001. Logarithm of linearly averaged RF power.

Positive cable loss correction (dB)Default +1.200 dB. Correct upstream once; 0…20, step .001.

External residual sensor correction (dB)Default +0.050 dB; internal instrument correction is already frozen in the indication. −3…+3, step .001.

2 · Evidence and eligibility

Calibration evidenceDefault documented; refers to the fictional fixture only.

Plane transformation evidenceDefault documented R1-TX → L-SENSOR; paired variants use A/B.

Loading evidenceDefault documented. Unknown cannot become a product pass.

First-order model evidenceDefault supported additive coordinate. Exact conversion is separate from a linearized mW moment estimate.

Uncertainty budget completenessRemoving a fixture source creates an omission. Restore it or justify a new complete model before accepting evidence.

3 · Edit uncertainty evidence (6 of 8 sources)

All magnitudes are nonnegative uncertainty evidence in dB; residual correction estimates stay zero. Standard/certificate/Type A rows use normal teaching distributions, not a proof of normality. Check correlation and double counting before adding a source.

U-CAL · stable dimension 1

U-CAL representationSelect the kind of supplied evidence; conversion to standard uncertainty follows its definition.

U-CAL expanded U (dB)Range 0…10; step 0.001.

U-CAL uncertainty unitThe equation requires dB; incompatible units are rejected.

U-CAL certificate kRange 0.1…5; step 0.1.

U-CABLE · stable dimension 2

U-CABLE representationSelect the kind of supplied evidence; conversion to standard uncertainty follows its definition.

U-CABLE standard u (dB)Range 0…10; step 0.001.

U-CABLE uncertainty unitThe equation requires dB; incompatible units are rejected.

U-MISMATCH · stable dimension 3

U-MISMATCH representationSelect the kind of supplied evidence; conversion to standard uncertainty follows its definition.

U-MISMATCH bound half-width a (dB)Range 0…10; step 0.001.

U-MISMATCH uncertainty unitThe equation requires dB; incompatible units are rejected.

U-REPEAT · stable dimension 4

U-REPEAT representationSelect the kind of supplied evidence; conversion to standard uncertainty follows its definition.

U-REPEAT sample s (dB)Range 0…10; step 0.001.

U-REPEAT uncertainty unitThe equation requires dB; incompatible units are rejected.

U-REPEAT independent repeat count nRange 2…10000; step 1.

U-DRIFT · stable dimension 5

U-DRIFT representationSelect the kind of supplied evidence; conversion to standard uncertainty follows its definition.

U-DRIFT bound half-width a (dB)Range 0…10; step 0.001.

U-DRIFT uncertainty unitThe equation requires dB; incompatible units are rejected.

U-RES · stable dimension 6

U-RES representationSelect the kind of supplied evidence; conversion to standard uncertainty follows its definition.

U-RES step q (dB)Range 0…10; step 0.001.

U-RES uncertainty unitThe equation requires dB; incompatible units are rejected.

4 · Set mirrored correlations

Diagonal entries are fixed at 1. Each pair is mirrored; unedited pairs are zero. Pairwise bounds do not establish positive semidefiniteness.

ρ(U-CAL, U-CABLE)Range -1…1; step 0.05.

ρ(U-CAL, U-MISMATCH)Range -1…1; step 0.05.

ρ(U-CAL, U-REPEAT)Range -1…1; step 0.05.

ρ(U-CAL, U-DRIFT)Range -1…1; step 0.05.

ρ(U-CAL, U-RES)Range -1…1; step 0.05.

ρ(U-CABLE, U-MISMATCH)Range -1…1; step 0.05.

ρ(U-CABLE, U-REPEAT)Range -1…1; step 0.05.

ρ(U-CABLE, U-DRIFT)Range -1…1; step 0.05.

ρ(U-CABLE, U-RES)Range -1…1; step 0.05.

ρ(U-MISMATCH, U-REPEAT)Range -1…1; step 0.05.

ρ(U-MISMATCH, U-DRIFT)Range -1…1; step 0.05.

ρ(U-MISMATCH, U-RES)Range -1…1; step 0.05.

ρ(U-REPEAT, U-DRIFT)Range -1…1; step 0.05.

ρ(U-REPEAT, U-RES)Range -1…1; step 0.05.

ρ(U-DRIFT, U-RES)Range -1…1; step 0.05.

5 · Freeze coverage and decision rule

Limit directionDefault upper limit; all limits remain in the original decision domain.

Decision ruleDefault interval containment. The guard band is an independent acceptance-policy choice.

Upper limit (dBm)TX-PWR-A default 19.700 dBm; internal synthetic limit, not a regulation.

Chosen expansion factor kDefault 2. No exact probability or consumer/producer risk is calculated from k.

6 · Compare distributions and improvements

Distribution workloadDefault 16384, with 4096-point prefix. Changing sample count does not change the acceptance rule.

Distribution hypothesisDefault declared. All-normal reinterprets the standardized scales under a different hypothesis.

Counterfactual standard-u multiplierDefault 0.50: halve each source in turn while retaining correlations. 0 removes that source uncertainty; 1 leaves it unchanged.

View only · the decision domain stays fixed

Interval diagram representationOnly changes the diagram; both numerical representations remain in the committed result table.

Committed Independent TX-PWR-A · Illustrative / Derived

supported below limit

The chosen expanded interval is compared with inclusive engineering limits. Evidence eligibility is evaluated before acceptance.

$\begin{aligned}y&=\text{indication}+\text{cable loss}\\&\quad+\text{sensor correction}+\text{residual corrections}\end{aligned}$ $18.05+(1.2)+(0.05)+0=19.3\,\mathrm{dBm}$ R1-TX; matched 50 Ω synthetic chain. Positive cable loss corrects upstream. Residual correction estimates are zero. p08-m01-power-budget-v1.

Corrected estimate: 19.3 dBm
Combined standard u: 0.180208213 dB
Expanded U · k=2: 0.360416426 dB

Display: up to 9 decimals (verification, not instrument resolution). Decisions retain full precision. k=2 is a chosen factor, not a risk or exact-95% selector. Under the additional assumption of exactly known Type B scales and independent inputs, a Welch–Satterthwaite calculation gives ν_eff≈19530.1; real certificate degrees of freedom are unknown. The canonical near-normal output and large conditional degrees of freedom support only approximate coverage.

Committed evidence budget · correction estimates remain separate · scroll within this table if needed
Source / evidence	Supplied representation	Standard u	Sensitivity c	Diagonal variance
U-CAL SYN-CERT-01: U=0.300 dB, k=2; normal teaching distribution	U=0.3 dB, k=2	0.15 dB	1	0.0225 dB²
U-CABLE SYN-CABLE-01: standard u; normal teaching distribution	u=0.06 dB	0.06 dB	1	0.0036 dB²
U-MISMATCH SYN-BOUND-01: supplied ±0.100 dB bound; rectangular approximation	±0.1 dB rectangular	0.057735027 dB	1	0.003333333333 dB²
U-REPEAT SYN-REPEAT-01: supplied log-reading s=0.120 dB; independent repeats; normal approximation for mean	s=0.12 dB, n=16	0.03 dB	1	0.0009 dB²
U-DRIFT SYN-DRIFT-01: zero estimate, supplied rectangular bound	±0.08 dB rectangular	0.046188022 dB	1	0.002133333333 dB²
U-RES SYN-RES-01: rounding step; assumed absent from supplied repeat scatter	step q=0.01 dB	0.002886751 dB	1	0.000008333333 dB²

Signed covariance contributions · all unlisted pairs are exactly zero
Pair	ρ	2 cᵢ cⱼ ρ uᵢ uⱼ
All pairs	0	0 dB²

Variance = 0.032475 dB². Correlation matrix valid: positive semidefinite. Eigenvalues: 1, 1, 1, 1, 1, 1. Values below −10⁻¹² are rejected.

Inspect the mirrored correlation matrix

Committed dimensionless correlation matrix · scroll within this table if needed
Source	U-CAL	U-CABLE	U-MISMATCH	U-REPEAT	U-DRIFT	U-RES
U-CAL	1	0	0	0	0	0
U-CABLE	0	1	0	0	0	0
U-MISMATCH	0	0	1	0	0	0
U-REPEAT	0	0	0	1	0	0
U-DRIFT	0	0	0	0	1	0
U-RES	0	0	0	0	0	1

Use the endpoints, not the width of a screen pixel, to judge containment. The distribution cross-check below is a separate interval.

Estimate and chosen expanded interval · original decision domain and exact mapping · scroll within this table if needed
Representation	Estimate	Lower endpoint	Upper endpoint
dBm	19.3	18.939583574	19.660416426
mW · exact mapping	85.11380382	78.335452676	92.478684342

Linearized u(p) = (ln 10 / 10) p u(y) = 3.531752559 mW. This derivative estimate does not make the exact mapped endpoints symmetric.

Committed decision configuration
Condition	Value
Rule / direction	containment / upper
Applicable limit	y ≤ 19.7 dBm
Fixed guard band	Not used by this rule
Evidence	Calibration documented; plane documented; loading documented; model supported; declared complete

Distribution cross-check

Halton indices 1…16384, bases 2, 3, 5, 7, 11, 13, 17, 19; no scrambling. Source dimensions stay fixed when rows move. Standard/certificate/Type A terms use a declared normal approximation; rectangular, triangular and rounding terms use their specified inverse distributions. Correlated all-normal cases use a symmetric PSD square root; a Gaussian dependence is never silently assigned to mixed marginals.

Simulated distribution summaries · dBm · central 95% quantiles, separate from k·u · scroll within this table if needed
Samples	Mean	Sample s	Median	2.5%	97.5%
4096	19.29935638	0.179736401	19.299011149	18.944750846	19.649350148
16384	19.29981587	0.180066315	19.300477659	18.946587256	19.65172924

Sample standard deviation uses N−1; quantiles use sorted linear interpolation h=(N−1)p. Prefix agreement is not proof of convergence. This fixed workload is a bounded distribution comparison, not the complete adaptive JCGM 101 procedure or an accredited result.

Choose the next improvement

Each counterfactual multiplies one source’s standard uncertainty by 0.5, preserving its correlations and all correction estimates. Negative improvement is possible when reducing just one side weakens shared-error cancellation. Ties remain equally ranked; these are not additive percentages owned by sources.

Counterfactual reduction · factor 0.5 · same measurement equation · scroll within this table if needed
Source	New U	Reduction in U	Decision
U-CAL	0.24979992 dB	0.110616506 dB	supported below limit
U-CABLE	0.345108679 dB	0.015307747 dB	supported below limit
U-MISMATCH	0.346265794 dB	0.014150632 dB	supported below limit
U-DRIFT	0.351425668 dB	0.008990758 dB	supported below limit
U-REPEAT	0.35665109 dB	0.003765336 dB	supported below limit
U-RES	0.360381742 dB	0.000034684 dB	supported below limit

Against the independent TX-PWR-A baseline: Δestimate=0 dB; ΔU=0 dB. This is a hypothetical model comparison, not new acquired evidence.

Read the complete committed measurement record

Complete measurement record · M08-01-DERIVED-A
Field	Frozen or committed content
Record ID	M08-01-DERIVED-A
Input / parent IDs	M08-01-RAW-A · SYN-CERT-01 · SYN-CABLE-01
Owner / module	08.1 · measurement engineer (fictional role)
Decision question	Does TX-PWR-A support the internal on-time mean conducted-power upper limit at R1-TX?
Competing hypotheses	H1: DUT output is too high. H2: indication is translated to the wrong plane. H3: shared calibration/thermal effects invalidate the small budget.
Requirement	REQ-TX-PWR-A-v1: R1-TX on-time mean ≤19.700 dBm; internal engineering limit, synthetic.
Declared decision rule	p08-m01-decision-rules-v1: containment; upper; lower=18, upper=19.7 dBm; k=2; g=0.4 dB.
Specimen / fixture	Illustrative p08-m01-power-budget-v1; Independent TX-PWR-A
Hardware / firmware / mode	SYN-HW-A1, SYN-FW-1.0, telemetry-TX-A; fixture SYN-FIXTURE-A1; local output-power variant of the portfolio QPSK case.
Supply / thermal / mechanical state	Supply 3.300 V; 298.15 K (25 °C) stable lab; open bench board, fixed cable route, no enclosure or antenna; settling excluded.
Frozen timestamp	Synthetic acquisition 2026-09-08T10:00:00Z; configuration evaluation fixed 2026-09-08 UTC.
Environment	Indoor laboratory, 25 °C; relative humidity unknown (not modelled); ambient RF coupling assumed negligible only in this synthetic fixture.
Stimulus / waveform / version	2.450e9 Hz carrier; generic QPSK 10e3 symbol/s, 20e3 uncoded bit/s, RRC 0.35, span 8 symbols; WAVE-P02-QPSK-v1, PRBS-9 state 0x1FF. Not a named wireless-standard mode.
Measurand / statistic	Sensor reports log10 of linearly averaged RF watts within each gate. Measurand is stable R1-TX on-time mean power, not PEP, period average, dBc or PSD.
Population	One fixed synthetic DUT state; 16 independent log-domain indication repeats; supplied sample s=0.120 dB. Does not estimate production yield or drift across days.
Observation / acquisition sequence	16 bursts at 1 s cadence; each burst 25.6 ms; local gate 2.0–23.6 ms (21.6 ms), excluding settling; power-path RF passband ±100 kHz about carrier; full-power capture assumed within this model.
Reference planes / loading	R1-TX = component RF output; L-SENSOR = local sensor connector; matched real positive 50 Ω interface. R2 antenna feed, S0 OTA and R3 receiver decisions are excluded.
Cable / fixture / protection ledger	R1-TX → SYN-CABLE-A1 (1.200 dB positive loss) → L-SENSOR → 50 Ω sensor termination. No external attenuator/protection/fixture loss added in this arithmetic fixture; physical protection suitability is unresolved for 08.2.
Instrument / firmware / options	SYN-SENSOR-A / serial SIM-001 / firmware SIM-1 / gated-power option SIM-GATE; fictional identities, no real safe ratings.
Settings / internal correction	Carrier 2.450 GHz; gated linear-power average then dBm display; q=0.010 dB; sensor internal correction frozen in the indication; external sensor residual +0.050 dB applied separately once.
Calibration / verification / validity	Calibration documented; plane documented; loading documented; first-order evidence supported; declared complete. These flags refer only to the synthetic fixture.
Immutable evidence	SYN-IND-01 / immutable supplied summary: indication 18.050 dBm, s=0.120 dB, n=16. Individual acquisition files are not supplied; the separate three-dot sketch is not this dataset. Custom indication/corrections, if edited, are hypothetical inputs derived from this retained source, not newly acquired data.
Derived correction / model version	uncertainty-decision-rule-builder/2.0: y = indication + cable loss + sensor correction + residual corrections; indication=18.05, cable=1.2, sensor=0.05, paired second=10. Zero residual estimates; each budget row describes uncertainty, not a new correction.
Uncertainty / covariance	6 active sources; declared marginals; correlations identity; complete values are in the committed budget.
Result	supported below limit: y=19.3 dBm; u_c=0.180208213 dB; U=0.360416426 dB; interval [18.939583574, 19.660416426] dBm.
Eligible inference	Conditional local engineering result only; coverage and evidence limitations remain attached.
Unresolved evidence / omissions	Real calibration chain/certificates, loading/mismatch model, instrument level/protection ratings, gate/bandwidth verification, reconnect and thermal stability are unknown. No accredited or regulatory conclusion.
Next discriminating measurement	08.2: verify actual permissible power/DC levels, cable/connector state, matching, protection and repeatable configuration; retain these raw evidence IDs.
Review trigger	Measurement engineer: review after cable reconnect, calibration change, firmware/waveform/gate/thermal change, or before any real use.

uncertainty-decision-rule-builder/2.0 · p08-m01-decision-rules-v1. No exact consumer/producer risk, real instrument safety, accreditation or conformity inference is implemented.

Completed one-page measurement definition & budget · canonical snapshot

TX-PWR-A · ready for a bench-planning review

Decision: REQ-TX-PWR-A-v1, on-time mean conducted power ≤19.700 dBm at R1-TX into the declared matched real 50 Ω chain. Interval containment, k=2, fixed before observation. Illustrative case only.

State and acquisition: SYN-HW-A1 / SYN-FW-1.0; 3.300 V; 25 °C; fixed bench board/cable; generic 2.450 GHz QPSK, PRBS-9 0x1FF; 256 symbols, 10 ksymbol/s, RRC .35. Gate 2.0–23.6 ms; power path ±100 kHz; 16 bursts, 1 s cadence. Internal sensor correction already in indication.

Evidence chain: M08-01-RAW-A retains SYN-IND-01 (18.050 dBm, supplied s=.120 dB, n=16). SYN-CERT-01 and SYN-CABLE-01 feed M08-01-DERIVED-A. At L-SENSOR add +.050 dB external residual sensor correction, then +1.200 dB cable correction to R1-TX. Other correction estimates zero.

Budget (standard u, dB): CAL .150; CABLE .060; MISMATCH .100/√3; REPEAT .120/√16; DRIFT .080/√3; RES .010/√12. Sensitivities +1; correlations zero. Quantization assumed absent from supplied s. Variance .032475 dB²; u_c=.180208212909 dB.

Result: 19.300 dBm ±.360416425819 dB (k=2); [18.939583574181,19.660416425819] dBm. Equivalent estimate 85.113803820238 mW, endpoints [78.335452675538,92.478684341760] mW. Supported below the local limit, conditional on supplied evidence and approximate coverage.

Reversal and next action: CAL/CABLE ρ=.5 gives U=.407308237088 dB and an inconclusive interval. Preserve M08-01-DERIVED-CORR separately. Resolve correlation; improved calibration u=.075 dB gives independent U=.249799919936 dB. Bench owner must verify actual level/DC protection, cable stability, matching, bandwidth and gate before real use. Reopen after reconnect, thermal, firmware or calibration change.

Scope: p08-measurement-record-v1; uncertainty-decision-rule-builder/2.0; all supplied evidence synthetic. No actual certificates, raw acquisition files or hardware safe ratings supplied. No product certification, production-yield or radiated-power inference.

Keep raw and derived records separate

Static snapshot lineage · earlier versions remain immutable
Record	Parents	Result / eligible inference
M08-01-RAW-A	Raw root	18.050 dBm at L-SENSOR is an indication only. Raw sensor indication cannot close the R1-TX decision before correction and evidence review.
M08-01-DERIVED-A	M08-01-RAW-A · SYN-CERT-01 · SYN-CABLE-01	Derived 19.300 dBm; u_c=0.180208212909 dB; U=0.360416425819 dB at k=2; interval [18.939583574181,19.660416425819] dBm. Supported below the internal limit under the declared synthetic interval rule; no statement about a real node or accreditation.
M08-01-DERIVED-CORR	M08-01-RAW-A · SYN-CERT-01 · SYN-CABLE-01	Derived 19.300 dBm; U=0.407308237088 dB; upper endpoint 19.707308237088 dBm. Inconclusive by interval containment. Preserve independent version; do not rewrite raw indication.

Audit the complete original raw record and inherited conditions

Complete measurement record · M08-01-RAW-A
Field	Frozen or committed content
Record ID	M08-01-RAW-A
Input / parent IDs	None (raw root)
Owner / module	08.1 · measurement engineer (fictional role)
Decision question	Does TX-PWR-A support the internal on-time mean conducted-power upper limit at R1-TX?
Competing hypotheses	H1: DUT output is too high. H2: indication is translated to the wrong plane. H3: shared calibration/thermal effects invalidate the small budget.
Requirement	REQ-TX-PWR-A-v1: R1-TX on-time mean ≤19.700 dBm; internal engineering limit, synthetic.
Declared decision rule	p08-m01-decision-rules-v1: inclusive upper interval containment; k=2, conditional coverage, fixed before evaluation.
Specimen / fixture	SYN-NODE-TX-A / p08-m01-power-budget-v1; one illustrative specimen; no real measured DUT.
Hardware / firmware / mode	SYN-HW-A1, SYN-FW-1.0, telemetry-TX-A; fixture SYN-FIXTURE-A1; local output-power variant of the portfolio QPSK case.
Supply / thermal / mechanical state	Supply 3.300 V; 298.15 K (25 °C) stable lab; open bench board, fixed cable route, no enclosure or antenna; settling excluded.
Frozen timestamp	Synthetic acquisition 2026-09-08T10:00:00Z; configuration evaluation fixed 2026-09-08 UTC.
Environment	Indoor laboratory, 25 °C; relative humidity unknown (not modelled); ambient RF coupling assumed negligible only in this synthetic fixture.
Stimulus / waveform / version	2.450e9 Hz carrier; generic QPSK 10e3 symbol/s, 20e3 uncoded bit/s, RRC 0.35, span 8 symbols; WAVE-P02-QPSK-v1, PRBS-9 state 0x1FF. Not a named wireless-standard mode.
Measurand / statistic	Sensor reports log10 of linearly averaged RF watts within each gate. Measurand is stable R1-TX on-time mean power, not PEP, period average, dBc or PSD.
Population	One fixed synthetic DUT state; 16 independent log-domain indication repeats; supplied sample s=0.120 dB. Does not estimate production yield or drift across days.
Observation / acquisition sequence	16 bursts at 1 s cadence; each burst 25.6 ms; local gate 2.0–23.6 ms (21.6 ms), excluding settling; power-path RF passband ±100 kHz about carrier; full-power capture assumed within this model.
Reference planes / loading	R1-TX = component RF output; L-SENSOR = local sensor connector; matched real positive 50 Ω interface. R2 antenna feed, S0 OTA and R3 receiver decisions are excluded.
Cable / fixture / protection ledger	R1-TX → SYN-CABLE-A1 (1.200 dB positive loss) → L-SENSOR → 50 Ω sensor termination. No external attenuator/protection/fixture loss added in this arithmetic fixture; physical protection suitability is unresolved for 08.2.
Instrument / firmware / options	SYN-SENSOR-A / serial SIM-001 / firmware SIM-1 / gated-power option SIM-GATE; fictional identities, no real safe ratings.
Settings / internal correction	Carrier 2.450 GHz; gated linear-power average then dBm display; q=0.010 dB; sensor internal correction frozen in the indication; external sensor residual +0.050 dB applied separately once.
Calibration / verification / validity	SYN-CERT-01 and SYN-CABLE-01 are supplied fictional calibration evidence. Reference-chain sketch SYN-SI-01 → SYN-TRANSFER-01 → SYN-SENSOR-A; u=0.150 dB aggregates the sensor chain. SYN-VERIFY-01 is a fictional check against a local ±0.400 dB criterion; not adjustment. Valid only for frozen frequency, loading, gate, level range and thermal state.
Immutable evidence	SYN-IND-01 / immutable supplied summary: indication 18.050 dBm, s=0.120 dB, n=16. Individual acquisition files are not supplied; the separate three-dot sketch is not this dataset.
Derived correction / model version	uncertainty-decision-rule-builder/2.0; indication retained; +1.200 dB cable, +0.050 dB residual sensor, other residual estimates 0 dB. No source applied twice.
Uncertainty / covariance	Independent supplied dB model: U-CAL .150; U-CABLE .060; U-MISMATCH .100/√3; U-REPEAT .120/√16; U-DRIFT .080/√3; U-RES .010/√12. Approximate normal treatment of the mean; quantization assumed absent from s.
Result	18.050 dBm at L-SENSOR is an indication only.
Eligible inference	Raw sensor indication cannot close the R1-TX decision before correction and evidence review.
Unresolved evidence / omissions	Real calibration chain/certificates, loading/mismatch model, instrument level/protection ratings, gate/bandwidth verification, reconnect and thermal stability are unknown. No accredited or regulatory conclusion.
Next discriminating measurement	08.2: verify actual permissible power/DC levels, cable/connector state, matching, protection and repeatable configuration; retain these raw evidence IDs.
Review trigger	Measurement engineer: review after cable reconnect, calibration change, firmware/waveform/gate/thermal change, or before any real use.

The custom committed record in the builder is a local hypothetical variant. The one-page sheet above always identifies itself as the canonical snapshot; printing a custom state retains both labels. No previous visit or saved workbook is needed.

Engineering decision → record update

Hand M08-01-RAW-A, M08-01-DERIVED-A and M08-01-DERIVED-CORR to the 08.2 bench review, together with the correction chain and unresolved physical setup evidence.

Your next measurement definition

Specify a different RF measurand—such as filter insertion loss at a named pair of planes or receiver sensitivity at a stated packet-error criterion. Choose the method, loading, waveform, bandwidth/gate, state and population. Identify at least one shared influence, write the measurement equation, justify every standard uncertainty, declare coverage and the decision rule, and defend the next improvement. Mark missing information unknown and give it an owner. A technically justified alternative is welcome; this task is ungraded.

Ungraded review

Check your understanding

Answer each question in your own words, then reveal the model answer.

01A sensor has a calibration sticker and a serial number. Is the R1-TX result metrologically traceable?
Model answer
Not established. Identify the reference, dated calibration links, their uncertainties, and applicability at 2.450 GHz, level, 50 Ω loading and gate. A complete correction from L-SENSOR to R1-TX is also needed. Record identity supports document history; it does not itself establish the result’s metrological traceability. The fictional chain in this lesson supplies no real calibration evidence.
02Does Type A mean random, and Type B mean systematic?
Model answer
No. Type A/B identify how standard uncertainty is evaluated. Statistical calibration comparisons can evaluate a systematic effect by Type A; a manufacturer or certificate can inform a Type B estimate of an effect that varies. In TX-PWR-A, the shared 0.150 dB calibration term does not shrink with 16 sensor repeats. Independence and overlap in the supplied evidence still need review.
03A residual correction at R1-TX is bounded by ±0.100 dB. What standard uncertainty belongs in the budget?
Model answer
A bound alone does not specify a distribution. If equal plausibility across that supplied interval is justified, u=0.100/√3=0.057735026919 dB. A justified symmetric triangular distribution instead gives 0.040824829046 dB. Explain the choice; real RF mismatch does not acquire a rectangular distribution simply because VSWR is known.
04Two readings share exactly the same 0.300 au offset uncertainty. What does subtraction do?
Model answer
With y=x₁−x₂, sensitivities +1 and −1, and ρ=+1, the variance is 0.09+0.09−0.18=0 au². This cancels that perfectly shared component only. Different planes, unequal sensitivities, reconnects or drift can leave a residual; no zero total uncertainty follows for real measurements without further evidence.
05Why is the 19.300 dBm baseline interval asymmetric in mW?
Model answer
The exact map is p=10^(y/10) mW. The estimate is 85.113803820238 mW; the endpoints are 78.335452675538 and 92.478684341760 mW. Exponentiation stretches the upper side. These are the same mapped R1-TX interval endpoints, not a symmetric mW ±U or a new decision rule.
06If a fixed 0.400 dB guard band does not accept a result, has the DUT failed its 19.700 dBm limit?
Model answer
No. This local upper acceptance rule requires y≤19.300 dBm; a result just above that acceptance limit can still be below the specification. Record “not accepted by this rule,” uncertainty and evidence conditions. Resolve an inconclusive interval or improve the measurement before asserting the DUT exceeds its limit. Formal conformity decisions and risk models require additional agreed procedures.

References and further study

Primary source access: 2026-09-08. Definitions and informative methods are paraphrased. Worked budgets, IDs, limits and graphs are original illustrative/derived fixtures; none is measured or normative product evidence.

MET-INDEX · BIPM / JCGM. Guides in Metrology. Live publication index, checked 8 September 2026. Consulted: GUM, amendment, supplements, GUM-6 and VIM listings. Publication identity/status only. JCGM 100:2008/Amd.1:2026 and GUM-5:2026 are now listed.
VIM · JCGM. International vocabulary of metrology. JCGM 200:2012, VIM third edition with minor corrections. Consulted: 2.3, 2.9, 2.16, 2.20–2.26, 2.39–2.44, 2.53, 3.11; annotated entries consulted. Vocabulary, calibration chain and uncertainty; definitions paraphrased, no accreditation claim.
GUM · JCGM. Guide to the expression of uncertainty in measurement. JCGM 100:2008(E), GUM 1995 with minor corrections. Consulted: 4.2–4.3, 5.1–5.2, 6; Annex G orientation. Standardization, sensitivities/covariance and conditional coverage; not a complete implementation.
GUM-AMD · JCGM. Amendment 1: Nonlinearity in measurement models. JCGM 100:2008/Amd.1:2026, first edition 2026. Consulted: Complete amendment: additions to 4.1.4, H.1.7 and bibliography. Significant nonlinearity can affect both the output estimate and its uncertainty.
GUM-6 · JCGM. Developing and using measurement models. JCGM GUM-6:2020, first edition 2020. Consulted: 8.3.4–8.3.6 logarithmic transformations and statistical integrity; 8.4 multi-stage models. General caution against uncertainty calculations in logarithmic units; the lesson’s supplied small-error dB model is an explicit restricted teaching assumption.
DIST · JCGM. Propagation of distributions using a Monte Carlo method. JCGM 101:2008, first edition 2008. Consulted: 5.2–5.5, 6.1, 6.4.9, 7.2–7.7. Assign distributions, propagate and summarize; finite deterministic Halton sampling here is not the full adaptive JCGM procedure. The normal repeat-mean approximation is declared separately.
RULE · JCGM. The role of measurement uncertainty in conformity assessment. JCGM 106:2012, first edition 2012. Consulted: 8.3.2 guarded acceptance; 9.3–9.5 specific/global risk distinctions. Guard bands versus risk calculation. Local rules do not establish a formal conformity route.
NIST-A · NIST / Taylor & Kuyatt. TN 1297: Appendix A, Law of Propagation of Uncertainty. 1994 edition; web page updated 11 September 2025. Consulted: A.1–A.5, equations A-1 through A-7. Measurement equation, covariance and independent repeat-mean standard uncertainty.
NIST-B · NIST / Taylor & Kuyatt. TN 1297: Type B Evaluation of Standard Uncertainty. 1994 edition, current web presentation. Consulted: 4.1–4.6. Reasoned distributions and conversion to standard uncertainty, not an arbitrary default for all RF mismatch.
NIST-K · NIST / Taylor & Kuyatt. TN 1297: Expanded Uncertainty. 1994 edition; parent index updated 6 May 2026. Consulted: 6.1–6.4. Coverage factor and distribution/degrees-of-freedom qualifications.
INV-NORMAL · QuantLib project / Peter J. Acklam algorithm. Inverse cumulative normal implementation. Official source retrieved 8 September 2026; local coefficients frozen as normal-inverse-acklam-v1. Consulted: InverseCumulativeNormal coefficients and tail branch. Algorithm cross-check; local inverse independently checked against Python statistics.NormalDist to 7e−9 absolute error on the used probability domain. No QuantLib runtime dependency.