Probability Plot — Data & Tools

Overview

A probability plot (also called a Normal Probability Plot) shows you several important things at a glance:

Distribution shape: If the data points lie approximately on a straight line, your data is normally distributed. Systematic deviations (S-curves, outliers, kinks) indicate skewness, outliers, or a different distribution.

Location and spread: The median (50% point) tells you the central location, and the slope of the line reflects the spread — a flat line means large spread, a steep line means small spread.

Estimating process capability: You can read off directly what fraction of your data lies inside or outside the specification limits by marking the limits on the x-axis and reading the corresponding percentage from the y-axis.

Spotting outliers and mixed distributions: Individual points far from the line are outliers. A kink in the middle often indicates that two processes are superimposed (e.g. two machines, two shifts).

In short: it is a quick visual tool to check whether your data is "well-behaved" and normally distributed and how your process behaves — before moving on to Cpk calculations or hypothesis tests.

Methodology

A normal probability plot is a graphical method for checking whether a sample is approximately normally distributed. Sorted observations are plotted against the theoretical quantiles of the standard normal distribution. If the points fall close to a straight line, normality is plausible.

Plotting Positions (Blom): For n observations, cumulative probabilities p_i = (i − 3/8) / (n + 1/4) are computed and converted to theoretical z-values via the inverse standard normal CDF.

Probability Axis (Y): The Y-axis shows percentages (1 %, 5 %, 10 %, …, 99 %) placed at the corresponding z-quantile positions — just like classical probability paper.

Reference Line: The dashed line passes through the first and third quartile (Q1/Q3) of the data. Use it as a visual yardstick: points on the line → normal, systematic deviations → different distribution shape.

Groups in the same plot: Optionally add a categorical column as grouping (e.g. shift, machine, batch). Each distinct group value yields its own series with its own Q1/Q3 fit line — letting you compare distribution shape, location and spread of the groups directly in the same plot.

Practical Example

Open the "Probability Plot" module.
Select the column "Hole Depth" as the value column.
The chart appears automatically — compare the points against the reference line.
If the points hug the line, working under the normality assumption is reasonable.

Interpretation

Typical Patterns

Points on the line → normality is plausible.
S-shaped pattern → mild or strong skewness.
Convex (curving up) → right-skewed (positive skew).
Concave (curving down) → left-skewed (negative skew).
Stair-step pattern → discrete or rounded data.
Individual points far off → potential outliers.
Points form multiple straight segments → mixed population (check stratification).

Pitfalls

Examples

This module ships with the following example datasets — load any of them in the app with a single click.

Q-Q plot: comparing two shifts — Project template

Two shifts of 40 measurements each — shift A ≈ N(μ=9.5, σ=1.5), shift B ≈ N(μ=10.8, σ=2.2). The probability plot shows two lines with different location and slope.

Q-Q plot: Weibull lifetimes — Project template

80 Weibull(k=2.5) lifetimes on the normal probability plot — visible curvature in the tails.

Q-Q plot: measurement resolution problem — Project template

80 bolt diameters measured with a gauge that is too coarse (resolution 0.1 mm versus process σ ≈ 0.15 mm). The probability plot shows clearly visible vertical stripes — a classic indicator of insufficient measurement resolution.