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Quality and Six Sigma Proposed system

Standards set the rules; Six Sigma statistics show whether a process keeps them

Which quality rulebooks would apply to a botanical ingredient plant, what each covers, and the statistics that turn specifications into measured control: SPC, capability, gauge R&R and designed experiments.

2 of 14quality rulebooks on the map are law: 21 CFR 111 and 117
39%of 1,938 Part 111 citations in fiscal 2025 fell in Subpart E, 14% of its sections
1statistical tool named in Part 111: a sound statistical sampling plan
19%of study variation from measurement in a published gauge R&R study

Status. EUTECNIQ has no laboratory, data, certification or accreditation. Charts use published data or labeled simulations.

Standards map

Two FDA rules are law; every other quality standard on this map is voluntary

Quality rulebooks for a botanical ingredient, by kind of authorityVerified editions, Oct 24, 2026
Click a segment to zoom, the centre to zoom out. Segment size shows structure only (one unit per listed element), not importance.Sources: eCFR 21 CFR 111 and 117; ISO catalogue pages for ISO 9001, 22000, 17025, 13053-1/-2 and 7870-2; FSSC; SQFI; GFSI; ICH; AIAG (checked Oct 24, 2026).
Data table: every element on the map
Kind of authorityRulebook (edition)Element
U.S. law (FDA)21 CFR 111, dietary supplement CGMPSpecifications (Subpart E)
U.S. law (FDA)21 CFR 111, dietary supplement CGMPQuality control (Subpart F)
U.S. law (FDA)21 CFR 111, dietary supplement CGMPMaster and batch records (Subparts H, I)
U.S. law (FDA)21 CFR 111, dietary supplement CGMPLaboratory operations (Subpart J)
U.S. law (FDA)21 CFR 111, dietary supplement CGMPComplaints and returns (Subparts N, O)
U.S. law (FDA)21 CFR 117, human food CGMP and preventive controlsCGMP (Subpart B)
U.S. law (FDA)21 CFR 117, human food CGMP and preventive controlsHazard analysis and risk-based preventive controls (Subpart C)
U.S. law (FDA)21 CFR 117, human food CGMP and preventive controlsSupply-chain program (Subpart G)
U.S. law (FDA)21 CFR 117, human food CGMP and preventive controlsRecords (Subpart F)
CertificationISO 9001:2026, quality management systems (edition 6)Quality management requirements for any organization
CertificationISO 9001:2026, quality management systems (edition 6)Internal audit and management review
CertificationISO 22000:2018, food safety management systemsHACCP principles (Codex)
CertificationISO 22000:2018, food safety management systemsPrerequisite programmes
CertificationISO 22000:2018, food safety management systemsInteractive communication
CertificationFSSC 22000 (version 6; version 7 published May 7, 2026)ISO 22000
CertificationFSSC 22000 (version 6; version 7 published May 7, 2026)Sector prerequisite programmes (ISO/TS 22002-x; ISO 22002-x:2025 in v7)
CertificationFSSC 22000 (version 6; version 7 published May 7, 2026)FSSC additional requirements
CertificationSQF Food Safety Code: Dietary Supplement Manufacturing, Edition 10SQF System Elements (Module 2)
CertificationSQF Food Safety Code: Dietary Supplement Manufacturing, Edition 10Food safety plan under Codex HACCP (element 2.4.3)
CertificationSQF Food Safety Code: Dietary Supplement Manufacturing, Edition 10Good industry practice module
AccreditationISO/IEC 17025:2017, testing and calibration laboratoriesImpartiality and confidentiality (clause 4)
AccreditationISO/IEC 17025:2017, testing and calibration laboratoriesPersonnel, facilities, equipment, traceability (clause 6)
AccreditationISO/IEC 17025:2017, testing and calibration laboratoriesMethods, measurement uncertainty, validity of results (clause 7)
AccreditationISO/IEC 17025:2017, testing and calibration laboratoriesManagement system (clause 8)
ICH guidance (drug)ICH Q8(R2), pharmaceutical development (2009)Target profile, critical quality attributes, design space
ICH guidance (drug)ICH Q9(R1), quality risk management (2023)Risk assessment, control, communication and review
ICH guidance (drug)ICH Q10, pharmaceutical quality system (2008)Management review and continual improvement
Statistical method standardsISO 13053-1 and -2:2011, Six Sigma (confirmed 2022)DMAIC methodology (part 1)
Statistical method standardsISO 13053-1 and -2:2011, Six Sigma (confirmed 2022)Tools and techniques (part 2)
Statistical method standardsISO 7870-2:2023, Shewhart control chartsControl limits and patterns
Statistical method standardsAIAG Measurement Systems Analysis, 4th edition (2010)%GRR and number-of-distinct-categories guidelines
Statistical method standardsAIAG and VDA FMEA Handbook, 1st edition (2019)Seven steps and action priority

FDA's Parts 111 and 117 bind; certificates, accreditation, ICH guidance and the statistical standards are chosen by the firm or required by customers.

Scope

No single certificate covers law, food safety, laboratory competence and management review

What each rulebook is, and what it is notRegulation and standards
Matrix of eight rulebooks against six properties: only Parts 111 and 117 are required by U.S. law; the ISO standards, FSSC 22000 and SQF are voluntary and audited by third parties; only FSSC 22000 and SQF are GFSI-recognized; Part 117, ISO 22000, FSSC 22000 and SQF require a food-safety hazard analysis; only ISO/IEC 17025 is a laboratory competence standardRequired by U.S.lawThird-partycertificate oraccreditationGFSI-recognizedschemeFood-safetyhazard analysisInternal audit andmanagementreviewLaboratorycompetencestandard21 CFR Part 111Dietary supplement CGMP, FDA21 CFR Part 111, Required by U.S. law: yes. Required for firms that manufacture, package, label or hold dietary supplements (21 CFR 111.1)21 CFR Part 117Food CGMP and preventive controls, FDA21 CFR Part 117, Required by U.S. law: yes. Required for food facilities, including dietary-ingredient operations, unless an exemption applies (21 CFR 117)21 CFR Part 117, Food-safety hazard analysis: yes. Subpart C hazard analysis and risk-based preventive controls (117.130), unless exempt; 117.5(e) exempts Part 111 supplement operationsISO 9001:2026Quality management systems, edition 6ISO 9001:2026, Third-party certificate or accreditation: yes. Certification by an accredited certification body; ISO itself does not certifyISO 9001:2026, Internal audit and management review: yes. Internal audit and management review clauses (9.2, 9.3 in the 2015 edition; the 2026 edition keeps that framework)ISO 22000:2018Food safety management systemsISO 22000:2018, Third-party certificate or accreditation: yes. Certification is optional (ISO); performed by certification bodiesISO 22000:2018, Food-safety hazard analysis: yes. Integrates the Codex HACCP principles (ISO)ISO 22000:2018, Internal audit and management review: yes. Same high-level structure as ISO 9001 (ISO)FSSC 22000 v6 / v7ISO 22000 + sector PRPs + scheme rulesFSSC 22000 v6 / v7, Third-party certificate or accreditation: yes. Certification scheme; version 7 published 7 May 2026, audits to v7 from 1 May 2027 (UKAS)FSSC 22000 v6 / v7, GFSI-recognized scheme: yes. Listed by GFSI as a recognized certification programme ownerFSSC 22000 v6 / v7, Food-safety hazard analysis: yes. Built on ISO 22000FSSC 22000 v6 / v7, Internal audit and management review: yes. Built on ISO 22000SQF Edition 10Food Safety Code: Dietary Supplement Mfg.SQF Edition 10, Third-party certificate or accreditation: yes. SQF certification; Edition 10 audits anticipated from January 1, 2027SQF Edition 10, GFSI-recognized scheme: yes. Listed by GFSI as a recognized certification programme ownerSQF Edition 10, Food-safety hazard analysis: yes. Element 2.4.3: food safety plan under the Codex General Principles of Food HygieneSQF Edition 10, Internal audit and management review: yes. Element 2.1.2.1 annual management review; 2.5.4.1 annual internal auditsISO/IEC 17025:2017Testing and calibration laboratoriesISO/IEC 17025:2017, Third-party certificate or accreditation: yes. Accreditation by an accreditation body (ILAC MRA signatories accredit testing and calibration labs to ISO/IEC 17025)ISO/IEC 17025:2017, Internal audit and management review: yes. Clause 8 management system requirements: 8.8 internal audits, 8.9 management reviewsISO/IEC 17025:2017, Laboratory competence standard: yes. Competence, impartiality and consistent operation of laboratories; 7.6 measurement uncertainty, 7.7 validity of resultsICH Q8(R2), Q9(R1), Q10Drug guidance, used as a referenceICH Q8(R2), Q9(R1), Q10, Internal audit and management review: yes. ICH Q10 pharmaceutical quality system includes management reviewyesno, or not part of that documentEditions and status as of October 24, 2026. Hover a dot for the clause or source.Eight rulebooks and the properties each one has: law, third-party audit, GFSI recognition, hazard analysis, management review, laboratory competenceWhat each rulebook is21 CFR Part 111Required by U.S. law21 CFR Part 117Required by U.S. lawFood-safety hazard analysisISO 9001:2026Third-party certificate or accreditationInternal audit and management reviewISO 22000:2018Third-party certificate or accreditationFood-safety hazard analysisInternal audit and management reviewFSSC 22000 v6 / v7Third-party certificate or accreditationGFSI-recognized schemeFood-safety hazard analysisInternal audit and management reviewSQF Edition 10Third-party certificate or accreditationGFSI-recognized schemeFood-safety hazard analysisInternal audit and management reviewISO/IEC 17025:2017Third-party certificate or accreditationInternal audit and management reviewLaboratory competence standardICH Q8(R2), Q9(R1), Q10Internal audit and management review
21 CFR 111.1, 117.5(e), 117.130 (eCFR, Oct 22, 2026); ISO 9001, 22000, 17025 pages; FSSC 22000 and UKAS bulletin (v7 published May 7, 2026); SQFI Dietary Supplement Manufacturing code, Edition 10; GFSI recognised programmes; ICH Q10 §4.1.

A plant making both bulk extracts and finished supplements would answer to Part 117 and Part 111 at once; certificates add evidence, not legal compliance.

Explanation, details and sources
RulebookKindChecked byEdition in force, Oct 24, 2026Does not cover
21 CFR Part 111Regulation (final)FDA investigatorseCFR current to Oct 22, 2026; final rule 72 FR 34752 (2007)Dietary-ingredient-only operations whose customers further process the ingredient (FDA SECG); drug manufacturing
21 CFR Part 117Regulation (final)FDA investigatorseCFR current to Oct 22, 2026; final rule 80 FR 55908 (2015)Subparts C and G do not apply to supplement operations that comply with Part 111 (§ 117.5(e))
ISO 9001:2026Voluntary standardAccredited certification bodies (ISO does not certify)Edition 6, published Sep 16, 2026; replaced ISO 9001:2015Food-safety hazard analysis; laboratory competence
ISO 22000:2018Voluntary standardCertification bodies; certification is optionalEdition 2; confirmed 2023; a revision (ISO/DIS 22000) is under developmentGFSI recognition on its own; laboratory competence
FSSC 22000Certification schemeLicensed certification bodiesVersion 6 (mandatory since Apr 1, 2024); Version 7 published May 7, 2026, all audits to v7 from May 1, 2027 (UKAS)U.S. legal compliance
SQFCertification schemeSQF certification bodiesEdition 10 released March 2026; audits anticipated from Jan 1, 2027 (SGS); code "Food Safety Code: Dietary Supplement Manufacturing" (FSC 31)U.S. legal compliance
ISO/IEC 17025:2017Voluntary standardAccreditation bodies (ILAC MRA signatories accredit testing labs to it)Edition 3; confirmed 2023Manufacturing GMP; product release
ICH Q8(R2), Q9(R1), Q10Drug guidanceDrug regulators; no authority over supplementsQ8(R2) Aug 2009; Q9(R1) Jan 18, 2023; Q10 Jun 4, 2008Dietary supplements as a legal requirement

Parts 111 and 117 require specifications, verification and records, not a particular statistical method. The only statistical tool Part 111 names is a "sound statistical sampling plan" for choosing which finished batches to test (§§ 111.75(c), 111.80(c)); Part 117 names none. The statistics below are one disciplined way to meet these rules.

Inspection data

Specifications and production records drew 57% of FDA's 1,938 Part 111 citations in fiscal 2025

Each Part 111 subpart's share of the rule against its share of the citationsGovernment data
For each of the 16 subparts of 21 CFR Part 111, its share of the 84 sections compared with its share of the 1,938 citations in FDA's fiscal 2025 Form 483 data: Subpart E, specifications, holds 14% of the sections and drew 39% of the citations; Subparts E, H and I together hold 19% of the sections and drew 57% of the citationsShare of Part 111 by subpart: 84 sections (eCFR) versus 1,938 citations (FDA, fiscal 2025)Share of the 84 sectionsShare of the 1,938 citations0%10%20%30%40%E Production and process control system (specifications)Subpart E, Production and process control system (specifications): 12 of 84 sections (14.3%)Subpart E, Production and process control system (specifications): 759 of 1,938 citations (39.2%)39.2% (759)F Quality controlSubpart F, Quality control: 11 of 84 sections (13.1%)Subpart F, Quality control: 216 of 1,938 citations (11.1%)11.1% (216)H Master manufacturing recordSubpart H, Master manufacturing record: 2 of 84 sections (2.4%)Subpart H, Master manufacturing record: 188 of 1,938 citations (9.7%)9.7% (188)I Batch production recordSubpart I, Batch production record: 2 of 84 sections (2.4%)Subpart I, Batch production record: 163 of 1,938 citations (8.4%)8.4% (163)J Laboratory operationsSubpart J, Laboratory operations: 5 of 84 sections (6.0%)Subpart J, Laboratory operations: 77 of 1,938 citations (4.0%)4.0% (77)D Equipment and utensilsSubpart D, Equipment and utensils: 4 of 84 sections (4.8%)Subpart D, Equipment and utensils: 75 of 1,938 citations (3.9%)3.9% (75)M Holding and distributingSubpart M, Holding and distributing: 6 of 84 sections (7.1%)Subpart M, Holding and distributing: 72 of 1,938 citations (3.7%)3.7% (72)C Physical plant and groundsSubpart C, Physical plant and grounds: 4 of 84 sections (4.8%)Subpart C, Physical plant and grounds: 67 of 1,938 citations (3.5%)3.5% (67)O Product complaintsSubpart O, Product complaints: 3 of 84 sections (3.6%)Subpart O, Product complaints: 66 of 1,938 citations (3.4%)3.4% (66)N Returned dietary supplementsSubpart N, Returned dietary supplements: 7 of 84 sections (8.3%)Subpart N, Returned dietary supplements: 65 of 1,938 citations (3.4%)3.4% (65)B PersonnelSubpart B, Personnel: 5 of 84 sections (6.0%)Subpart B, Personnel: 53 of 1,938 citations (2.7%)2.7% (53)K Manufacturing operationsSubpart K, Manufacturing operations: 6 of 84 sections (7.1%)Subpart K, Manufacturing operations: 49 of 1,938 citations (2.5%)2.5% (49)G Components, packaging and labelsSubpart G, Components, packaging and labels: 6 of 84 sections (7.1%)Subpart G, Components, packaging and labels: 43 of 1,938 citations (2.2%)2.2% (43)L Packaging and labeling operationsSubpart L, Packaging and labeling operations: 6 of 84 sections (7.1%)Subpart L, Packaging and labeling operations: 37 of 1,938 citations (1.9%)1.9% (37)P Records and recordkeepingSubpart P, Records and recordkeeping: 2 of 84 sections (2.4%)Subpart P, Records and recordkeeping: 8 of 1,938 citations (0.4%)0.4% (8)A General provisionsSubpart A, General provisions: 3 of 84 sections (3.6%)Subpart A, General provisions: 0 of 1,938 citations (0.0%)0.0% (0)Citations: inspections ending Oct 1, 2024 to Sep 30, 2025, electronic-tool Form 483s only. A citation is an inspector's observation, not a finding of harm.Part 111 subparts: share of 84 sections versus share of 1,938 fiscal 2025 citations; Subpart E (specifications) leadsSections versus citations, by subpartsectionscitations (FY2025)E Production and process control system (specifications)39%F Quality control11%H Master manufacturing record10%I Batch production record8%J Laboratory operations4%D Equipment and utensils4%M Holding and distributing4%C Physical plant and grounds3%O Product complaints3%N Returned dietary supplements3%B Personnel3%K Manufacturing operations3%G Components, packaging and labels2%L Packaging and labeling operations2%P Records and recordkeeping0%A General provisions0%FDA Form 483 data, fiscal 2025; eCFR section counts.
FDA, Inspection observations FY2025 (Foods sheet), downloaded Oct 24, 2026; eCFR 21 CFR Part 111 structure, Oct 22, 2026. Grouping by subpart computed for this page (src/modules/qual_six/compute/p111.py).
Data table: sections and citations by subpart
SubpartTitle (eCFR)SectionsShare of 84CitationsShare of 1,938Citation types
ERequirement to Establish a Production and Process Control System1214.3%75939.2%33
FProduction and Process Control System: Requirements for Quality Control1113.1%21611.1%41
HProduction and Process Control System: Requirements for the Master Manufacturing Record22.4%1889.7%5
IProduction and Process Control System: Requirements for the Batch Production Record22.4%1638.4%5
JProduction and Process Control System: Requirements for Laboratory Operations56.0%774.0%10
DEquipment and Utensils44.8%753.9%13
MHolding and Distributing67.1%723.7%7
CPhysical Plant and Grounds44.8%673.5%19
OProduct Complaints33.6%663.4%7
NReturned Dietary Supplements78.3%653.4%4
BPersonnel56.0%532.7%8
KProduction and Process Control System: Requirements for Manufacturing Operations67.1%492.5%9
GProduction and Process Control System: Requirements for Components, Packaging, and Labels and for Product That You Receive for Packaging or Labeling as a Dietary Supplement67.1%432.2%17
LProduction and Process Control System: Requirements for Packaging and Labeling Operations67.1%371.9%9
PRecords and Recordkeeping22.4%80.4%2
AGeneral Provisions33.6%00.0%0

Subpart E holds 14% of Part 111's sections and drew 39% of the citations; writing measurable specifications comes before any statistics.

Explanation, details and sources

Five years of the same data, by subpart and section, are on Quality system; a market view is on Competitive landscape. Record, audit-trail and traceability controls, the other half of the records problem, are on Digital lab.

DMAIC

DMAIC orders the work: define what matters, prove the measurement, then improve and hold the gain

Define, Measure, Analyze, Improve, Control: the tool for each questionSchematic
DMAIC roadmap: Define (SIPOC, CTQ tree), Measure (gauge R&R, baseline capability), Analyze (Pareto, fishbone, screening DOE, FMEA), Improve (factorial DOE, confirmation runs), Control (SPC with run rules, capability review); tools marked for this page or the operational excellence libraryDefineWhat matters to thecustomer?MeasureCan we trust the numbers?AnalyzeWhat drives the variation?ImproveWhich settings fix it?ControlDoes the gain hold?SIPOC mapthis pageCTQ tree from 111.70this pageProject charteroperational excellenceGauge R&R (MSA)this pageBaseline capabilitythis pageValue stream mapoperational excellencePareto and fishboneoperational excellenceScreening DOEthis pageFMEAthis pageFactorial DOEthis pageConfirmation runsthis pageGap analysisoperational excellenceSPC with run rulesthis pageCapability reviewthis pageOEE trackingoperational excellenceSolid boxes: worked on this page with published data or labeled simulations. Dashed boxes: in the operational excellence library.DMAIC roadmap with the tools for each phaseDefineWhat matters to the customer?SIPOC mapthis pageCTQ tree from 111.70this pageProject charteroperational excellenceMeasureCan we trust the numbers?Gauge R&R (MSA)this pageBaseline capabilitythis pageValue stream mapoperational excellenceAnalyzeWhat drives the variation?Pareto and fishboneoperational excellenceScreening DOEthis pageFMEAthis pageImproveWhich settings fix it?Factorial DOEthis pageConfirmation runsthis pageGap analysisoperational excellenceControlDoes the gain hold?SPC with run rulesthis pageCapability reviewthis pageOEE trackingoperational excellence
ISO 13053-1:2011 (DMAIC methodology) and ISO 13053-2:2011 (tools and techniques), both confirmed 2022; Montgomery 2019.
SIPOC map of a spray-dried botanical extractIllustrative
SIPOC map of a spray-dried botanical extract: suppliers, inputs, six process steps from receipt to quality-control release, outputs and customersS · SuppliersGrowers and wildcollectorsIngredient brokersSolvent and carriersuppliersUtilities: steam, water,powerI · InputsDried plant material, one lotEthanol and purified waterCarrier, e.g. maltodextrinSpecification and masterrecordP · ProcessReceive, quarantine,identity testMillExtractFilter and concentrateSpray dryBlend, pack, QC releaseO · OutputsStandardized dry extractlotCertificate of analysisBatch production recordC · CustomersSupplement manufacturers(Part 111)Food manufacturers (Part117)Auditors and FDAinvestigatorsIllustrative map of a typical extract process; not an EUTECNIQ process, supplier list or customer list.SIPOC map of a spray-dried botanical extractS · Suppliers• Growers and wild collectors• Ingredient brokers• Solvent and carrier suppliers• Utilities: steam, water, powerI · Inputs• Dried plant material, one lot• Ethanol and purified water• Carrier, e.g. maltodextrin• Specification and master recordP · Process1. Receive, quarantine, identity test2. Mill3. Extract4. Filter and concentrate5. Spray dry6. Blend, pack, QC releaseO · Outputs• Standardized dry extract lot• Certificate of analysis• Batch production recordC · Customers• Supplement manufacturers (Part 111)• Food manufacturers (Part 117)• Auditors and FDA investigatorsIllustrative; not an EUTECNIQ process.
SIPOC (suppliers, inputs, process, outputs, customers): ASQ, "SIPOC diagram". Example process is generic.

The operational excellence library works DMAIC end to end on one example; this page supplies the statistics each phase needs.

Define

A critical-to-quality tree turns "what the label says" into ten measurable characteristics

From customer need to the five specification categories of 21 CFR 111.70(e)Illustrative
Critical-to-quality tree: the need 'every lot is what the label says' splits into the five specification categories of 21 CFR 111.70(e): identity, purity, strength, composition and limits on contamination; each becomes two measurable characteristics, either variables judged by capability indices or attributes judged by defect ratesCustomer need21 CFR 111.70(e) categoryCritical-to-quality characteristic (example)Data type and metricEvery lot is what thelabel saysIdentityRight plant, right partBotanical identity confirmed by a fit-for-purposemethodAttributepass or fail: DPMONo known adulterant species detectedAttributepass or fail: DPMOPurityOnly what belongs thereForeign matter within limitVariablecapability: Cp, CpkResidual solvent within limitVariablecapability: Cp, CpkStrengthEnough of what mattersMarker content within specificationVariablecapability: Cp, CpkLot-to-lot marker variationVariablecapability: Cp, CpkCompositionSame make-up every lotChromatographic fingerprint matches the referenceAttributepass or fail: DPMOWater content and particle size in rangeVariablecapability: Cp, CpkLimits on contaminationNothing harmfulLead, arsenic, cadmium, mercury below limitsVariablecapability: Cp, CpkNamed pathogens absentAttributepass or fail: DPMOBranch names are the specification categories of 21 CFR 111.70(e). Characteristics are typical examples, not EUTECNIQ specifications.Critical-to-quality tree built on the five 21 CFR 111.70(e) specification categoriesEvery lot is what the label saysCustomer needIdentityRight plant, right part• Botanical identity confirmed by a fit-for-purpose method(attribute)• No known adulterant species detected (attribute)PurityOnly what belongs there• Foreign matter within limit (variable)• Residual solvent within limit (variable)StrengthEnough of what matters• Marker content within specification (variable)• Lot-to-lot marker variation (variable)CompositionSame make-up every lot• Chromatographic fingerprint matches the reference(attribute)• Water content and particle size in range (variable)Limits on contaminationNothing harmful• Lead, arsenic, cadmium, mercury below limits (variable)• Named pathogens absent (attribute)
21 CFR 111.70(e): specifications for identity, purity, strength and composition, and limits on contamination (eCFR, Oct 22, 2026). Test methods: USP, ICH and COA.

Variables earn capability indices; pass-or-fail attributes earn defect rates. Either way, the specification limit comes first.

Measure

A gauge R&R study splits observed variation into the parts and the measurement system

Where the variance goes in a crossed gauge R&R studySchematic with standard equations
Variance decomposition in a crossed gauge R&R study: total observed variance equals part-to-part variance plus measurement-system variance; measurement-system variance equals repeatability plus reproducibility; reproducibility equals operator plus operator-by-part interaction; each estimated from ANOVA mean squaresTotal observed variance σ²total​what the data showPart-to-part σ²P​(MSP​ − MSPO​) / (o·r)Measurement system σ²GRR​repeatability + reproducibilityRepeatability σ²E​MSE​: same operator, same partReproducibilityoperator σ²O​ = (MSO​ − MSPO​) / (p·r)interaction σ²PO​ = (MSPO​ − MSE​) / r%GRR = 100 · σGRR​ / σtotal​ndc = 1.41 · σP​ / σGRR​, truncatedp parts × o operators × r trials (MS: ANOVA mean square). A negativeestimate is reported as zero.
Expected mean squares as printed by SAS PROC VARCOMP (METHOD=GRR); Burdick, Borror and Montgomery 2003; ndc formula: Minitab, methods and formulas.
Operators included (published study)
%GRR of study variation19.0%
%Contribution of GRR3.60%
%Tolerance (6σGRR)20.1%
Distinct categories (ndc)7
Repeatability share of GRR variance28.3%
Interaction p-value5.1 × 10⁻⁷
AIAG MSA 4th ed. guideline for %GRRmay be acceptable, depending on the application

Measurements by part and operator, and the variance componentsPublished data
Data table: the 90 published measurements (°C/W)
PartOp 1 t1Op 1 t2Op 1 t3Op 2 t1Op 2 t2Op 2 t3Op 3 t1Op 3 t2Op 3 t3
1373837414140414241
2424143424242434243
3303131313131293028
4424342434343424242
5283029293029312929
6424243454545444645
7252627282830292727
8404040434242434341
9252525272928262626
10353434353534353435
ANOVA at the current settings
SourceDFSSMSF
Parts93,935.96437.33162.27
Operators239.2719.637.28
Parts × operators1848.512.705.27
Repeatability (error)6030.670.51
Total894,054.40
Data: Houf RE, Berman DB. IEEE Trans CHMT 1988;11(4):516–520, as listed in SAS/STAT 14.1 User's Guide, PROC VARCOMP Example 121.2 (specification 18–58 °C/W). Guidelines: AIAG MSA 4th ed. (2010), as quoted by Minitab.
Method, assumptions and limits
What it calculates
A crossed two-way random-effects ANOVA gauge study: variance components for parts, operators, the part-by-operator interaction and repeatability; %GRR of study variation, %Contribution, %Tolerance and the number of distinct categories. The what-if mode computes the same metrics directly from standard deviations you enter.
Equations
σ²E = MSE; σ²PO = (MSPO − MSE)/r; σ²O = (MSO − MSPO)/(p·r); σ²P = (MSP − MSPO)/(o·r); negative estimates are set to zero. σ²GRR = σ²E + σ²O + σ²PO. %GRR = 100·σGRR/σtotal; %Contribution = 100·σ²GRR/σ²total; %Tolerance = 100·6σGRR/(USL − LSL); ndc = 1.41·σP/σGRR, truncated (minimum 1). When the interaction p-value exceeds 0.05 (Minitab's default "alpha to remove interaction"), the interaction is pooled into repeatability.
Variables and units
p = 10 parts, o = 1–3 operators, r = 3 trials; thermal performance in °C per watt.
Acceptance guidance
AIAG MSA 4th edition (2010), as quoted by Minitab: %GRR below 10% acceptable; 10–30% acceptable depending on the application, cost of the device, cost of repair and other factors; above 30% not acceptable; ndc should be 5 or more. These are guidelines, not regulatory limits.
Valid range
Balanced crossed designs only. At least two operators must stay selected. What-if inputs are clamped to the slider ranges.
Does not establish
Bias, linearity or stability of the gauge; the adequacy of any EUTECNIQ method; or analytical method validation under ICH Q2(R2) or USP, which is a separate exercise.
References
SAS/STAT 14.1 PROC VARCOMP Example 121.2; Houf and Berman 1988; Burdick, Borror and Montgomery 2003; Minitab support: "Is my measurement system acceptable?", number of distinct categories, default settings.
Verification
Reproduces every sum of squares, mean square and variance component printed by SAS (e.g., Var(part) 48.29259, Var(operator) 0.56461, Var(interaction) 0.72798, Var(error) 0.51111, PTR 0.20145). Independent reference: tests/numerics/ref/qual_quality-six-sigma.py.

In the published study, measurement took 19% of the study variation and ndc is 7: inside AIAG's "may be acceptable" band.

Control

A control chart separates routine variation from a real change

Live X̄ chart of capsule fill weight with run rules: simulated streamSimulated data
Subgroups of 5 capsules; mean 500 mg, SD 9 mg; illustrative specification 460–540 mg. Limits from the first 25 subgroups. Press "Shift the mean" and watch the rule numbers appear.Rules: Western Electric (1956) zone rules 1–4 and the six-point trend rule, as listed in NIST/SEMATECH e-Handbook §6.3.2; Nelson 1984. Seeded normal random numbers.
Rule numbers used on the chart
NumberSignal
1One point beyond 3σ of the plotted statistic
2Two of the last three beyond 2σ, same side
3Four of the last five beyond 1σ, same side
4Eight in a row on one side of the centre line
5Six in a row steadily rising or falling
What each run rule looks likeSchematic
Five run rules shown on control-chart zones: 1 one point beyond 3 sigma; 2 two of three beyond 2 sigma on one side; 3 four of five beyond 1 sigma on one side; 4 eight in a row on one side of the centre line; 5 six in a row rising or fallingRule 1: ordinary pointRule 1: ordinary pointRule 1: ordinary pointRule 1: ordinary pointRule 1: ordinary pointRule 1: part of the signal1One point beyond 3σ+3σ+2σ+1σCL−1σ−2σ−3σRule 2: ordinary pointRule 2: ordinary pointRule 2: ordinary pointRule 2: part of the signalRule 2: ordinary pointRule 2: part of the signal2Two of three beyond 2σ,same sideRule 3: ordinary pointRule 3: part of the signalRule 3: part of the signalRule 3: ordinary pointRule 3: part of the signalRule 3: part of the signal3Four of five beyond 1σ,same sideRule 4: part of the signalRule 4: part of the signalRule 4: part of the signalRule 4: part of the signalRule 4: part of the signalRule 4: part of the signalRule 4: part of the signalRule 4: part of the signal4Eight in a row on onesideRule 5: part of the signalRule 5: part of the signalRule 5: part of the signalRule 5: part of the signalRule 5: part of the signalRule 5: part of the signal5Six in a row rising orfallingRules 1–4: Western Electric zone rules; rule 5: trend rule (both as listed by NIST/SEMATECH). Red points complete the pattern. Schematic.
NIST/SEMATECH e-Handbook of Statistical Methods, §6.3.2 (WECO rules and trend rule).
Run rules detect small shifts sooner and raise false alarmsModel output
Average run length against the size of a sustained mean shift: with no shift, the 3 sigma rule alone gives a false alarm every 370 points on average, adding Western Electric rules 2 to 4 every 92 points and adding the trend rule every 78; for a 1 sigma shift the run rules signal after about 9 points instead of 44125102050100200500Average run length (points, log scale)00.511.522.53Sustained shift of the mean (σ of the plotted statistic)3σ rule only (exact)3σ rule only (exact): 0, 3703σ rule only (exact): 0.25, 2813σ rule only (exact): 0.50, 1553σ rule only (exact): 0.75, 81.23σ rule only (exact): 1, 43.93σ rule only (exact): 1.25, 25.03σ rule only (exact): 1.50, 15.03σ rule only (exact): 2, 6.303σ rule only (exact): 2.50, 3.243σ rule only (exact): 3, 2+ rules 2–4 (simulated)+ rules 2–4 (simulated): 0, 91.7+ rules 2–4 (simulated): 0.25, 57.5+ rules 2–4 (simulated): 0.50, 27.5+ rules 2–4 (simulated): 0.75, 14.7+ rules 2–4 (simulated): 1, 9.29+ rules 2–4 (simulated): 1.25, 6.47+ rules 2–4 (simulated): 1.50, 4.89+ rules 2–4 (simulated): 2, 3.12+ rules 2–4 (simulated): 2.50, 2.20+ rules 2–4 (simulated): 3, 1.67+ rules 2–5 (simulated)+ rules 2–5 (simulated): 0, 78.3+ rules 2–5 (simulated): 0.25, 52.0+ rules 2–5 (simulated): 0.50, 26.6+ rules 2–5 (simulated): 0.75, 14.5+ rules 2–5 (simulated): 1, 9.21+ rules 2–5 (simulated): 1.25, 6.49+ rules 2–5 (simulated): 1.50, 4.85+ rules 2–5 (simulated): 2, 3.15+ rules 2–5 (simulated): 2.50, 2.21+ rules 2–5 (simulated): 3, 1.67With no shift (false alarms)3σ rule only (exact)370 points between false alarms+ rules 2–4 (simulated)92 points between false alarms+ rules 2–5 (simulated)78 points between false alarmsChamp and Woodall (1987) report 91.75 forrules 1–4 with no shift; this simulation gives91.67.
3σ rule: ARL = 1/p (exact, normal model; NIST §6.3.2.1 gives about 371 in control). Run rules: Monte Carlo, 40,000 runs per shift, known parameters (src/modules/qual_six/compute/arl.py). Check: Champ CW, Woodall WH. Technometrics 1987;29(4):393–399 (91.75, quoted by NIST).
Data table: average run length by shift
Shift (σ)3σ rule only+ rules 2–4+ rules 2–5
0370.491.778.3
0.25281.157.552.0
0.5155.227.526.6
0.7581.214.714.5
143.99.39.2
1.2525.06.56.5
1.515.04.94.8
26.33.13.1
2.53.22.22.2
32.01.71.7

Run rules catch a 1σ shift after about 9 points instead of 44, at the price of a false alarm every 92 points instead of 370.

Capability

Cp and Cpk together fix the expected defect rate; the sigma level adds a 1.5σ convention

Normal process, two-sided specificationppm = 106[Φ(−3Cpk) + Φ(−3(2Cp − Cpk))]
Expected outside specification1,350 ppm
Beyond the nearer limit1,350 ppm
Zbench (σ)3.00
Sigma level, 1.5σ convention4.50
Observed Cp with measurement error1.33
Observed Cpk with measurement error1.00

The capability plane: lines of equal defect rate, and the process they describeNormal-model calculation
Reference values (NIST §6.1.6, centered process)
Cp = CpkUSL − LSLRejects (NIST)This calculator
1.006σ0.27%2,700 ppm
1.338σ64 ppm63 ppm (Cp = 4/3)
1.6610σ0.6 ppm0.57 ppm (Cp = 5/3)
2.0012σ2 ppb0.002 ppm
NIST/SEMATECH e-Handbook §6.1.6; Montgomery 2019; 1.5σ shift: Harry and Lawson 1992, a convention questioned by Coskun and Ialongo 2020; Zbench from the total tail area.
Method, assumptions and limits
What it calculates
For a normal process with a two-sided specification, the expected fraction outside the limits from Cp and Cpk, the benchmark Z, the sigma level under the 1.5σ convention, and the indices that would be observed if measurement error adds to process variation.
Equations
The nearer limit lies 3Cpk standard deviations from the mean and the farther limit 3(2Cp − Cpk). ppm = 106[Φ(−3Cpk) + Φ(−3(2Cp − Cpk))]. Zbench = Φ−1(1 − p). Sigma level (convention) = Zbench + 1.5. With σ2observed = σ2process + σ2measurement, observed Cp = Cp/√(1 + g2), g = σm/σp; Cpk scales the same way when the gauge is unbiased.
Valid range
0.5 ≤ Cp ≤ 2.5; Cpk is held at or below Cp (a larger value is impossible). Normality and statistical control are assumed; skewed data (for example, contaminant results near a detection limit) need other methods.
The 1.5σ convention
Six Sigma tables add 1.5σ to the long-term Z so that "6σ" corresponds to 3.4 defects per million. It is a convention from Motorola's practice, not a law of nature; EUTECNIQ would report measured within- and between-lot variation instead.
Does not establish
The capability of any real process, the stability of a process, or its shelf life. Capability from real data, with confidence intervals, is in the operational excellence library.
Verification
Reproduces the NIST table of rejects against Cp; independent reference: tests/numerics/ref/qual_quality-six-sigma.py.

A centered Cpk of 1.33 means about 63 ppm outside specification (NIST: 64 ppm); measurement error lowers the observed index.

With the spread unchanged (Cp 1.33), moving the mean 1σ toward a limit raises the expected rate from 63 to 1,350 ppmNormal-model calculation
Two normal distributions inside the same two-sided specification, eight standard deviations wide (Cp 1.33). Centered, the process puts 63.3 parts per million outside the limits. Moved one standard deviation toward the upper limit (Cpk 1.00), it puts 1,350 parts per million outside, almost all beyond the nearer limit. Computed from the normal distribution; a mathematical illustration, not process data.
Montgomery, Introduction to Statistical Quality Control, 8th ed. (2019), ch. 8; NIST/SEMATECH e-Handbook §6.1.6; 1.5σ convention, Harry & Lawson 1992. Mathematical illustration, not process data. Generated illustration, EUTECNIQ. Full-size SVG
Improve

A two-level factorial ranks seven effects from eight runs

Model in coded units (−1, +1)ŷ = b0 + Σ bixi + Σ bijxixj + b123x1x2x3
Terms in the model
Residual SD (ohms)0.304
Residual degrees of freedom5
Best predicted cornerX1 +, X2 −
Predicted impedance there (ohms)4.64

Cube of the eight runs and the ranked coefficientsPublished data (NIST)
Data table: NIST eddy current probe study (23 full factorial)
Run (standard order)X1 turns (90 / 180)X2 distance (0.38 / 1.14)X3 gauge (40 / 48)Impedance (ohms)
1−−−1.70
2+−−4.57
3−+−0.55
4++−3.39
5−−+1.51
6+−+4.59
7−++0.67
8+++4.29
Coefficients (NIST §5.6.1.5); an effect, high minus low, is twice the coefficient
TermCoefficient
Mean2.65875
X11.55125
X2−0.43375
X30.10625
X1·X20.06375
X1·X30.12375
X2·X30.14875
X1·X2·X30.07125
NIST/SEMATECH e-Handbook of Statistical Methods, §5.6.1 (eddy current probe sensitivity case study): data, coefficients and residual standard deviations.
Method, assumptions and limits
What it calculates
Least-squares coefficients of the 23 full factorial (orthogonal, so each coefficient is the same whichever terms are kept), predictions at the eight corners, and the residual standard deviation of the chosen model.
Equations
bt = (1/8) Σ xt,i yi with x = ±1; residual SD = √(Σ(y − ŷ)2/(8 − 1 − k)) for k terms.
Why this dataset
It is a public, fully documented two-level factorial with published coefficients, so every number can be checked. The method transfers directly to extraction or drying factors (for example solvent ratio, temperature, time); this page does not claim results for any botanical process.
Valid range
Predictions inside the cube only; a two-level design cannot detect curvature, which needs centre points or a response-surface design.
Verification
Matches NIST's coefficients and its residual standard deviations for each nested model (1.74106, 0.57272, 0.30429, 0.26737, 0.23341, 0.19121, 0.18031 ohms). Independent reference: tests/numerics/ref/qual_quality-six-sigma.py.

Two main effects carry the study: adding X1 and X2 cuts the residual SD from 1.74 to 0.30 ohms (NIST).

Explanation, details and sources

A factorial study at laboratory scale finds which factors matter; carrying the chosen settings to pilot and commercial scale, and validating the process there, is covered on Scale-up and tech transfer.

Analyze

FMEA ranks failure modes before they happen; the 2019 AIAG-VDA handbook replaced the RPN with action priority

Seven steps of a failure mode and effects analysisSchematic
The seven-step FMEA of the 2019 AIAG and VDA handbook, from planning and preparation to results documentation; the handbook's Action Priority tables replace the risk priority numberPlanning andpreparationscope, teamStructure analysisprocess stepsFunction analysisrequirementsFailure analysismode, effect, causeRisk analysisS, O, D, priorityOptimizationactions, ownersResultsdocumentationreportRisk priority number (older practice)RPN = S × O × D on 1–10 ordinal scales. Equal products can hide verydifferent risks: S10·O1·D1 and S1·O10·D1 both give 10.Action priority (AIAG & VDA, 2019)Tables assign High, Medium or Low priority to each combination of S, O andD; the handbook introduced them to replace the RPN.Steps from the AIAG and VDA FMEA Handbook announcement (June 3, 2019). The table values are in the handbook and are not reproduced here.
AIAG, "AIAG and VDA release new automotive FMEA handbook," June 3, 2019; ICH Q9(R1) (2023) for risk-management formality.

A worked FMEA with its risk map is in the operational excellence library.

See the quality system these tools would serve

Programs, release decisions and design-space controls, each on its own page.