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Calculator Library / Measurement Systems

MSA / Gage R&R Studio

Run a professional crossed-study variable Gage R&R analysis with ANOVA support, comparison tools, stakeholder reporting, and broader measurement-system modules. The studio keeps the core average-range calculator path intact while extending the page into a fuller MSA workspace.

Studio modes

Measurement-system workflows

Current default mode: crossed variable Gage R&R using the average-range method with ANOVA support. This preserves the existing calculator path while the broader MSA modules stay on the same page.

Available now

Variable Gage R&R

Crossed study, average-range method, EV/AV/GRR/PV/TV, percent study variation, and variance contribution review.

Available now

ANOVA variable study

Variance components, ndc, tolerance framing, and richer operator-by-part diagnostics.

Available now

Bias / linearity / stability

Extended variable-measurement checks for reference-value accuracy, range effects, and time drift.

Available now

Attribute MSA

Agreement analysis, false accept / false reject exposure, and appraiser-to-standard comparisons.

Current mode

Crossed variable Gage R&R workspace

Average-range method: GRR = sqrt(EV² + AV²), TV = sqrt(GRR² + PV²)

Studio foundation

This workspace keeps the underlying crossed-study math intact while adding study metadata, clearer workflow framing, saved studies, diagnostics, exports, and broader MSA modules on the same URL.

Study scenarios

Save, reload, export, and import study setups

Study data

Build the crossed study with rows or paste-in data

# Operator Part Trial Measured value Actions

Use one row per reading in the format: Operator, Part, Trial, Measured value. This current mode expects a balanced crossed study with repeated trials for every operator-part combination. Editing the row grid updates the pasted-text field automatically.

Breakdown

Variance contribution

Component Value Percent of Total Variance
ANOVA source DF SS MS

Release roadmap

Studio rollout status

1

Workspace shell

Done in this slice: studio naming, metadata, mode framing, and a cleaner shell.

2

Saved studies

Local persistence, study metadata capture, and import/export.

3

ANOVA + ndc

Done in this slice: ANOVA, ndc, tolerance framing, and stronger variable-study decision support.

4

Diagnostics + comparison

Variance charts, interaction diagnostics, saved-study comparison, and stakeholder exports.

5

Advanced MSA modes

Bias, linearity, stability, and attribute agreement are now included on-page.

Diagnostics

Variance profile

The chart will update after the study runs.

Diagnostics

Operator-by-part interaction

Flat, roughly parallel lines indicate lower operator-part interaction risk.

Comparison

Compare current study to a saved baseline

Metric Current Baseline Delta
Select a saved study to compare.

Comparison highlights whether the current measurement system improved or regressed versus a saved baseline.

Reporting

Stakeholder-ready export

Decision bandMarginal
Primary riskGauge variation
Recommended next moveReview study

The export packages the current study metadata, summary metrics, interpretation, and diagnostic notes into a standalone report.

Advanced MSA modules

Bias, linearity, stability, and attribute agreement

Bias and linearity

Enter reference, observed pairs. Use repeated observations across the reference range for linearity.

Reference Mean observed Bias

Run the module to evaluate mean bias and whether bias changes across the measurement range.

Stability

Enter sequence, value pairs to check drift over time.

Mean-
Average moving range-
Drift slope-

Run the module to evaluate short-term drift and moving-range behavior.

Attribute agreement

Enter part, standard, appraiser, response. Use pass/fail, yes/no, accept/reject, or good/bad style responses.

Appraiser Agreement to standard False accept False reject

Run the module to evaluate appraiser agreement and classification risk.

How to use the advanced modules

  • Use bias when the gauge must be accurate to a known reference.
  • Use linearity when accuracy may change across the working range.
  • Use stability when the same standard is checked over time.
  • Use attribute agreement when the measurement decision is categorical.

Instructions

How to use the current studio mode

  1. Run a crossed study with multiple operators, multiple parts, and repeated trials.
  2. Set the study metadata for the characteristic, unit, and optional tolerance.
  3. Enter each reading as operator, part, trial, and measured value.
  4. Click Run variable Gage R&R to estimate EV, AV, GRR, PV, TV, and percent study variation.
  5. Review both total gauge contribution and part variation, because a gauge can look bad simply because the study parts do not span enough real process variation.

What This MSA / Gage R&R Studio Helps You Decide

This studio helps quality, metrology, and manufacturing teams judge whether a measurement system is capable enough to support process decisions. The current mode separates equipment-driven repeatability from operator-driven reproducibility and compares both to actual part-to-part variation in a crossed study.

Use it before launching control plans, capability studies, improvement projects, validation work, or acceptance criteria that depend on reliable measurement.

Current Core Formula

Measure Logic Meaning
EVAverage within-part range / d2(trials)Equipment variation, or repeatability.
AVOperator-average spread adjusted for EVReproducibility between operators.
GRRsqrt(EV² + AV²)Total gauge variation.
TVsqrt(GRR² + PV²)Total study variation including part variation.

Why This Is Now a Studio Instead of Just a Calculator

The original calculator only handled one narrow crossed-study workflow. The studio foundation keeps that default mode available, but the page is now structured to support broader measurement-system analysis without splitting traffic across multiple overlapping tools.

That expansion now includes ANOVA, ndc, tolerance framing, saved-study comparison, stakeholder reporting, attribute agreement, bias, linearity, and stability on the same URL.

How to Interpret the Current Results

MSA / Gage R&R Studio Frequently Asked Questions

What is repeatability?

Repeatability is the variation seen when the same operator measures the same part multiple times with the same gauge.

What is reproducibility?

Reproducibility is the variation introduced by different operators using the same measurement method.

What does the current studio release calculate?

This release calculates a crossed variable Gage R&R study with average-range and ANOVA views, ndc, tolerance framing, study comparison, stakeholder reporting, bias, linearity, stability, and attribute-agreement modules.

Is Gage R&R the only measurement-system check I need?

No. Bias, linearity, stability, discrimination, and attribute agreement can matter depending on the application, customer requirement, and decision risk.

What is the common acceptance rule for percent study variation?

Under 10% is usually strong, 10% to 30% is conditional, and above 30% often requires measurement-system improvement before relying on the results.

Related Templates and Guides

${escapeHtml(analysis.studyName)} — MSA / Gage R&R Studio Report

Characteristic: ${escapeHtml(analysis.characteristic)} | Unit: ${escapeHtml(analysis.unit)} | Method: ${escapeHtml(analysis.method)}

Decision band
${escapeHtml(analysis.decisionBand)}
% Study Variation
${grrFormat(analysis.percentStudy, 1)}%
ANOVA Gage R&R
${grrFormat(analysis.anova.components.grr)}
ndc
${grrFormat(analysis.ndc, 1)}

Executive summary

${escapeHtml(document.getElementById('msa-report-summary').textContent)}

Core metrics

MetricValue
Repeatability (EV)${grrFormat(analysis.ev)}
Reproducibility (AV)${grrFormat(analysis.av)}
Total Gage R&R${grrFormat(analysis.grr)}
Part variation${grrFormat(analysis.pv)}
Total variation${grrFormat(analysis.tv)}
% Tolerance${analysis.percentTolerance == null ? '-' : `${grrFormat(analysis.percentTolerance, 1)}%`}

Interpretation

`; const blob = new Blob([html], { type: 'text/html;charset=utf-8' }); const url = URL.createObjectURL(blob); const link = document.createElement('a'); link.href = url; link.download = `${sanitizeIdentifier(analysis.studyName)}_msa_report.html`; document.body.appendChild(link); link.click(); link.remove(); URL.revokeObjectURL(url); } async function copyExecutiveSummary() { if (!state.latestAnalysis) { showError('Run the current study before copying the summary.'); return; } const summary = `${state.latestAnalysis.studyName}: ${document.getElementById('msa-report-summary').textContent}`; try { if (navigator.clipboard?.writeText) { await navigator.clipboard.writeText(summary); clearError(); } else { throw new Error('Clipboard access is unavailable in this browser.'); } } catch (error) { showError(error.message || 'The summary could not be copied.'); } } function runBiasLinearity() { try { const pairs = parseSimplePairs(document.getElementById('msa-bias-data').value, 2, (parts) => { const reference = Number(parts[0]); const observed = Number(parts[1]); if (!Number.isFinite(reference) || !Number.isFinite(observed)) { throw new Error('Bias / linearity rows must contain numeric reference and observed values.'); } return { reference, observed, bias: observed - reference }; }); const groups = [...new Set(pairs.map(pair => pair.reference))].sort((a, b) => a - b).map((reference) => { const entries = pairs.filter(pair => pair.reference === reference); const meanObserved = mean(entries.map(entry => entry.observed)); return { reference, meanObserved, bias: meanObserved - reference }; }); const regression = computeLinearRegression(groups.map(group => ({ x: group.reference, y: group.bias }))); const avgBias = mean(pairs.map(pair => pair.bias)); document.getElementById('msa-bias-body').innerHTML = groups.map(group => `${grrFormat(group.reference, 3)}${grrFormat(group.meanObserved, 3)}${formatSigned(group.bias, 3)}`).join(''); document.getElementById('msa-bias-summary').textContent = `Average bias is ${formatSigned(avgBias, 4)} ${document.getElementById('msa-unit').value || ''}. Bias-vs-reference slope is ${formatSigned(regression.slope, 4)} per unit of reference, so ${Math.abs(regression.slope) < 0.05 ? 'linearity appears reasonably stable across the entered range.' : 'linearity should be reviewed because bias changes across the entered range.'}`; clearError(); } catch (error) { showError(error.message || 'Bias / linearity analysis failed.'); } } function runStability() { try { const points = parseSimplePairs(document.getElementById('msa-stability-data').value, 2, (parts) => { const sequence = Number(parts[0]); const value = Number(parts[1]); if (!Number.isFinite(sequence) || !Number.isFinite(value)) { throw new Error('Stability rows must contain numeric sequence and value pairs.'); } return { x: sequence, y: value }; }).sort((a, b) => a.x - b.x); const values = points.map(point => point.y); const movingRanges = points.slice(1).map((point, index) => Math.abs(point.y - points[index].y)); const regression = computeLinearRegression(points); document.getElementById('msa-stability-mean').textContent = grrFormat(mean(values), 4); document.getElementById('msa-stability-mr').textContent = movingRanges.length ? grrFormat(mean(movingRanges), 4) : '0.0000'; document.getElementById('msa-stability-slope').textContent = formatSigned(regression.slope, 5); document.getElementById('msa-stability-summary').textContent = `Average moving range is ${movingRanges.length ? grrFormat(mean(movingRanges), 4) : '0.0000'} and drift slope is ${formatSigned(regression.slope, 5)} per sequence step. ${Math.abs(regression.slope) < 0.005 ? 'No strong drift signal is visible in the entered sequence.' : 'The entered sequence shows drift that should be investigated before trusting long-run stability.'}`; clearError(); } catch (error) { showError(error.message || 'Stability analysis failed.'); } } function runAttributeMsa() { try { const rows = parseSimplePairs(document.getElementById('msa-attribute-data').value, 4, (parts) => { const part = parts[0]; const standard = normalizeDecision(parts[1]); const appraiser = parts[2]; const response = normalizeDecision(parts[3]); if (!part || !standard || !appraiser || !response) { throw new Error('Attribute rows must contain part, standard, appraiser, and response values.'); } return { part, standard, appraiser, response }; }); const appraisers = [...new Set(rows.map(row => row.appraiser))]; const output = appraisers.map((appraiser) => { const subset = rows.filter(row => row.appraiser === appraiser); const agree = subset.filter(row => row.standard === row.response).length; const falseAccept = subset.filter(row => row.standard === 'reject' && row.response === 'accept').length; const falseReject = subset.filter(row => row.standard === 'accept' && row.response === 'reject').length; return { appraiser, agreement: subset.length ? (agree / subset.length) * 100 : 0, falseAccept: subset.length ? (falseAccept / subset.length) * 100 : 0, falseReject: subset.length ? (falseReject / subset.length) * 100 : 0 }; }); const overallAgreement = rows.length ? (rows.filter(row => row.standard === row.response).length / rows.length) * 100 : 0; document.getElementById('msa-attribute-body').innerHTML = output.map(row => `${escapeHtml(row.appraiser)}${grrFormat(row.agreement, 1)}%${grrFormat(row.falseAccept, 1)}%${grrFormat(row.falseReject, 1)}%`).join(''); document.getElementById('msa-attribute-summary').textContent = `Overall agreement to the standard is ${grrFormat(overallAgreement, 1)}%. False accepts expose escape risk, while false rejects expose unnecessary scrap or rework.`; clearError(); } catch (error) { showError(error.message || 'Attribute MSA failed.'); } } function updateGrr() { try { updateStudyMeta(); const rows = state.rows.map((row, index) => { const operator = String(row.operator || '').trim(); const part = String(row.part || '').trim(); const trial = String(row.trial || '').trim(); const rawValue = String(row.value ?? '').trim(); const value = Number(rawValue); if (!operator && !part && !trial && !rawValue) { return null; } if (!operator || !part || !trial || !Number.isFinite(value)) { throw new Error(`Row ${index + 1} contains invalid data.`); } return { operator, part, trial, value }; }).filter(Boolean); if (!rows.length) { throw new Error('Add at least one row to the study before running the analysis.'); } syncTextareaFromRows(); const operators = [...new Set(rows.map((row) => row.operator))]; const parts = [...new Set(rows.map((row) => row.part))]; const trials = [...new Set(rows.map((row) => row.trial))]; if (operators.length < 2 || parts.length < 2 || trials.length < 2) { throw new Error('Crossed variable Gage R&R needs at least 2 operators, 2 parts, and 2 trials.'); } if (!d2[trials.length] || !d2[operators.length] || !d2[parts.length]) { throw new Error('This current studio mode supports up to 10 operators, parts, or trials for the d2 constants.'); } const cellMap = new Map(); rows.forEach((row) => { const key = `${row.operator}|${row.part}`; if (!cellMap.has(key)) { cellMap.set(key, []); } cellMap.get(key).push(row.value); }); const cellRanges = []; for (const operator of operators) { for (const part of parts) { const key = `${operator}|${part}`; const values = cellMap.get(key); if (!values || values.length !== trials.length) { throw new Error(`Missing repeated trials for operator ${operator}, part ${part}.`); } cellRanges.push(range(values)); } } const tolerance = Number(document.getElementById('msa-tolerance').value); const hasTolerance = Number.isFinite(tolerance) && tolerance > 0; const rbar = mean(cellRanges); const ev = rbar / d2[trials.length]; const operatorMeans = operators.map((operator) => mean(rows.filter((row) => row.operator === operator).map((row) => row.value))); const partMeans = parts.map((part) => mean(rows.filter((row) => row.part === part).map((row) => row.value))); const ro = range(operatorMeans); const rp = range(partMeans); const avTerm = ro / d2[operators.length]; const pvTerm = rp / d2[parts.length]; const av = safeSqrt((avTerm ** 2) - ((ev ** 2) / (parts.length * trials.length))); const pv = safeSqrt((pvTerm ** 2) - ((ev ** 2) / (operators.length * trials.length))); const grr = safeSqrt((ev ** 2) + (av ** 2)); const tv = safeSqrt((grr ** 2) + (pv ** 2)); const evContribution = tv > 0 ? (ev ** 2) / (tv ** 2) : 0; const avContribution = tv > 0 ? (av ** 2) / (tv ** 2) : 0; const grrContribution = tv > 0 ? (grr ** 2) / (tv ** 2) : 0; const pvContribution = tv > 0 ? (pv ** 2) / (tv ** 2) : 0; const percentStudy = tv > 0 ? (grr / tv) * 100 : 0; const anova = buildAnovaAnalysis(rows, operators, parts, trials); const percentTolerance = hasTolerance ? ((6 * anova.components.grr) / tolerance) * 100 : null; const ndc = Number.isFinite(anova.ndc) ? anova.ndc : 999; document.getElementById('grr-operators').textContent = operators.length; document.getElementById('grr-parts').textContent = parts.length; document.getElementById('grr-trials').textContent = trials.length; document.getElementById('msa-method-output').textContent = document.getElementById('msa-method').value || 'Crossed variable'; document.getElementById('grr-ev').textContent = grrFormat(ev); document.getElementById('grr-av').textContent = grrFormat(av); document.getElementById('grr-grr').textContent = grrFormat(grr); document.getElementById('grr-pv').textContent = grrFormat(pv); document.getElementById('grr-tv').textContent = grrFormat(tv); document.getElementById('grr-percent-study').textContent = `${grrFormat(percentStudy, 1)}%`; document.getElementById('grr-anova-grr').textContent = grrFormat(anova.components.grr); document.getElementById('grr-anova-pv').textContent = grrFormat(anova.components.pv); document.getElementById('grr-ndc').textContent = ndc >= 999 ? '999+' : grrFormat(ndc, 1); document.getElementById('grr-percent-tolerance').textContent = percentTolerance == null ? '-' : `${grrFormat(percentTolerance, 1)}%`; const decisionBand = percentStudy < 10 && ndc >= 5 && (percentTolerance == null || percentTolerance < 30) ? 'Strong' : (percentStudy <= 30 && ndc >= 2 && (percentTolerance == null || percentTolerance <= 60) ? 'Marginal' : 'High risk'); document.getElementById('grr-decision-band').textContent = decisionBand; document.getElementById('grr-status').textContent = decisionBand === 'Strong' ? 'This measurement system appears strong across study variation, discrimination, and the currently entered tolerance framing.' : (decisionBand === 'Marginal' ? 'This measurement system may be usable, but the study variation, ndc, and tolerance exposure should be reviewed carefully against application risk.' : 'This measurement system is not yet decision-grade across study variation, discrimination, or tolerance framing and likely needs improvement before process conclusions are trusted.'); document.getElementById('grr-guidance-1').textContent = `Repeatability contributes ${(evContribution * 100).toFixed(1)}% of total observed variance, while reproducibility contributes ${(avContribution * 100).toFixed(1)}%.`; document.getElementById('grr-guidance-2').textContent = `Part variation contributes ${(pvContribution * 100).toFixed(1)}% of total observed variance. The ANOVA Gage R&R estimate is ${grrFormat(anova.components.grr)} and the ANOVA part variation estimate is ${grrFormat(anova.components.pv)}.`; document.getElementById('grr-guidance-3').textContent = hasTolerance ? `ndc is ${grrFormat(ndc, 1)} and %Tolerance is ${grrFormat(percentTolerance, 1)}%. ndc below 5 or %Tolerance above 30% should trigger closer review even if percent study variation looks acceptable.` : `ndc is ${grrFormat(ndc, 1)}. Add a tolerance if you want the studio to frame the Gage R&R result against specification width as well as study variation.`; document.getElementById('grr-table-body').innerHTML = [ ['Repeatability (EV)', grrFormat(ev), `${grrFormat(evContribution * 100, 1)}%`], ['Reproducibility (AV)', grrFormat(av), `${grrFormat(avContribution * 100, 1)}%`], ['Total Gage R&R', grrFormat(grr), `${grrFormat(grrContribution * 100, 1)}%`], ['Part Variation (PV)', grrFormat(pv), `${grrFormat(pvContribution * 100, 1)}%`], ['ANOVA interaction', grrFormat(anova.components.interaction), tv > 0 ? `${grrFormat((Math.max(anova.components.interaction ** 2, 0) / (anova.components.tv ** 2 || 1)) * 100, 1)}%` : '0.0%'], ['% Tolerance', percentTolerance == null ? '-' : `${grrFormat(percentTolerance, 1)}%`, hasTolerance ? 'Entered specification width' : 'Add tolerance to enable'] ].map((row) => `${row[0]}${row[1]}${row[2]}`).join(''); document.getElementById('grr-anova-body').innerHTML = [ ['Part', anova.dfs.part, grrFormat(anova.sums.part), grrFormat(anova.means.part)], ['Operator', anova.dfs.operator, grrFormat(anova.sums.operator), grrFormat(anova.means.operator)], ['Operator × Part', anova.dfs.interaction, grrFormat(anova.sums.interaction), grrFormat(anova.means.interaction)], ['Repeatability', anova.dfs.repeatability, grrFormat(anova.sums.repeatability), grrFormat(anova.means.repeatability)] ].map((row) => `${row[0]}${row[1]}${row[2]}${row[3]}`).join(''); state.latestAnalysis = { rows, operators, parts, trials, ev, av, grr, pv, tv, evContribution, avContribution, grrContribution, pvContribution, percentStudy, anova, percentTolerance, ndc, decisionBand, studyName: document.getElementById('msa-study-name').value || 'Crossed Gage R&R Example', characteristic: document.getElementById('msa-characteristic').value || 'Critical diameter', unit: document.getElementById('msa-unit').value || '', method: document.getElementById('msa-method').value || 'Crossed variable / average-range + ANOVA' }; updateDiagnosticsAndReporting(state.latestAnalysis); clearError(); persistDraft(); } catch (error) { state.latestAnalysis = null; showError(error.message); } } document.getElementById('msa-entry-body').addEventListener('input', (event) => { const index = Number(event.target.dataset.index); const field = event.target.dataset.field; if (!Number.isInteger(index) || !field || !state.rows[index]) { return; } state.rows[index][field] = event.target.value; syncTextareaFromRows(); persistDraft(); }); document.getElementById('msa-entry-body').addEventListener('click', (event) => { const button = event.target.closest('[data-action]'); if (!button) return; const index = Number(button.dataset.index); if (!Number.isInteger(index) || !state.rows[index]) return; if (button.dataset.action === 'duplicate') { state.rows.splice(index + 1, 0, { ...state.rows[index] }); } if (button.dataset.action === 'delete' && state.rows.length > 1) { state.rows.splice(index, 1); } renderRows(); updateGrr(); }); document.getElementById('msa-add-row-btn').addEventListener('click', () => { state.rows.push(createEmptyRow()); renderRows(); }); document.getElementById('msa-apply-paste-btn').addEventListener('click', () => { try { syncRowsFromTextarea(); updateGrr(); } catch (error) { showError(error.message); } }); document.getElementById('grr-calc-btn').addEventListener('click', updateGrr); document.getElementById('grr-reset-btn').addEventListener('click', () => { document.getElementById('msa-study-name').value = 'Crossed Gage R&R Example'; document.getElementById('msa-characteristic').value = 'Critical diameter'; document.getElementById('msa-unit').value = 'mm'; document.getElementById('msa-tolerance').value = ''; state.rows = parseGrrData(grrDefaults).map(row => ({ ...row, value: String(row.value) })); renderRows(); updateStudyMeta(); updateGrr(); }); document.getElementById('msa-study-name').addEventListener('input', updateStudyMeta); document.getElementById('msa-characteristic').addEventListener('input', updateStudyMeta); document.getElementById('msa-unit').addEventListener('input', persistDraft); document.getElementById('msa-tolerance').addEventListener('input', persistDraft); document.getElementById('msa-saved-studies').addEventListener('change', (event) => { state.selectedStudyId = event.target.value || ''; clearError(); }); document.getElementById('msa-save-study-btn').addEventListener('click', saveStudy); document.getElementById('msa-update-study-btn').addEventListener('click', updateSelectedStudy); document.getElementById('msa-load-study-btn').addEventListener('click', loadSelectedStudy); document.getElementById('msa-delete-study-btn').addEventListener('click', deleteSelectedStudy); document.getElementById('msa-export-json-btn').addEventListener('click', exportStudyJson); document.getElementById('msa-import-json-btn').addEventListener('click', () => document.getElementById('msa-import-file').click()); document.getElementById('msa-import-file').addEventListener('change', (event) => importStudyJson(event.target.files?.[0])); document.getElementById('msa-run-compare-btn').addEventListener('click', runStudyComparison); document.getElementById('msa-export-report-btn').addEventListener('click', exportStakeholderReport); document.getElementById('msa-copy-summary-btn').addEventListener('click', copyExecutiveSummary); document.getElementById('msa-run-bias-btn').addEventListener('click', runBiasLinearity); document.getElementById('msa-run-stability-btn').addEventListener('click', runStability); document.getElementById('msa-run-attribute-btn').addEventListener('click', runAttributeMsa); loadSavedStudies(); renderSavedStudies(); restoreDraft(); document.getElementById('msa-bias-data').value = document.getElementById('msa-bias-data').value || biasDefaults; document.getElementById('msa-stability-data').value = document.getElementById('msa-stability-data').value || stabilityDefaults; document.getElementById('msa-attribute-data').value = document.getElementById('msa-attribute-data').value || attributeDefaults; runBiasLinearity(); runStability(); runAttributeMsa();