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CivOps AI Academy · M09SPC and Inspection: Charts, Run Rules, Capability, Gauges and First Articles
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Chapter 1 · Purpose, scope and standards

Characteristics, plans and the edge of the module

Statistical process control (SPC) means measuring a few parts at set intervals, plotting the result, and reacting when the plot shows the process has changed. This chapter says what the module builds, what it leaves to other modules, the idea of a characteristic and a control plan, and the standards the module is measured against.

20 min13 tables11 capabilities7 governing standards

By the end of this chapter you can

  • Say what the SPC and inspection module replaces and what it leaves to M08 and M10.
  • Define a characteristic and a control plan line, and say what a plan line must state.
  • Name the governing standards and what each one is used for in the module.

What the module does

The module collects characteristic data at the right frequency, charts it in real time with configurable run rules, forces a documented reaction to every signal, computes capability correctly, and manages inspection plans, sampling, gauge studies and first article inspection. It replaces the real-time SPC and inspection tools a business usually pays for. The module specification names Advantive (InfinityQS ProFicient and Enact) [1][2], Minitab Real-Time SPC, WinSPC, SQCpack, 1factory, High QA and DataLyzer.

What those tools sell is not the picture of a chart. It is the discipline behind it: a number is entered once, tied to a lot and an order, judged by rules on every point, and when a rule fires somebody must answer. This module builds that discipline on the platform's shared spine, so parts, machines, people and lots are the same rows every other module uses.

What is in, and what is not

The edge of SPC and inspectionInside: characteristics and control plans, sampling and inspection plans, data capture and control charts, run rules and required reaction, capability and gage R&R studies, and first article inspection. Outside, each with its owner: laboratory samples in M10, the NCR and CAPA workflow in M08, and digital forms in M01, which send readings in. INSIDE SPC AND INSPECTION (M09)Characteristicsand control plansSampling andinspection plansData captureand control chartsRun rules andrequired reactionCapability andgage R&R studiesFirst articleinspection (AS9102)OUTSIDE, WITH ITS OWNERLaboratory samplesowned by M10NCR and CAPA workflowowned by M08Digital formsM01 sends readings in
The edge of SPC and inspection. Inside: characteristics and control plans, sampling and inspection plans, data capture and charts, run rules and required reaction, capability and gage R&R, first article inspection. Outside, each with its owner: laboratory samples (M10), the NCR and CAPA workflow (M08), and digital forms (M01), which send readings in.
  • In: characteristics and control plans; sampling and inspection plans for receiving, in-process, final and first article inspection; data capture by hand, gauge, machine tag or form; control charts for measured and counted data, including EWMA and CUSUM, with Western Electric and Nelson run rules; a required reaction to every signal with assignable cause and corrective action codes, and escalation to an NCR; capability (Cp, Cpk, Pp, Ppk, and non-normal methods); measurement system analysis; and AS9102 first article reports.
  • Out: laboratory sample management (module M10) and the NCR and CAPA workflow (module M08). When a signal needs a nonconformance record, this module escalates and keeps a link; the record itself belongs to M08.

A characteristic is the thing you measure

A characteristic is one measured or counted feature of a part or process: a bore diameter, a seal temperature, a count of scratches. Everything else in the module hangs from it. Each one has a code, a name, a type (variable for a measured number, attribute for a count or a pass-fail), a unit, and for a measured one a nominal value with a lower and an upper specification limit (lsl and usl). A special class marks the ones that matter most: none, cc (critical), sc (significant) or key. The type of gauge, the number of decimals the gauge reads and an optional machine data tag (so the value can arrive by itself) complete the row.

Specification limits say what the customer or the design will accept. They are not control limits. Control limits come from how the process behaves, and chapter 3 keeps the two apart.

A control plan says how each one is watched

A control plan is a header (a plan number, the item, a revision, a phase of prototype, pre-launch or production, and a status of draft, approved or superseded, with an optional link to the FMEA, the risk analysis it came from) and a list of lines in the AIAG format. Each line names the process step, the characteristic, the evaluation method, the sample size, the frequency, the control method and the reaction plan: what the operator does when the measurement is not what it should be. A line with no reaction plan is a chart that nobody has to answer.

From characteristic to violationA control plan has many lines. Each line measures one characteristic. A characteristic is charted by a chart; a chart has many subgroups; a subgroup has many measurements and can open a violation. spc_control_planspc_control_plan_linespc_characteristichas manymeasuresspc_chartcharted byspc_subgrouphas manyspc_measurementhas manyspc_violationcan openThe plan line carries the sample size, frequency, control method and reaction plan.
From characteristic to violation. A control plan has many lines; each line measures one characteristic; a chart watches the characteristic; its subgroups hold measurements and can open a violation.

Eleven capabilities in three tiers

The capability map lists what the module does, and each capability carries a tier. MVP must exist for a small or mid-size plant to cancel the incumbent subscription with confidence. STD is parity with mainstream tools. BIC marks best-in-class differences. MVP and STD are required for the course; BIC is advanced work.

CapabilityWhat it doesTier
Characteristics and control plansA characteristic per item or operation with nominal, limits, special class and gauge type; plan lines with method, sample size, frequency and reaction planMVP
Inspection and sampling plansReceiving, in-process, final and audit inspections; Z1.4 acceptance quality limit (AQL) plans, skip-lot and accept-on-zero (c=0); inspection lots with accept or reject decisionsSTD
Data captureOperator entry with limits feedback; gauge input by USB, serial or Bluetooth; automatic from tags; from M01 forms; timestamped with lot and order contextMVP
Control chartsX-bar R, X-bar S, I-MR, p, np, c, u, EWMA, CUSUM; subgroup management; short-run (target and Z) chartsMVP
Run rulesWestern Electric and Nelson rules, configurable per chart, evaluated on every point in real timeMVP
Required reactionAcknowledgement with assignable cause and corrective action codes; auto-escalation to an NCR or hold; notificationsMVP
Control limit governanceLimits basis (historical, standard or manual); recalculation with approval and an audit trail; never recalculated silentlySTD
CapabilityCp, Cpk (within), Pp, Ppk (overall), expected ppm; normality test and non-normal methods; only on stable processesSTD
Measurement system analysis (MSA)Crossed and nested gage R&R (ANOVA and average-range), %GRR, ndc; bias, linearity, stability; attribute agreement (kappa)STD
First article inspectionAS9102 Forms 1 to 3 with ballooned characteristics and resultsBIC
DashboardsPlant-wide signal board, Cpk heat map, violation response timesSTD

The standards, and what each one is used for

StandardUsed in this module for
AIAG SPC Reference Manual (2nd edition) [5]Chart selection, subgrouping, control limits, capability
AIAG MSA Reference Manual (4th edition) [5]Gage R&R, bias, linearity, stability, attribute studies
ISO 7870-2:2023 [6]Shewhart control charts
ISO 22514 series [6]Process capability and performance
ANSI/ASQ Z1.4 and Z1.9; ISO 2859-1 [6]Attribute and variables acceptance sampling
SAE AS9102C [4]The first article inspection requirement (Forms 1 to 3)
Western Electric Statistical Quality Control Handbook (1956); Nelson (1984)Run rules for non-random patterns (chapter 3)

Knowledge check

What is a characteristic in this module?

Knowledge check

Which of these does the SPC and inspection module leave to another module?

References

  1. Advantive: SPC tools and ProFicient (named in the module specification). https://www.advantive.com/?p=1379
  2. FitGap: InfinityQS ProFicient overview (named in the module specification). https://us.fitgap.com/products/infinityqs-proficient
  3. NIST/SEMATECH e-Handbook of Statistical Methods: What are control charts? (section 6.3.1). https://www.itl.nist.gov/div898/handbook/pmc/section3/pmc31.htm
  4. SAE International: AS9102C, Aerospace First Article Inspection Requirement. https://www.sae.org/standards/content/as9102c/
  5. AIAG: publisher of the SPC and MSA Reference Manuals. https://www.aiag.org/
  6. ISO: the standards catalogue (search for ISO 7870-2, ISO 22514 and ISO 2859-1). https://www.iso.org/

Chapter 2 · The data model and who may do what

Thirteen tables and six roles

How the module stores readings, limits and signals decides what you can ever prove. Thirteen tables hold the plan, the data, the reaction and the studies. Six roles, with rules for two people, keep the record honest. This chapter is the reference for your agent in Sessions 2 and 3.

25 min13 tables6 roles5 soft-link columns

By the end of this chapter you can

  • Name the thirteen spc_ tables, group them, and say what each one holds.
  • Say why readings and limits are typed numbers, and why five columns that point at other modules' tables are plain uuid columns.
  • Name the six roles and the rules that need two different people.

Thirteen tables on the shared spine

Every table starts with the standard columns every platform table has: id, tenant_id, created_at, created_by, updated_at, updated_by, row_version, archived_at and ext. The module has no parts list, machine list, people table or lot table of its own: it points at core_item, core_equipment (machines and gauges), core_person, core_lot, core_uom, core_data_tag, core_reason_code, core_e_signature and the rest of the spine. Its own tables share the prefix spc_.

Thirteen tables in four groupsDefine: characteristic, control plan and control plan line. Plan the inspection: sampling plan, inspection plan and inspection lot. Chart and react: chart, subgroup, measurement and violation. Prove: capability study, MSA study and first article report. DEFINE WHAT TO MEASUREspc_characteristicfeature, limitsspc_control_planplan headerspc_control_plan_linehow, how oftenPLAN THE INSPECTIONspc_sampling_planscheme, AQLspc_inspection_plantype per itemspc_inspection_lotdecisionCHART AND REACTspc_charttype, rules, limitsspc_subgroupstatisticsspc_measurementone readingspc_violationsignal and responsePROVEspc_capability_studyCp, Cpk, Pp, Ppkspc_msa_studygage R&R, biasspc_fai_reportAS9102 forms
Thirteen tables in four groups. Define what to measure (characteristic, control plan, plan line); plan the inspection (sampling plan, inspection plan, inspection lot); chart and react (chart, subgroup, measurement, violation); prove (capability study, MSA study, first article report).

The table below is the full definition: every column the module adds to the standard ones, with its type and whether it is required (marked req). Types are written as in the specification: text, int, num (a decimal number), bool, ts (a timestamp with time zone), date, qty (a quantity), uuid and json; an arrow means a foreign key to that table; in {…} lists the only allowed values.

TableHoldsColumns: type, req = required
spc_characteristicThe measured or counted featurecode text req, unique; item_id → core_item; operation_ref (soft link to mes_operation_definition); name text req; char_type req in {variable, attribute}; uom_id → core_uom; nominal num; lsl num; usl num; special_class req in {none, cc, sc, key}; gauge_type text; data_tag_id → core_data_tag; decimals int
spc_control_planControl plan headerplan_no text req, unique; item_id → core_item req; revision text req; phase req in {prototype, pre_launch, production}; status req in {draft, approved, superseded}; fmea_ref (soft link to qms_fmea)
spc_control_plan_lineOne line of the plan, in the AIAG formatcontrol_plan_id → spc_control_plan req; process_step text req; characteristic_id → spc_characteristic req; evaluation_method text; sample_size int; frequency text; control_method text; reaction_plan text
spc_sampling_planA sampling schemecode text req, unique; scheme req in {fixed, z14_aql, z19, skip_lot, c_zero, hundred_pct}; aql num; inspection_level text; params json
spc_inspection_planInspection plan per item and typeitem_id → core_item req; inspection_type req in {receiving, in_process, final, first_article, audit, source}; sampling_plan_id → spc_sampling_plan; characteristics json; active bool req
spc_inspection_lotOne inspection, with its decisioninspection_plan_id → spc_inspection_plan req; lot_id → core_lot; lot_qty qty; sample_size int; status req in {open, in_progress, decided}; decision req in {pending, accept, reject, conditional}; inspector_id → core_person; decided_at ts; quality_event_ref (soft link to qms_quality_event)
spc_chartChart configuration and current limitscharacteristic_id → spc_characteristic req; equipment_id → core_equipment; chart_type req in {xbar_r, xbar_s, imr, p, np, c, u, ewma, cusum, short_run}; subgroup_size int req; rules json req; ucl num; cl num; lcl num; ucl_r num; lcl_r num; limits_basis req in {historical, standard, manual}; limits_set_at ts; limits_set_by → core_person; limits_approval_signature_id → core_e_signature
spc_subgroupStatistics of one samplechart_id → spc_chart req; seq int req; ts ts req; n int req; mean num; range_val num; stdev num; defects num; defectives num; inspected num; lot_id → core_lot; operation_run_ref (soft link to mes_operation_run)
spc_measurementOne reading or attribute observationcharacteristic_id → spc_characteristic req; subgroup_id → spc_subgroup; inspection_lot_id → spc_inspection_lot; value num; attribute_result in {pass, fail}; defect_count int; measured_at ts req; measured_by → core_person; gauge_equipment_id → core_equipment; source req in {manual, gauge, tag, form, import}
spc_violationA run-rule signal and the required responsechart_id → spc_chart req; subgroup_id → spc_subgroup req; rule_code text req; detected_at ts req; acknowledged_by → core_person; acknowledged_at ts; assignable_cause_code_id → core_reason_code; corrective_action text; escalated_event_ref (soft link to qms_quality_event); status req in {open, acknowledged, closed}
spc_capability_studyCapability over a periodcharacteristic_id → spc_characteristic req; period_start ts req; period_end ts req; n int req; mean num; sigma_within num; sigma_overall num; cp num; cpk num; pp num; ppk num; distribution text; normality_p num; expected_ppm num; stable bool
spc_msa_studyA measurement system analysisstudy_no text req, unique; gauge_equipment_id → core_equipment req; characteristic_id → spc_characteristic; study_type req in {grr_crossed, grr_nested, bias, linearity, stability, attribute_agreement}; method req in {anova, average_range, kappa, other}; operators int; parts int; trials int; data json; pct_grr num; ndc int; result in {acceptable, marginal, unacceptable}; performed_at date
spc_fai_reportAS9102 first article reportfai_no text req, unique; item_id → core_item req; part_revision text; serial_no text; form1 json; form2 json; form3 json req; status req in {draft, complete, approved, rejected}; approved_signature_id → core_e_signature

Typed numbers, and five soft-link columns

Readings, specification limits and control limits are numeric columns, not text and not one JSON blob. A single blob for all readings is a pitfall this course adds to the specification's three: it makes limits, charts and capability impossible to query. The decimals column on the characteristic says how many places the gauge reads, and the server rounds to it.

Five columns are soft links pointing at four tables: plain uuid columns with a comment saying which table they will point to, and no foreign key. They are operation_ref (to the MES module's mes_operation_definition), operation_run_ref (to mes_operation_run), fmea_ref (to qms_fmea) and the two event references quality_event_ref (on spc_inspection_lot) and escalated_event_ref (on spc_violation), both to qms_quality_event. The other modules may not be installed, and a foreign key to a table that does not exist would stop the migration.

Six roles, and rules for two people

The roles are jobs, not names, and each maps to a row in the spine's core_job_role. The operator measures at the machine. The inspector does receiving, in-process, final and first article inspection. The quality engineer owns characteristics, control plans, charts, studies and imports. The quality approver (usually the quality manager) approves control limits, control plans and first article reports. The supervisor answers and closes signals in their own area. The manager reads the board and changes nothing.

Who may do whatA grid of six roles by six actions. Operator and inspector measure and acknowledge. Quality engineer acknowledges, closes, proposes limits and reads the board. Quality approver approves limits and reads the board. Supervisor acknowledges, closes and reads the board. Manager only reads the board. MeasureAcknowledgeClosePropose limitsApprove limitsRead boardOperatorYesYesInspectorYesYesQuality engineerYesYesYesYesQuality approverYesYesSupervisorYesYesYesManagerYesA person never closes what they acknowledged, and never approves limits they proposed.
Who may do what. Operator and inspector measure and acknowledge. The quality engineer acknowledges, closes, proposes limits and reads the board. The quality approver approves limits. The supervisor acknowledges and closes in their own area. The manager only reads.

Row-level security is generated from the Role and Exposure Matrix, so every right a later session needs must be in the matrix first. This module adds rules that involve two different people (a design choice of this course, not a requirement of the specification): the person who acknowledged a violation may not close it; the person who proposed new limits may not approve them; an inspector may not approve their own first article report. Nobody gets delete: a correction is a new row, a new revision or the archived_at column.

Events and screens

DirectionEvents
Publishesspc.violation.detected, spc.violation.closed, spc.inspection_lot.rejected, spc.capability.below_target
Consumesfrm.submission.submitted (a reading from an M01 form); mes.operation_run.started (triggers an in-process inspection); wms.receipt.qc_required (triggers a receiving inspection)

The screens sit on the platform's three surfaces. The operator surface (a phone screen at the machine) shows the characteristic with its limits beside a large number box and a full-width Save button, and queues readings on the device when offline. The supervisor surface lists signals to answer. The manager surface is a board readable from across the room. The quality engineer's plan and chart screens, and the approver's limits screen, are desk screens. The server, not the browser, decides whether a reading is inside its specification limits.

Exercise · Describe one characteristic as rows15 minutes

You need: One real measured feature from the slice you chose in Session 1, its drawing or work instruction, and your AI coding agent

Work on paper or in a text file first; the agent comes in at step 5.

Outcome: A one-page description of a real characteristic and its plan line, with the sample rows your agent produced, checked against the module's table.

Knowledge check

Why is operation_ref on spc_characteristic a plain uuid column and not a foreign key?

Knowledge check

Which rule needs two different people?

References

  1. MetricGate: control charts, Western Electric rules, Cp/Cpk (named in the module specification). https://metricgate.com/blogs/control-charts-process-monitoring/
  2. iFactory: real-time SPC rule engines, Western Electric and Nelson (named in the module specification). https://ifactoryapp.com/quality-control-management/real-time-spc-monitoring-software
  3. NIST/SEMATECH e-Handbook of Statistical Methods: Process or product monitoring and control (chapter 6). https://www.itl.nist.gov/div898/handbook/pmc/pmc.htm
  4. AIAG: publisher of the SPC and MSA Reference Manuals. https://www.aiag.org/

Chapter 3 · From a reading to an answered signal

Charts, run rules and the required reaction

A control chart separates ordinary variation from a change worth acting on. Run rules decide, on every point, which is which. The module's promise is the last step: a signal cannot be closed until a person has recorded what caused it and what was done.

30 min10 chart types8 Nelson rules3 violation statuses

By the end of this chapter you can

  • Choose a chart type for measured and for counted data, and keep control limits apart from specification limits.
  • State the eight Nelson rules, and find signals in a plotted series.
  • Describe the violation workflow, including who may close, and how control limits are governed.

Two kinds of variation, and two kinds of limit

Every process varies. A control chart (invented by Walter Shewhart and standardised for charts in ISO 7870-2 [3]) plots a statistic over time against a centre line and limits set from the process's own behaviour, usually three standard deviations (sigma) either side [1]. A point inside the limits with no pattern is ordinary variation: leave the process alone. A point or pattern outside what ordinary variation would produce is a signal: something changed, and there is a cause to find.

Control limitsSpecification limits
Where they come fromThe process's own dataThe customer or the design
What they answerHas the process changed?Is this part acceptable?
In the moduleucl, cl and lcl on spc_chartlsl and usl on spc_characteristic
Who may change themOnly through an approval with a signatureOnly by a revised specification

A point can be inside specification and out of control, or the reverse. The two answers are separate, and the capture route reports both.

Choosing the chart

Choosing a control chartThree starting points. A measured number: individuals and moving range for one reading at a time, X-bar and R for small subgroups, X-bar and S for larger ones. Units counted pass or fail: np for a constant sample size, p when it varies. Flaws counted on a unit: c for the same area, u when it varies. EWMA and CUSUM catch small steady drifts. What do you have?A measured numberOne reading at a timeI-MRSmall subgroupsX-bar RLarger subgroupsX-bar SUnits: pass or failSample size constantnp chartSample size variesp chartFlaws on a unitSame area or countc chartArea or count variesu chartSmall, steady drifts: add EWMA or CUSUM on the same data.
Choosing a control chart. A measured number: individuals and moving range (I-MR) for one reading at a time, X-bar and R for small subgroups, X-bar and S for larger ones. Units counted as pass or fail: np for a constant sample size, p when it varies. Flaws counted on a unit: c for the same area, u when it varies. EWMA and CUSUM catch small, steady drifts.
chart_typePlotsUse when
imrEach reading and the moving range between neighboursOnly one reading is available at a time (a batch, a daily value)
xbar_rSubgroup mean and rangeA small subgroup is taken at each check
xbar_sSubgroup mean and standard deviationSubgroups are larger
pFraction of units defectivePass-fail units, sample size varies
npNumber of units defectivePass-fail units, sample size constant
cNumber of flawsFlaws counted on a constant area or count
uFlaws per unitArea or count varies
ewmaExponentially weighted moving averageSmall, steady shifts matter
cusumCumulative sum of departures from a targetSmall, steady shifts matter
short_runTarget or Z-scaled valuesMany short runs of different parts on one chart (best in class)

For an X-bar and R chart the limits come from the average range multiplied by a constant that depends on the subgroup size. Those constants are printed in the AIAG SPC Reference Manual and in ISO 7870-2. Type them from the table in your copy, never from memory, and test them: the module's definition of done is that the chart constants and rule detection reproduce a published reference dataset exactly.

Run rules: reading the pattern

Walking a point past the limit is not the only sign of a change. The Western Electric handbook (1956) and Nelson (1984) list patterns that random variation rarely makes [1][2]. The module evaluates them on every point, in real time, and which rules are on is a setting of each chart (the rules column).

Nelson ruleThe patternUsually means
1One point more than 3 sigma from the centre lineA sudden change or an outlier
2Nine points in a row on the same side of the centre lineA shift of the average
3Six points in a row steadily rising or fallingA trend, such as tool wear
4Fourteen points in a row alternating up and downTwo alternating causes, such as two machines or two shifts
5Two of three points in a row more than 2 sigma out on the same sideA shift beginning
6Four of five points in a row more than 1 sigma out on the same sideA smaller shift
7Fifteen points in a row within 1 sigma of the centre line, either sideToo little variation: mixed streams or limits set too wide
8Eight points in a row more than 1 sigma out on either sideTwo streams, or overcontrol
36 readings on an individuals chartThirty-six synthetic readings with centre line 10.00 and limits 9.70 and 10.30, drawn to scale. Point 13 is 10.34, beyond the upper limit (Nelson rule 1). Points 21 to 29 are nine in a row above the centre line (Nelson rule 2). No other rule fires. UCL 10.30+2 sigma+1 sigmaCL 10.00-1 sigma-2 sigmaLCL 9.70Rule 1: point 13 beyond the upper limitRule 2: nine in a row above the centre line, signal at point 2915101520253035
36 readings on an individuals chart. Centre line 10.00, limits 9.70 and 10.30, so one sigma is 0.10; drawn to scale. Point 13 is 10.34, beyond the upper limit (rule 1). Points 21 to 29 are nine in a row above the centre line (rule 2). With all eight rules on, nothing else fires. The data is synthetic, made for the lab.

The required reaction

When a rule fires, the module inserts a spc_violation with the rule code and the time of detection, in the same database transaction as the point, so a point and its violation exist together or not at all. A chart with no approved limits collects points and evaluates nothing.

One violation from signal to closeA point breaks a run rule and an open violation is made. It becomes acknowledged once an assignable cause code and a corrective action are recorded. A different person closes it. A serious one can be escalated to an action item or an NCR in M08. A point breaksa run ruleopendetected_at setacknowledgedcause and actionclosedby someone elseNeeds a cause codeand a corrective actionA different personcloses itEscalate if neededaction item, or NCR in M08Signal response time = minutes from detected_at to acknowledged_at.
One violation from signal to close. A point breaks a run rule and a violation opens. It is acknowledged once an assignable cause code and a corrective action are recorded. A different person closes it. A serious one can be escalated to an action item or an NCR in M08.
  • open: a rule has fired and nobody has answered.
  • acknowledged: a person has recorded an assignable cause code (a coded reason from the quality reason codes, such as tool wear or wrong material) and the corrective action taken. The database refuses an acknowledgement missing either.
  • closed: a different person has reviewed the answer and closed it. The database refuses a close with no cause code and corrective action.

The median minutes from detected_at to acknowledged_at is the signal response time, the first KPI of the module. When a signal needs a hold on a lot or a nonconformance, the supervisor escalates it: an action item is created with a link back, and, where M08 is installed, the id of its quality event is stored in escalated_event_ref.

Control limits are governed

Control limits are part of the controlled process, so changing them needs approval and is audit-trailed. A limit's basis is historical (computed from a stable period), standard or manual. A proposal is made by the quality engineer, approved by a different person, the quality approver, with an e-signature, and the approve route writes the new limits together with limits_set_at, limits_set_by and limits_approval_signature_id. The database refuses any other change to those columns.

Exercise · Find the signals before you code them20 minutes

You need: Graph paper, a spreadsheet or any plotting tool, a ruler, and your AI coding agent

The 36 readings below are the reference data used in Session 4. They are synthetic, made up for the lab, and add up to 360.65; check your copy.

Outcome: A plotted chart with two circled signals, a note that no other rule fires, and a unit test that proves your agent's engine finds the same two.

36 synthetic readings, in order, 12 to a line
10.03 9.88 10.06 10.12 9.95 9.91 10.05 9.86 10.08 9.97 10.13 9.92
10.34 10.08 9.98 9.89 10.07 10.01 10.02 9.90 10.05 10.09 10.03 10.14
10.02 10.06 10.01 10.11 10.04 9.96 9.87 10.10 9.93 9.99 10.08 9.92

Knowledge check

A measured part is in specification but the chart shows nine points in a row above the centre line. What is true?

Knowledge check

Which is true of closing a violation in this module?

Knowledge check

You count defective units in samples that change in size from lot to lot. Which chart fits?

References

  1. MetricGate: control charts, Western Electric rules, Cp/Cpk (named in the module specification). https://metricgate.com/blogs/control-charts-process-monitoring/
  2. iFactory: real-time SPC rule engines, Western Electric and Nelson (named in the module specification). https://ifactoryapp.com/quality-control-management/real-time-spc-monitoring-software
  3. ISO: the standards catalogue (search for ISO 7870-2, Shewhart control charts). https://www.iso.org/
  4. NIST/SEMATECH e-Handbook of Statistical Methods: What are variables control charts? (section 6.3.2). https://www.itl.nist.gov/div898/handbook/pmc/section3/pmc32.htm
  5. ASQ: control chart. https://asq.org/quality-resources/control-chart

Chapter 4 · Proving the process, the gauge and the lot

Capability, gauges, sampling and cut-over

A stable process can still be a poor one, and a good-looking number from a poor gauge means nothing. This chapter covers how capability is computed without the commonest error, how a gauge is judged, how a lot is accepted, what a first article report holds, and how the module is checked before the old tool is retired.

25 min4 indices%GRR bands 10 and 304 KPIs

By the end of this chapter you can

  • State the difference between Cpk and Ppk, and why capability is reported only with a stability flag.
  • Read a gage R&R result against the %GRR and ndc rules.
  • Describe an inspection lot decision, the three AS9102 forms, and the four module KPIs.

Capability: how well could the process meet the specification?

Capability compares the spread of the process with the width of the specification [1]. Four indices are in use. Cp and Cpk use the variation within subgroups (sigma within, estimated from the subgroup ranges or the moving range). Pp and Ppk use the overall variation of all the data (sigma overall). Cp and Pp ignore where the process is centred; Cpk and Ppk punish an off-centre mean.

IndexFormulaSigma used
Cp(usl − lsl) ÷ (6 × sigma within)Within subgroups
Cpkthe smaller of (usl − mean) and (mean − lsl), divided by (3 × sigma within)Within subgroups
Pp(usl − lsl) ÷ (6 × sigma overall)Overall
Ppkthe smaller of (usl − mean) and (mean − lsl), divided by (3 × sigma overall)Overall
Cp and Cpk on a bell curveTwo normal curves with sigma 0.10 between a lower specification limit of 9.70 and an upper limit of 10.30, drawn to scale. Centred on 10.00, Cp and Cpk are both 1.00. Shifted to a mean of 10.05, Cp stays 1.00 and Cpk falls to 0.83. LSL 9.70USL 10.309.609.709.809.9010.0010.1010.2010.3010.40Centred, mean 10.00: Cp 1.00, Cpk 1.00Shifted, mean 10.05: Cp 1.00, Cpk 0.83Both curves: sigma 0.10, so six sigma fills the whole 0.60 specification width.
Cp and Cpk on a bell curve. Sigma 0.10, specification 9.70 to 10.30, drawn to scale. Centred on 10.00, Cp and Cpk are both 1.00. With the mean at 10.05 Cp stays 1.00 and Cpk falls to 0.83: (10.30 − 10.05) ÷ 0.30. The numbers are synthetic.

Do not confuse this picture with the chart in chapter 3. Here 9.70 and 10.30 are a tighter, made-up specification chosen to make the arithmetic easy; in chapter 3 the same numbers were control limits, and the seed characteristic you load in Session 2 has a specification of 9.60 to 10.40. Specification limits come from the drawing; control limits come from the process.

  • Expected ppm: the parts per million expected outside the specification, from the distribution fitted.
  • Normality: the indices above assume a normal distribution. The module stores a normality test result and, when the data is not normal, the distribution or method used (the distribution column).
  • Targets: the specification gives 1.33 as an example Cpk target and 1.67 for special characteristics. Falling below a target publishes spc.capability.below_target.
  • Stable first: capability describes a stable process. A study is saved with stable true only if the rules engine found no signal in its period; otherwise it carries stable false and a flag on the screen.

The gauge first: measurement system analysis

Every reading carries the gauge's own variation. A measurement system analysis (MSA) measures how much, so a capability figure is not an artefact of a poor gauge. The module stores crossed and nested gage R&R studies (by ANOVA, analysis of variance, or the average-range method), bias, linearity, stability, and attribute agreement (by kappa, a measure of agreement beyond chance) [2]. The AIAG manual's usual layout is 10 parts, 3 operators and 3 trials, 90 readings, measured blind in random order.

Reading a gage R&R resultA scale from 0 to 40 percent drawn to scale: under 10 percent is acceptable, 10 to 30 percent is marginal, over 30 percent is not acceptable. A gauge at 12 percent falls in the marginal band. Under 10%10% to 30%: marginalOver 30%0%10%20%30%40%acceptablenot acceptableA gauge at 12% is marginal%GRR is the share of the variation that belongs to the gauge and its operators.ndc, the number of distinct categories the gauge tells apart, should be at least 5.
Reading a gage R&R result. Under 10% is acceptable, 10% to 30% is marginal, over 30% is not acceptable; a gauge at 12% is marginal. ndc, the number of distinct categories, should be at least 5.

%GRR is the share of the variation that belongs to the gauge and its operators. Marginal gauges need a plan (training, a better fixture or another gauge), and capability figures taken with them are marked provisional.

Inspection and sampling: deciding about a lot

Charts watch a process. Inspections decide about a lot. An spc_inspection_plan says which characteristics are checked for an item at a receiving, in-process, final, first article, audit or source inspection, and which sampling plan applies. The sampling schemes are fixed (a stated number), z14_aql and z19 (ANSI/ASQ Z1.4 for attributes and Z1.9 for variables), skip_lot, c_zero (accept only if no defect is found in the sample) and hundred_pct (every piece). The acceptance quality limit (AQL) is the quality level the Z1.4 tables treat as satisfactory. Sample sizes and accept or reject numbers come from the tables in the standard [5], never from memory.

One inspection lotA lot arrives and the inspection plan picks a sampling scheme. A sample is drawn and measured, and the lot is decided: accept, conditional or reject. A rejected lot raises an action item and the event spc.inspection_lot.rejected. A lot arrivescore_lotPlan and schemespc_inspection_planDraw and measurespc_measurementDecidespc_inspection_lotacceptlot releasedconditionalnamed conditionrejectlot heldAction and eventspc.inspection_lot.rejectedScheme: fixed, z14_aql, z19,skip_lot, c_zero or hundred_pct.Sample sizes come from thestandard's tables, not memory.
One inspection lot. A lot arrives, the plan picks a scheme, a sample is drawn and measured, and the lot is decided: accept, conditional or reject. A rejected lot raises an action item and the event spc.inspection_lot.rejected.

First article inspection

A first article inspection (FAI) proves a new or changed part can be made to the drawing. SAE AS9102C [3] defines three forms: Form 1, part number accountability; Form 2, product accountability, covering raw materials, specifications, special processes and functional testing; and Form 3, characteristic accountability, verification and compatibility evaluation, in which each drawing characteristic is numbered (ballooned) and given a result. The module stores the three forms as JSON on spc_fai_report (Form 3 is required), with a status of draft, complete, approved or rejected. The inspector may not approve their own report; the quality approver signs it.

Measuring the module, and cutting over

KPIDefinition
Signal response timeMedian minutes from violation to acknowledgement with cause
Cpk at or above target, coverageCharacteristics meeting the Cpk target (for example 1.33; 1.67 for special) divided by all characteristics
Receiving acceptance rateAccepted inspection lots divided by inspected lots
%GRRGauges with %GRR under 10% are acceptable; 10% to 30% are marginal

To retire the old tool, export its characteristics, specification limits and historical measurements, and reload the history so that limits and capability can be recomputed and compared with the incumbent's own figures. That comparison is the validation check. Imported history is run through the rules engine in report-only mode, so last year's signals appear in a report and not as open violations that page the floor. Run both tools side by side for at least a week, explain every difference, and cancel only after the cut-over works and the final export is stored.

Definition of doneHow it is shown
Chart constants and rule detection reproduce a published reference dataset exactlyA unit test on the reference data
Cp, Cpk, Pp and Ppk match a reference statistics package to 3 decimalsA second tool: a spreadsheet using the manual's formulas, or the free R language
Every violation requires a coded response before closingA query for closed violations with no cause code returns no rows
Exercise · Ask your own data for Cpk and Ppk20 minutes

You need: At least 25 subgroups of one characteristic from your old tool or from the platform, its specification limits, a spreadsheet, and your AI coding agent

Use real history from the slice you chose in Session 1. If you have none yet, use the 36 readings from chapter 3 with limits 9.70 and 10.30, treating each reading as its own subgroup.

Outcome: A table of Cp, Cpk, Pp and Ppk for one real characteristic with its stable flag, confirmed by a second calculation to three decimals, and a note on which sigma the old tool used.

Knowledge check

Which sigma does Cpk use, and which does Ppk use?

Knowledge check

A gauge study returns %GRR of 18%. How is the gauge judged?

Knowledge check

Where do the sample size and accept number for a Z1.4 plan come from?

References

  1. NIST/SEMATECH e-Handbook of Statistical Methods: Process or product monitoring and control (chapter 6, including process capability). https://www.itl.nist.gov/div898/handbook/pmc/pmc.htm
  2. NIST/SEMATECH e-Handbook of Statistical Methods: Measurement process characterization (chapter 2). https://www.itl.nist.gov/div898/handbook/mpc/mpc.htm
  3. SAE International: AS9102C, Aerospace First Article Inspection Requirement. https://www.sae.org/standards/content/as9102c/
  4. AIAG: publisher of the SPC and MSA Reference Manuals. https://www.aiag.org/
  5. ISO: the standards catalogue (search for ISO 22514 and ISO 2859-1). https://www.iso.org/

Chapter 5 · 12 questions · 80% passes

Final assessment

Twelve questions across the element. Score 80% (10 of 12) to pass. Your LMS records your score and each answer; you can review the chapters and try again.

15 min12 questions≈ 15 minutesRetake allowed

Choose one answer for each question, then submit. You will see the right answer and why for every question.

1. Which sigma does Cpk use?
2. A capability study covers a period in which the rules engine found signals with no known cause. How is it saved?
3. Who may close a violation in this module?
4. How may control limits on a chart be changed?
5. Which is Nelson rule 2?
6. On the 36-reading reference data (centre line 10.00, limits 9.70 and 10.30), with all eight Nelson rules on, what fires?
7. A gage R&R study gives %GRR of 22%. How is the gauge judged?
8. You count defective units in samples whose size varies. Which chart do you use?
9. What is the difference between control limits and specification limits?
10. What does the c=0 sampling scheme mean?
11. Which AS9102 form records each numbered (ballooned) characteristic with its result?
12. How is history from the old SPC tool used during migration?