Graphical analysis in DMAIC
Graphical tools are used throughout Measure and Analyze to understand the distribution and behavior of the output variable Y before running formal statistical tests. The exam tests not only how to read each chart but which chart answers which question.
Chart selection guide
| Chart | Question answered | When to use |
|---|---|---|
| Histogram | What is the shape of the distribution? Is it normal, skewed, bimodal? | First look at any continuous variable; check for normality before capability analysis |
| Box plot (box-and-whisker) | Where is the median, how wide is the spread, are there outliers? | Comparing the same Y across multiple groups (shifts, machines, operators) |
| Run chart / time-series plot | Is the process stable over time? Are there trends, shifts, or cycles? | Before drawing control limits; check for non-random patterns in Measure |
| Scatter plot (XY plot) | Is there a relationship between X and Y? | Before regression; explore potential causes in Analyze |
| Multi-vari chart | Which category of variation (positional, cyclical, temporal) is largest? | Early Analyze to direct investigation; see Multi-vari analysis → |
| Probability plot | Does the data follow a specified distribution? | Normality check before capability or hypothesis tests; look for S-curves or steps |
Box plot anatomy
The box plot encodes five statistics visually:
- Bottom whisker: extends to the smallest data point that is within Q1 − 1.5×IQR (the minimum, if there are no low outliers)
- Bottom edge of box: first quartile (Q1, 25th percentile)
- Line inside box: median (Q2, 50th percentile)
- Top edge of box: third quartile (Q3, 75th percentile)
- Top whisker: extends to the largest data point that is within Q3 + 1.5×IQR (the maximum, if there are no high outliers); points beyond either fence are plotted individually as outliers
A standard box plot does not show the mean (some software adds a mean symbol). If the exam asks you to compare means across groups, you need a means comparison test (t-test, ANOVA) after the box plot.
Run chart patterns
A run chart uses visual rules (not control limits) to flag non-random behavior. The point counts below are common rules of thumb; thresholds vary by source (for example, some healthcare run-chart rules use 6 points for a shift and 5 for a trend). Common patterns:
- Trend: 6+ consecutive points rising or falling → process is drifting
- Run: 8+ consecutive points on the same side of the median → process shifted
- Oscillation: alternating up-down-up-down → over-adjustment or two alternating streams
Common exam traps
- A histogram with a bimodal shape usually means two populations are mixed — different shifts, raw material lots, or machines. Split the data and analyze separately before calculating capability.
- Scatter plot correlation ≠ causation. A strong scatter-plot correlation is a hypothesis, not proof. Formal regression analysis quantifies the relationship; a DOE confirms causality.
- Run chart vs control chart. A run chart needs no control limits, so it is a quick first look and works with limited data. It does not replace a control chart for judging statistical control; control limits are normally set once about 20–25 subgroups are available, and limits calculated from data that contain special causes are inflated.
Try 5 free CSSBB practice questions on graphical analysis tools.
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