5.2 Classic Quality Tools

5.2 Classic Quality Tools

In the 1960s, Kaoru Ishikawa formalized the 7 Basic Tools of Quality Control (7 Basic QC Tools). Ishikawa posited that 95% of process quality problems could be solved using these seven fundamental visual and quantitative techniques. Every ASQ Certified Quality Engineer must master the construction, interpretation, and deployment of each tool.

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1. Process Flowchart

A Process Flowchart is a graphical representation of the sequential steps, decisions, inputs, and outputs of a process. It establishes a baseline understanding of how a process actually operates versus how it was designed to operate.

• Standard Symbols:
  • Oval (Terminator): Start or stop boundary.
  • Rectangle (Process Step): Task or action performed.
  • Diamond (Decision Point): Question requiring a Yes/No branch.
  • Parallelogram (Input/Output): Data or raw material entry/exit.
• CQE Application: Flowcharts reveal process bottlenecks, unnecessary inspection loops, redundant handling, and non-value-added activities during initial project scoping.

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2. Check Sheet

A Check Sheet is a structured manual data-gathering form tailored for real-time data collection at the point of activity. It ensures standardized data collection and minimizes recording bias.

• Types of Check Sheets:
  • Defect Tally Sheet: Counts occurrence frequency across pre-identified defect categories.
  • Defect Location Map (Measles Chart): Visual diagram of a physical component where inspectors mark defect locations (e.g., paint blemishes on an auto body panel).
  • Process Parameter Log: Tracks routine machine settings or operational readings over time.
• CQE Application: Serves as the primary data collection tool to feed histograms, Pareto charts, and control charts.

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3. Pareto Chart

A Pareto Chart is a specialized dual-axis bar chart that ranks defect causes in descending order of frequency or financial impact. It operationalizes Vilfredo Pareto's 80/20 Rule, popularized in quality by Joseph M. Juran as separating the "vital few" causes from the "useful many."

  Frequency (Bar)                                Cumulative % (Line)
    100 +--------------------------------------+ 100%
        | [XXXX]                               | 80%
     75 | [XXXX]  [YYYY]                       |
     50 | [XXXX]  [YYYY]  [ZZZZ]               | 50%
     25 | [XXXX]  [YYYY]  [ZZZZ]  [AAAA]       |
      0 +---+-------+-------+-------+----------+ 0%
          Burr   Cracks  Solder   Scratch
          (50)    (30)    (12)      (8)

Pareto Construction Step-by-Step

1. Categorize defect data collected from check sheets.
2. Rank defect categories in descending order by count or monetary cost.
3. Calculate individual percentages and cumulative percentages: $\text{Cumulative \%}_k = \frac{\sum_{i=1}^{k} \text{Count}_i}{\text{Total Count}} \times 100\%$
4. Plot defect categories on the horizontal axis, absolute frequencies on the primary left vertical axis, and cumulative percentage line on the secondary right vertical axis.

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4. Fishbone (Ishikawa / Cause-and-Effect) Diagram

The Fishbone Diagram visually structures potential root causes contributing to a specific quality problem (effect). The main problem statement is placed in the "head" of the fish, while major cause categories form the primary bones.

The 6 Ms Framework for Manufacturing

• Manpower (People): Operator training, fatigue, skill level, ergonomics.
• Machine (Equipment): Tool wear, calibration, spindle runout, maintenance.
• Material: Raw material variation, lot-to-lot inconsistencies, shelf life.
• Method (Process): Inadequate work instructions, standard SOP clarity, feed rates.
• Measurement: Gage accuracy, operator readout error, thermal expansion of gages.
• Milieu / Mother Nature (Environment): Ambient temperature, humidity, vibration, lighting.

(Note: Service environments frequently utilize the 4 Ps: Policies, Procedures, People, Plant).
By systematically applying 5-Why Analysis along each branch, engineers trace back to the ultimate root cause.

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5. Histogram

A Histogram is a bar graph representing the frequency distribution of continuous quantitative data (e.g., shaft diameters, tensile strength). It groups data into adjacent, non-overlapping intervals (bins).

Bin Selection Rules

To avoid over-smoothing or excessive noise, the recommended number of bins ($k$) for sample size $n$ can be estimated using Sturges' Rule or the square root rule:

$k = \sqrt{n} \quad \text{or} \quad k = 1 + 3.322 \log_{10}(n)$ $\text{Bin Width} = \frac{\text{Maximum Value} - \text{Minimum Value}}{k}$

Distribution Morphologies

• Normal (Bell-shaped): Symmetric, single peak; typical of natural common cause variation.
• Skewed Right (Positive): Tail extends to the right; common in cycle times and zero-bound variables.
• Bimodal: Two distinct peaks; indicates data mixed from two separate machines, shifts, or suppliers.
• Truncated / Cut-off: Heartbeat pattern cut off abruptly; indicates 100% sorting or screening inspection has removed non-conforming parts.

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6. Scatter Diagram (Correlation Plot)

A Scatter Diagram plots paired bivariate continuous data ($(X_i, Y_i)$) on a Cartesian grid to evaluate the strength and direction of the relationship between an independent variable ($X$) and a dependent variable ($Y$).

• Interpretation:
  • Positive Linear Correlation: As $X$ increases, $Y$ increases ($r \approx +1.0$).
  • Negative Linear Correlation: As $X$ increases, $Y$ decreases ($r \approx -1.0$).
  • No Correlation: Data points form a diffuse cloud ($r \approx 0.0$).
  • Non-Linear Correlation: Quadratic or exponential curvature requiring non-linear modeling.
• CQE Caution: Correlation does not prove causality. Controlled experiments (DOE) are required to establish true cause-and-effect relationships.

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7. Run Chart and Statistical Control Chart

A Run Chart plots process data sequentially over time relative to a central line (typically the median) to identify trends, shifts, or runs.
A Control Chart upgrades a run chart by adding upper and lower statistical control limits calculated from process data:

$\text{UCL} = \bar{X} + 3\sigma_{\bar{X}}$ $\text{Center Line (CL)} = \bar{X}$ $\text{LCL} = \bar{X} - 3\sigma_{\bar{X}}$

• Purpose: Distinguishes common cause variation (inherent noise in a stable process) from special cause variation (assignable signals like broken tooling or operator error).

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Summary Matrix of the 7 Basic QC Tools