OPEXSTUDIO
← All lessons and training aids OPEX learning notes / Quality tools

Record defects without changing the denominator

Define the inspected unit and each nonconformity category.. Follow the visual, practise a decision, then check your thinking.

Fictional teaching examples and AI-generated illustrations. Proposed changes and goals are not achieved results. Use the written instructions and check local conditions before applying a method.

Download this exact reviewed edition ↗

Teaching view 1 of 2

Record defects without changing the denominator

A unit-by-category check sheet records six distinct affected covers and eight fault marks among 50 inspected covers. Category tallies reconcile to 3 scratches, 2 burrs, 2 missing labels and 1 other fault. The two labelled measures are 12% nonconforming units and 0.16 faults per inspected cover.
Original OPEX teaching diagram. Follow the steps below, then try the practice question. View full size ↗

A useful check sheet makes the unit of observation visible. One rejected product can contain several distinct nonconformities, so a tally of faults is not automatically a count of failed products. Define each category, the inspection opportunity and the observation window before recording. Pilot the sheet with more than one observer and resolve ambiguous classifications. Keep identifiers or source labels that enable a later investigation without collecting unnecessary personal data. Record the denominator alongside the tally. Only then calculate a rate or compare shifts; a larger count may simply reflect a larger amount inspected.

Follow the method

  1. Unit record / multiple faults allowed
  2. Category tally
  3. 6 / 50 units = 12% nonconforming
  4. 8 / 50 = 0.16 faults per unit

Read the example carefully

50 inspected; 6 nonconforming units; 8 nonconformities.

12% of units are nonconforming.

0.16 nonconformities per unit is a different measure.

Teaching view 2 of 2

Reconcile units and fault marks before reporting a rate

A completed record links six affected covers to eight category marks and distinguishes 12% nonconforming from 0.16 faults per inspected cover.
Original OPEX teaching diagram. Follow the steps below, then try the practice question. View full size ↗

Fictional case: an incoming-inspection team checks 50 covers during one defined receipt window. The core illustration retains six nonconforming units and eight nonconformities. Inspector Arun must produce a record that another inspector can reproduce. The supervisor has called both numbers “rejects”, making the reported rate ambiguous.

Follow the method

  1. Nonconforming units
  2. Nonconformities per unit
  3. Category reconciliation

Read the example carefully

Reconcile against U01’s original observation, correct the duplicate with a traceable amendment, and preserve the legitimate burr entry.

Correcting a duplicate is not deleting an inconvenient result. The source record and amendment explain why the total changes.

Apply the method

Six affected units, eight recorded faults

Record one inspection consistently and reconcile nonconforming units separately from the total number of nonconformities.

Fictional case: an incoming-inspection team checks 50 covers during one defined receipt window. The core illustration retains six nonconforming units and eight nonconformities. Inspector Arun must produce a record that another inspector can reproduce. The supervisor has called both numbers “rejects”, making the reported rate ambiguous.

Role: Incoming inspector and quality record owner

Normal condition

Each inspected cover has one identity; every observed category is recorded once under an agreed definition; total inspected units and affected-unit count remain explicit.

The gap

U01 and U02 each have two different faults. Counting every mark as a different rejected cover would exaggerate the fraction of units affected.

  • This is a complete fictional 50-unit inspection record, not a sampling acceptance plan.
  • Category definitions describe observed conditions; they do not prove process causes.
Supplied case inputs
Unit or populationRecorded condition
U01Scratch and burr
U02Scratch and missing label
U03 / U04Burr / scratch respectively
U05 / U06Missing label / other respectively
Remaining 44 coversNo recorded nonconformity in this inspection
  1. Agree on the observable definitions

    Arun defines the inspected unit as one cover and clarifies the scratch, burr, missing-label and other categories with examples. The team records uncertainty for adjudication instead of guessing a category.

    Why: A neat tally is unreliable when inspectors apply different definitions. A check sheet is a collection form; ticking a procedural checklist is a different use.

    Evidence: The sheet states unit, window, categories and the rule for ambiguous observations.

  2. Pilot the recording method

    Two inspectors independently classify a small set before live collection. They discuss ambiguous examples and revise wording before the receipt window starts.

    Why: The pilot exposes unusable categories or insufficient writing space. Agreement during discussion does not by itself establish a complete measurement-system study.

    Evidence: The released form has a revision and the agreed observation instructions.

  3. Keep unit identity and multiple marks

    Arun enters U01 through U06 once each and retains both categories on U01 and U02. He records the total population inspected, including the 44 with no recorded faults.

    Why: Fault tallies without the inspected population cannot yield a unit rate. Multiple faults on one unit are permitted and must not create duplicate units.

    Evidence: Six distinct affected IDs; eight category marks; fifty inspected IDs accounted for.

  4. Reconcile before calculating

    He sums category counts: scratches 3, burrs 2, missing labels 2 and other 1. He separately counts the six unique affected units.

    Why: The sum of category marks answers how many nonconformities were observed. A distinct-unit count answers how many inspected units were affected.

    Evidence: 3 + 2 + 2 + 1 = 8 faults; six unique nonconforming units.

  5. Publish two labelled measures

    The report states 6/50 = 12% nonconforming units and 8/50 = 0.16 nonconformities per inspected unit. Both retain the window and inspection scope.

    Why: These rates answer different questions. Neither says that 16% of units failed, and neither establishes a process trend from this one window.

    Evidence: A reviewer can trace each numerator and denominator to the same source sheet.

Completed inspection summary
MeasureCalculationInterpretation
Nonconforming units6 ÷ 50 = 12%Fraction of inspected covers with at least one fault
Nonconformities per unit8 ÷ 50 = 0.16All recorded faults divided by inspected covers
Category reconciliation3 + 2 + 2 + 1 = 8Matches the eight unit-level category marks

A scratch is entered twice

A second transcription of U01’s same scratch appears in the summary.

Reconcile against U01’s original observation, correct the duplicate with a traceable amendment, and preserve the legitimate burr entry.

Correcting a duplicate is not deleting an inconvenient result. The source record and amendment explain why the total changes.

Corrected category count refers to one scratch observation on U01, not two.

Reconcile a different receipt

New fictional receipt: 40 covers are inspected. A has scratch+burr, B has scratch, C has missing label, D has burr+missing label. The other 36 have no recorded fault.

Changed practice inputs
Affected IDFaults
AScratch, burr
BScratch
CMissing label
DBurr, missing label

Your task

  1. Calculate nonconforming-unit percentage and nonconformities per inspected unit.
  2. Prepare category totals and prove that every mark is counted.
  3. State how an uninspected cover would affect the denominator.

Prepare your worksheet

  • Inspected population
  • Distinct affected IDs
  • Category tally
  • Two labelled calculations
  • Uncertainty or amendment
Reveal the answer and reasoning

Four distinct affected units out of 40 gives 10%. Six nonconformities out of 40 gives 0.15 per inspected unit.

Scratches, burrs and missing labels each occur twice. Their sum is six. An uninspected cover must not silently enter the inspected denominator; either inspect it under the defined scope or report the actual inspection amount.

Worked answer record
MeasureNumerator / denominatorResult
Nonconforming units4 / 4010%
Nonconformities per unit6 / 400.15
Category totals2 + 2 + 26

Check these interpretations

  • 0.15 faults per unit is not 15% nonconforming units.
  • Counting only problem units loses the inspected denominator.

Check your work

  • Reconcile both counts independently.
  • Retain multiple faults on a unit.
  • Make ambiguous inspection scope visible.

Run a practice session

Materials

  • Blank unit-by-category grid
  • Six fictional unit cards
  • Separate receipt exercise
  1. Define a unit · 5 minutes

    Can one cover contribute two marks?

  2. Demonstrate the tally · 7 minutes

    Keep U01 visible while calculating both numerators.

  3. Reconcile the changed receipt · 9 minutes

    Where does each of the six marks come from?

  4. Debrief · 5 minutes

    What information would a tally-only summary lose?

Debrief

  • Ask learners to explain 10% and 0.15 in ordinary language.
  • Use an ambiguous scratch to discuss definition quality rather than force agreement.

Draw the four affected practice units before doing the arithmetic.

Transfer into the work

Owner: Inspection process owner

Record: Released collection form and reconciled summary

Review: After the pilot and at the next scheduled data review

Evidence: Different reviewers reproduce the counts from the same original records

Correct definitions, training or record capture before comparing rates across windows.

Build on reliable methods

Sources and further reading

  • ASQ: Check sheet ↗

    Define the observed event, collection period and recording fields; pilot the form before repeated use.

    Public primary-source summary; underlying paid standards/forms are not reproduced.
Free learning resources

Take the lesson into your team.

Read the lessons online or use these PDFs to prepare, practise and review with your team. No sign-in needed.

Facilitators and team leads

Facilitator guide

Case objectives, demonstration plans, debriefs, common mistakes and application checks across all 81 workplace cases and method lessons.

Download Facilitator guide PDF · 166 pages · 65.1 MB
Learners and improvement teams

Learner workbook

Printable case worksheets, blank observation records and five calculation exercises; answers are separate.

Download Learner workbook PDF · 169 pages · 10.7 MB
Learners after practice and facilitators

Answer key and coaching notes

Reasoned sample responses, worked calculations and coaching guidance; fictional examples are clearly labelled.

Download Answer key and coaching notes PDF · 105 pages · 8.5 MB
Practitioners and facilitators seeking detailed worked methods

Method and application reference

The native method mechanisms and worked applications for all 68 detailed lessons, in a separate bookmarked portrait reference.

Download Method and application reference PDF · 141 pages · 10.2 MB
Self-study learners and workshop groups

Illustrated systems atlas

Five illustrated system chapters: 15 Flare concept maps and 26 original workplace teaching cards, with links to all 81 supporting cases and method lessons.

Download Illustrated systems atlas PDF · 69 pages · 55.8 MB
Connect the methods

Use the next tool for the next question.

  • A defined inspected unit
  • Agreed event definitions
Explore all chapters and detailed lessons →