Process Capability Plot with Specification Limits — Makie.jl

A process capability plot displays a histogram of measured process data overlaid with a fitted normal distribution curve and vertical lines for specification limits (LSL, USL) and target value. Capability indices (Cp, Cpk) are annotated on the plot to quantify how well the process meets specifications. This is a standard tool in quality engineering and Six Sigma for assessing whether a manufacturing or production process is capable of consistently producing output within tolerance.

Process Capability Plot with Specification Limits rendered with Makie.jl

Julia source (Makie.jl)

# anyplot.ai
# histogram-capability: Process Capability Plot with Specification Limits
# Library: makie 0.22.10 | Julia 1.11.9
# Quality: 87/100 | Created: 2026-06-20

using CairoMakie
using Colors
using Random
using Statistics

Random.seed!(42)

# Theme tokens
const THEME       = get(ENV, "ANYPLOT_THEME", "light")
const PAGE_BG     = THEME == "light" ? colorant"#FAF8F1" : colorant"#1A1A17"
const ELEVATED_BG = THEME == "light" ? colorant"#FFFDF6" : colorant"#242420"
const INK         = THEME == "light" ? colorant"#1A1A17" : colorant"#F0EFE8"
const INK_SOFT    = THEME == "light" ? colorant"#4A4A44" : colorant"#B8B7B0"
const INK_MUTED   = THEME == "light" ? colorant"#6B6A63" : colorant"#A8A79F"

const IMPRINT_PALETTE = [
    colorant"#009E73",
    colorant"#C475FD",
    colorant"#4467A3",
    colorant"#BD8233",
    colorant"#AE3030",
    colorant"#2ABCCD",
    colorant"#954477",
    colorant"#99B314",
]

# Data — shaft diameter measurements (mm), slightly off-center process
const N      = 200
const LSL    = 9.95
const USL    = 10.05
const TARGET = 10.00

measurements = randn(N) .* 0.015 .+ 10.012

mu    = mean(measurements)
sigma = std(measurements)
cp    = (USL - LSL) / (6 * sigma)
cpk   = min((USL - mu) / (3 * sigma), (mu - LSL) / (3 * sigma))

# Normal distribution curve scaled to histogram counts
n_bins           = 20
approx_bin_width = (maximum(measurements) - minimum(measurements)) / n_bins
x_curve          = range(LSL - 0.012, USL + 0.012, length = 400)
pdf_vals         = @. exp(-0.5 * ((x_curve - mu) / sigma)^2) / (sigma * sqrt(2π))
pdf_scaled       = pdf_vals .* N .* approx_bin_width

y_ceil = maximum(pdf_scaled) * 1.4

# Plot
fig = Figure(
    resolution      = (1600, 900),
    fontsize        = 14,
    backgroundcolor = PAGE_BG,
)

ax = Axis(
    fig[1, 1];
    title             = "histogram-capability · julia · makie · anyplot.ai",
    titlesize         = 20,
    titlecolor        = INK,
    xlabel            = "Shaft Diameter (mm)",
    ylabel            = "Count",
    xlabelsize        = 14,
    ylabelsize        = 14,
    xticklabelsize    = 12,
    yticklabelsize    = 12,
    xlabelcolor       = INK,
    ylabelcolor       = INK,
    xticklabelcolor   = INK_SOFT,
    yticklabelcolor   = INK_SOFT,
    xtickcolor        = INK_SOFT,
    ytickcolor        = INK_SOFT,
    backgroundcolor   = PAGE_BG,
    topspinevisible   = false,
    rightspinevisible = false,
    leftspinecolor    = INK_SOFT,
    bottomspinecolor  = INK_SOFT,
    xgridvisible      = false,
    ygridcolor        = RGBAf(INK.r, INK.g, INK.b, 0.12f0),
    yminorgridvisible = false,
    xminorgridvisible = false,
)

# Shaded reject zones outside spec limits (vspan! — Makie-native region primitive)
vspan!(ax, [LSL - 0.015, USL], [LSL, USL + 0.015]; color = (IMPRINT_PALETTE[5], 0.08f0))

# Histogram bars — first Imprint series (brand green)
hist!(ax, measurements;
    bins        = n_bins,
    color       = IMPRINT_PALETTE[1],
    strokecolor = PAGE_BG,
    strokewidth = 1.0,
)

# Normal distribution curve — Imprint blue
lines!(ax, collect(x_curve), pdf_scaled;
    color     = IMPRINT_PALETTE[3],
    linewidth = 2.5,
)

# Specification limit lines — matte red dashed (semantic: spec boundary / error)
vlines!(ax, [LSL, USL];
    color     = IMPRINT_PALETTE[5],
    linewidth = 2.0,
    linestyle = :dash,
)

# Target (nominal) line — ochre dashed
vlines!(ax, [TARGET];
    color     = IMPRINT_PALETTE[4],
    linewidth = 2.0,
    linestyle = :dash,
)

ylims!(ax, 0, y_ceil)
xlims!(ax, LSL - 0.015, USL + 0.015)

# Limit and target labels
label_y = y_ceil * 0.94
text!(ax, LSL + 0.001, label_y;
    text     = "LSL",
    align    = (:left, :top),
    fontsize = 12,
    color    = IMPRINT_PALETTE[5],
)
text!(ax, TARGET + 0.001, label_y;
    text     = "Target",
    align    = (:left, :top),
    fontsize = 12,
    color    = IMPRINT_PALETTE[4],
)
text!(ax, USL - 0.001, label_y;
    text     = "USL",
    align    = (:right, :top),
    fontsize = 12,
    color    = IMPRINT_PALETTE[5],
)

# Capability annotation — upper right, below limit labels
cp_rounded  = round(cp,  digits = 2)
cpk_rounded = round(cpk, digits = 2)
text!(ax, USL - 0.003, y_ceil * 0.72;
    text     = "Cp  = $(cp_rounded)\nCpk = $(cpk_rounded)",
    align    = (:right, :top),
    fontsize = 14,
    color    = INK,
)

# Save
save("plot-$(THEME).png", fig; px_per_unit = 2)

Part of Process Capability Plot with Specification Limits on anyplot.ai.

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