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Quality Control (4 Qualities, Statistics, QC 7 Tools, Sampling Inspection, ISO 9001)

Production Management Planning Grade 3 生産管理プランニング (BC検定) · ビジネス・キャリア検定 生産管理プランニング3級 · Written by Tokutei Pass based on the official study texts; not copied verbatim.

1. The 4 Qualities (Required, Design, Manufacturing, Guaranteed Quality), Substitute Characteristics, and PDCA

Product quality is grasped along the flow of corporate activities as the 'Four Qualities': (1) Required Quality demanded by customers and the market; (2) Design Quality (target quality / nerai no hinshitsu) aimed for at the planning and design stage based on those requirements; (3) Manufacturing Quality (quality of conformance / dekibae no hinshitsu) actually produced according to design drawings; and (4) Guaranteed Quality (market quality) assured to customers during usage, including sales and after-sales service.

Furthermore, the inherent quality requirements consumers truly desire—such as easy to use, durable, smooth to write with—are called True Characteristics, but because they cannot be measured directly, they are translated into quantifiable, measurable values like dimensions, hardness, or tensile strength called Substitute Characteristics (quality characteristics).

In shop-floor quality control, the ironclad rules are 'Quality must be built into the process, not inspected in' and 'The next process is the customer (do not accept, do not make, and do not pass on defects),' controlling variation across the 4Ms: Man (operators), Machine (equipment), Material, and Method.

Daily operations maintain quality by running the SDCA cycle (Standardize → Do → Check → Act) following work standards, while further improvements and problem solving run the PDCA cycle (Plan → Do → Check → Act) to spiral quality upward.

1. The 4 Qualities (Required, Design, Manufacturing, Guaranteed Quality), Substitute Characteristics, and PDCA

Key points


  • Flow of the 4 Qualities: (1) Required Quality (market needs) → (2) Design Quality (target quality) → (3) Manufacturing Quality (conformance quality) → (4) Guaranteed Quality (quality at the usage and service stage).

  • True Characteristic = the customer's inherent requirement (e.g., durability) / Substitute Characteristic = quantifiable measured values (tensile strength, dimensions) set to assure the true characteristic.

  • Control variation in the 4Ms (Man, Machine, Material, Method) and rotate SDCA for maintenance and PDCA for improvement to build quality into the process.
WordMeaning
Four Qualities (Required quality, Design quality, Manufacturing quality, Guaranteed quality)
Target quality & Conformance quality, True characteristics & Substitute characteristics
The next process is the customer
PDCA cycle and SDCA cycle

2. Types of Data (Continuous / Discrete) and Basic Statistics (Mean, Median, Range, Variance, Standard Deviation)

Quality data falls into two types. Continuous values measured with instruments—such as length (mm), weight (g), temperature (℃), or time (seconds)—are called Continuous Data (Variables / Keiryouchi), and their distribution primarily follows the Normal Distribution.

In contrast, discrete data counted in whole units (1 piece, 2 pieces) is called Discrete Data (Attributes / Keisuuchi). Within discrete data, the number or proportion of nonconforming (defective) units follows the Binomial Distribution, whereas the number of defects (nonconformities) such as cloth scratches or paint specks follows the Poisson Distribution.

Statistics representing the central location (representative value) of data include the Mean (Average, x-bar), found by dividing the sum of all data by sample size n; the Median, the middle value when data is arranged in ascending order (or average of the two middle values if n is even); and the Mode, the most frequently occurring value.

Meanwhile, statistics representing data dispersion (spread) include the Range (R = Maximum - Minimum); the Sum of Squares of Deviations (S), found by subtracting the mean from each data point, squaring the differences, and summing them; the Unbiased Variance (V = S ÷ (n - 1)), dividing S by degrees of freedom (n - 1); and the Sample Standard Deviation (s = √V), the positive square root of variance.

Key points


  • Continuous Data (length, weight, temperature) → Normal Distribution / Discrete Data (counted quantities) → Number of defective units follows Binomial Distribution; number of defects follows Poisson Distribution.

  • Central tendency: Mean = Sum ÷ n / Median = middle value when sorted in order / Mode = most frequent value.

  • Dispersion measures: Range R = Max - Min / Unbiased Variance V = Sum of Squares S ÷ (n - 1) / Standard Deviation s = √V.

  • Example: 5 measurements (7, 9, 11, 11, 12 mm) → Mean = (7 + 9 + 11 + 11 + 12) ÷ 5 = 10 mm, Median = 11 mm, Mode = 11 mm, Range R = 12 - 7 = 5 mm

  • Example: Same 5 data points (mean 10 mm) → Sum of squares S = (7 - 10)² + (9 - 10)² + (11 - 10)² + (11 - 10)² + (12 - 10)² = 16, Unbiased variance V = 16 ÷ (5 - 1) = 4, Sample standard deviation s = √4 = 2 mm
WordMeaning
Continuous data (Normal distribution) and discrete data (Binomial / Poisson distribution)
Mean, Median, and Mode
Range (R) and Sum of Squares of Deviations (S)
Unbiased Variance (V) and Standard Deviation (s)

3. Characteristics and Selection of Statistical Charts (Radar Chart, Z-Chart, etc.)

To present numerical data visually and clearly, statistical charts are selected according to purpose. Bar Charts are used for comparing magnitude across categories, while Line Charts are used for showing upward or downward trends over time.

To show the breakdown or composition ratio (%) of each item relative to the whole, Pie Charts and Band (Stacked Bar) Charts are suitable; stacking multiple band charts vertically makes year-by-year or plant-by-plant composition changes immediately clear.

A chart that plots multiple evaluation items (e.g., the 6 items P, Q, C, D, S, M or worker multi-skill levels) on axes radiating from a center to display overall balance and weaknesses as a web-like polygon is called a Radar Chart (Spiderweb Chart).

Furthermore, a chart that plots three line graphs of sales or production on a single chart—(1) Monthly total, (2) Cumulative monthly total, and (3) Moving annual total (sum of the most recent 12 months)—forming the letter Z to capture short-term fluctuations and long-term trends simultaneously is called a Z-Chart.

Key points


  • Bar Chart = comparing sizes / Line Chart = time-series trends and changes / Pie & Band Charts = grasping breakdown and composition ratios (%).

  • Radar Chart (Spiderweb Chart) = ideal for comparing overall balance, strengths, and weaknesses across multiple evaluation criteria.

  • Z-Chart = uses 3 lines (Monthly, Cumulative, Moving Annual Total) to grasp long-term trends free of seasonal fluctuations as well as target achievement.
WordMeaning
Bar chart, line chart, pie chart, and band chart
Radar Chart (spiderweb chart)
Z-Chart (monthly, cumulative, and moving annual total)

4. The QC 7 Tools (1) (Pareto Chart, Cause-and-Effect Diagram, Check Sheet, Stratification)

The foundational toolkit for organizing and analyzing shop-floor numerical data is the QC 7 Tools. First, the Pareto Chart combines a bar graph sorting defect items or causes in descending order of frequency or loss amount with a line graph showing the cumulative percentage (%), clarifying which vital priority problem should be tackled first.

Second, the Cause-and-Effect Diagram places the resulting characteristic (such as a defect) at the right end of a central spine and systematically branches the contributing factors (such as the 4Ms) into large, medium, and small bones; because it resembles a fish skeleton, it is also called a Fishbone Chart (Ishikawa Diagram).

Third, a Check Sheet is a pre-formatted table printed with check items so operators can easily record data or verify inspection points without omission (divided into recording check sheets and confirmation/inspection check sheets).

Fourth, Stratification is the practice of dividing collected data into subgroups (strata) sharing common attributes—such as by material supplier, machine number, operator, or day/night shift—rather than lumping all data together, comparing them to uncover the true source of variation (used together with histograms and scatter diagrams).

Key points


  • Pareto Chart = descending bar chart by category + cumulative percentage line chart, used to identify the top-priority improvement theme.

  • Cause-and-Effect Diagram (Fishbone Chart) = systematically organizes cause-and-effect relationships between a result (characteristic) and its causes (4M factors).

  • Stratification = separating data into groups (strata) by machine, material lot, or operator to compare and pinpoint the cause of differences.

  • Example: 100 total defects (1st: dimensional defect 50, 2nd: surface scratch 30, others: 20) → Cumulative percentage of top 2 items on Pareto chart = (50 + 30) ÷ 100 × 100 = 80%
WordMeaning
Pareto Chart (priority orientation and ABC analysis)
Cause-and-Effect Diagram (Fishbone Chart)
Check Sheet (for data recording and for inspection)
Stratification (subgroup comparison)

5. The QC 7 Tools (2) (Histogram Shapes, Scatter Diagram, Control Chart)

Fifth, a Histogram (frequency distribution chart) divides the range of continuous data into intervals (classes) and plots the number of data points (frequency) in each class as vertical bars to examine central location, spread shape, and margin relative to specification limits.

Regarding histogram shapes, besides the normal symmetrical Bell-Shaped (General/Normal) Type, there is the Comb-Shaped (Multimodal Teeth) Type caused when class width is not an integer multiple of the measurement scale, and the Cliff-Like (Truncated) Type sharply cut off on one side when nonconforming items have been screened out.

Additionally, the Plateau Type occurs when multiple lots with slightly different means are mixed; the Isolated Island Type occurs when a small amount of abnormal data or measurement error is mixed in; and the Twin-Peak (Bimodal) Type occurs when outputs from two machines or two material suppliers with different means are mixed (Plateau and Twin-Peak types require Stratification).

Sixth, a Scatter Diagram plots paired variables (e.g., firing temperature x and hardness y) on horizontal and vertical axes to examine their correlation (positive correlation = upward slope to the right, negative correlation = downward slope to the right, or no correlation).

Seventh, a Control Chart evaluates over time whether a process is in a stable state or affected by assignable (special) causes by drawing an Upper Control Limit (UCL) and Lower Control Limit (LCL) at plus and minus 3 standard deviations (±3σ) above and below the Center Line (CL).

On a control chart, a process is judged abnormal not only when a point falls outside the control limits, but also when points inside the limits exhibit a Run (7 to 9 or more consecutive points on one side of the center line), a continuous upward or downward Trend, or Periodicity (cycles).

5. The QC 7 Tools (2) (Histogram Shapes, Scatter Diagram, Control Chart)

Key points


  • Histogram shapes: Cliff-like = 100% screening removal of out-of-spec items / Twin-peak = mixture of 2 machines or materials with different means (needs stratification) / Isolated island = minor inclusion of abnormal data or measurement error.

  • Scatter Diagram = examines correlation between 2 variables (y increases as x increases = positive correlation; y decreases as x increases = negative correlation).

  • Control Chart = draws UCL and LCL at CL ± 3σ; judges the process abnormal if points fall outside limits or show a Run or Trend even within limits.
WordMeaning
Histogram (cliff-like, twin-peak, isolated island, comb-shaped)
Scatter Diagram (positive correlation and negative correlation)
Control Chart (UCL, CL, LCL: 3-sigma method)
Control chart abnormality rules (out-of-limits, Run, Trend)

6. Classification of Inspections and Sampling Inspection (OC Curve, Producer's Risk α, Consumer's Risk β)

Inspection is the act of measuring or testing items and comparing the results against acceptance criteria to judge whether individual items are conforming (good) or nonconforming (defective) or whether a lot is accepted or rejected. By stage, there are receiving, in-process, and final inspections; by method, destructive, non-destructive, and Sensory Inspection using the human five senses.

By sample coverage, inspection is divided into 100% (Total) Inspection and Sampling Inspection. Critical safety parts where even one defect threatens human life or expensive one-off products require 100% Inspection, whereas Destructive Testing (like tensile breaking tests), high-volume cheap screws, and continuous fluids or powders cannot undergo 100% inspection and necessitate Sampling Inspection.

Because sampling inspection examines only random samples drawn from a lot, two types of probabilistic judgment errors are unavoidable. The curve plotting the relationship between a lot's true fraction defective and its probability of acceptance is called the OC Curve (Operating Characteristic Curve).

The Type I error is the probability that a good lot (at Acceptable Quality Level, AQL) happens to yield many defective samples and is mistakenly rejected; this is called Producer's Risk (α: Type I error / hasty error, typically set around 5%).

The Type II error is the probability that a bad lot (at Limiting Quality, LQ, which should be rejected) happens to yield mostly good samples and is mistakenly accepted; this is called Consumer's Risk (β: Type II error / careless error, typically set around 10%).

Key points


  • Destructive tests, high-volume low-cost items, and liquids/powders can only use Sampling Inspection / Life-critical safety components require 100% Inspection.

  • Producer's Risk (α: hasty error) = probability of mistakenly rejecting a good lot, harming the producer.

  • Consumer's Risk (β: careless error) = probability of mistakenly accepting a bad lot, harming the consumer.
WordMeaning
100% inspection and sampling inspection (destructive and sensory inspection)
OC Curve (Operating Characteristic Curve)
Producer's Risk (α: Type I / hasty error)
Consumer's Risk (β: Type II / careless error)

7. Two Types of QC Story (Problem-Solving vs Task-Achieving) and 3 Proof Requirements of the PL Law

The QC Story improvement procedure has two types: the Problem-Solving QC Story, which investigates causes of existing defects or worsened conditions to restore the desired state (Theme selection → Current status → Target setting → Cause analysis → Countermeasures → Effect confirmation → Standardization); and the Task-Achieving QC Story, which aims for new product development or unprecedented ambitious goals (Theme selection → Selecting focal attack points & Target setting → Studying measures → Pursuing a success scenario).

In addressing nonconformities, besides recurrence prevention (corrective action) that removes root causes of overt/existing nonconformities that have already occurred, proactive prevention (preventive action) that predicts and prevents latent/potential nonconformities before they occur is vital. If a product defect causes damage to a consumer's life, body, or property, the law providing victim relief is the Product Liability Act (PL Law).

The PL Law adopts Strict Liability (no-fault / defect liability) regardless of the manufacturer's intent or negligence; when victims claim damages, they need only prove three elements: (1) a Defect existed in the product, (2) Damage occurred, and (3) a Causal Relationship existed between the defect and the damage.

Products covered by the PL Law are manufactured or processed movables (real estate, unprocessed agricultural goods, and standalone software are excluded), and defects are classified into three types: (1) Design Defects, (2) Manufacturing Defects, and (3) Instruction/Warning Defects (inadequate manuals, etc.).

Key points


  • Problem-Solving QC Story = performs cause analysis on existing problems to remove root causes / Task-Achieving QC Story = pursues focal attack points and measures/success scenarios for attractive new goals.

  • Three requirements a victim must prove under the PL Law: (1) Product Defect, (2) Occurred Damage, (3) Causal Relationship between the two (proving manufacturer intent or negligence is NOT required).

  • The PL Law covers manufactured or processed movables, and its 3 defect types are Design Defects, Manufacturing Defects, and Instruction/Warning Defects.
WordMeaning
Problem-Solving QC Story and Task-Achieving QC Story
Product Liability Act (PL Law) and Victim's 3 proof requirements
Overt nonconformity (corrective action) and Latent nonconformity (preventive action)
Design, Manufacturing, and Instruction/Warning Defects

8. FMEA / FTA and ISO 9001 (2015 Edition Emphasis & 7 Quality Management Principles)

Two reliability analysis techniques used to prevent failures and defects at the design and process stages are FMEA and FTA. FMEA (Failure Mode and Effects Analysis) is a Bottom-Up Method that starts from potential failure modes of individual component parts (such as wire breakage or wear) and traces upward to evaluate their impact on the overall system.

In contrast, FTA (Fault Tree Analysis) is a Top-Down Method that starts from an undesirable major accident (the Top Event) and unfolds its causal pathways downward like tree roots using logic symbols (AND gates, OR gates) to identify root causes.

Meanwhile, the international standard family for Quality Management Systems (QMS)—the ISO 9000 Series—consists of ISO 9000 (fundamentals and vocabulary), ISO 9001 (requirements used for third-party certification), and ISO 9004 (guidelines for sustained success). In particular, the current ISO 9001:2015 edition emphasizes understanding the Context of the Organization, Actions to Address Risks and Opportunities, and managing Documented Information (integrating procedures and records).

The 7 Quality Management Principles set forth in the ISO 9000 series are: (1) Customer focus, (2) Leadership, (3) Engagement of people, (4) Process approach, (5) Improvement, (6) Evidence-based decision making, and (7) Relationship management.

Key points


  • FMEA (Failure Mode and Effects Analysis) = Bottom-Up Method building upward from component failures to system-wide effects / FTA (Fault Tree Analysis) = Top-Down Method drilling downward from a Top Event into causes.

  • ISO 9001 = specifies the Requirements of a Quality Management System, grounded in the 7 Principles (Customer focus, Leadership, Process approach, etc.).

  • Key concepts of ISO 9001:2015: Understanding the Context of the Organization, Actions to Address Risks and Opportunities (prevention), and maintaining/retaining Documented Information.
WordMeaning
FMEA (bottom-up) and FTA (top-down)
ISO 9001 (Quality Management System requirements)
Actions to address risks and opportunities, Documented information
7 Quality Management Principles

High-Frequency Exam Points and Memory Aids

In Chapter 5 (Questions 26 to 29), definitions of the 4 Qualities (Required → Design → Manufacturing → Guaranteed) and calculation problems finding the Mean, Median, Range R, and Unbiased Variance V (dividing sum of squares S by n - 1) from 5 data points are exam staples.

For data classification, Continuous Data = Normal Distribution and Discrete Data (defectives = Binomial Distribution, scratches/defects = Poisson Distribution) appear frequently, as do Histogram shapes (cliff-like, twin-peak, comb-shaped) and Control Chart rules (±3σ limits, and Runs or Trends within limits indicating abnormality).

The distinction between Producer's Risk α (hasty error = rejecting a good lot) and Consumer's Risk β (careless error = accepting a bad lot) in sampling inspection, as well as Problem-Solving QC Story (cause analysis) vs Task-Achieving QC Story (selecting attack points and studying measures), are also frequently tested.

Furthermore, master the 3 elements a victim must prove under the PL Law ((1) Defect, (2) Damage, (3) Causal relationship—proving negligence is unnecessary) alongside ISO 9001:2015 keywords (Actions to address risks and opportunities, Documented information).

Key points


  • 4 Qualities (Required → Design → Manufacturing → Guaranteed), Continuous Data (Normal) & Discrete Data (defectives = Binomial, defects = Poisson), Unbiased Variance V = S ÷ (n - 1).

  • Problem-Solving type (cause analysis to remove root cause) vs Task-Achieving type (selecting attack points & pursuing measures); Producer's Risk α (rejecting good lot) vs Consumer's Risk β (accepting bad lot).

  • PL Law's 3 proof requirements = Defect, Damage, Causal relationship (strict no-fault liability); ISO 9001:2015 = Risks and opportunities, Documented information.
WordMeaning
Four Qualities and Unbiased Variance (S ÷ (n - 1))
Problem-Solving and Task-Achieving QC Stories
Producer's Risk α and Consumer's Risk β
3 Proof Requirements of the PL Law and ISO 9001:2015

Quality Control (QC7, Sampling, ISO 9001)

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Official references

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