A Statistical Process Control (SPC) chart displaying sample means (X-bar) and ranges (R) plotted over time against control limits. The chart includes a center line representing the process mean, Upper Control Limit (UCL) and Lower Control Limit (LCL) at ±3 sigma, and optional warning limits at ±2 sigma. Out-of-control points are highlighted to signal process instability. This is a fundamental tool in manufacturing quality control and Six Sigma methodology for monitoring process stability.
# anyplot.ai
# spc-xbar-r: Statistical Process Control Chart (X-bar/R)
# Library: makie 0.22.10 | Julia 1.11.9
# Quality: 88/100 | 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 IMPRINT_PALETTE = [
colorant"#009E73", # 1 — brand green (first series)
colorant"#C475FD", # 2 — lavender
colorant"#4467A3", # 3 — blue
colorant"#BD8233", # 4 — ochre
colorant"#AE3030", # 5 — matte red (control limits / out-of-control)
colorant"#2ABCCD", # 6 — cyan
colorant"#954477", # 7 — rose
colorant"#99B314", # 8 — lime
]
const ANYPLOT_AMBER = colorant"#DDCC77" # warning / caution semantic anchor
# SPC control chart constants for subgroup size n = 5
const n_sub = 5
const A2 = 0.577 # X-bar ±3σ factor
const D4 = 2.115 # R-chart UCL factor
const d2 = 2.326 # unbiasing constant (R-bar → σ estimate)
# Data: shaft diameter measurements (mm) — CNC machining, 30 subgroups × 5 parts
const n_samples = 30
measurements = 25.00 .+ 0.04 .* randn(n_samples, n_sub)
# Inject known out-of-control signals at fixed positions
measurements[8, :] = [25.22, 25.24, 25.21, 25.23, 25.25] # X-bar above UCL
measurements[19, :] = [24.74, 24.76, 24.73, 24.78, 24.75] # X-bar below LCL
measurements[25, :] = [24.92, 25.28, 24.90, 25.24, 24.94] # Wide range → R above UCL
# Subgroup statistics
sample_means = [mean(measurements[i, :]) for i in 1:n_samples]
sample_ranges = [maximum(measurements[i, :]) - minimum(measurements[i, :]) for i in 1:n_samples]
x_bar_bar = mean(sample_means)
r_bar = mean(sample_ranges)
# X-bar control limits (±3σ) and warning limits (±2σ)
ucl_xbar = x_bar_bar + A2 * r_bar
lcl_xbar = x_bar_bar - A2 * r_bar
sigma_xbar = r_bar / (d2 * sqrt(n_sub))
uwl_xbar = x_bar_bar + 2.0 * sigma_xbar
lwl_xbar = x_bar_bar - 2.0 * sigma_xbar
# R chart control limits (LCL=0 when D3=0 for n<7; only show UCL and warning)
ucl_r = D4 * r_bar
uwl_r = r_bar + (2.0 / 3.0) * (ucl_r - r_bar)
# Out-of-control point indices
ooc_xbar = findall(m -> m > ucl_xbar || m < lcl_xbar, sample_means)
in_ctrl_xbar = findall(m -> lcl_xbar <= m <= ucl_xbar, sample_means)
ooc_r = findall(r -> r > ucl_r, sample_ranges)
in_ctrl_r = findall(r -> r <= ucl_r, sample_ranges)
xs = collect(1:n_samples)
x_right = Float64(n_samples) + 0.7 # x-position for right-edge limit labels
# Title (length scaling: only shrink if > 67 chars)
title_str = "Shaft Diameter QC · spc-xbar-r · julia · makie · anyplot.ai"
n_chars = length(title_str)
ratio = n_chars > 67 ? 67.0 / n_chars : 1.0
title_fs = max(14, round(Int, 20.0 * ratio))
grid_c = RGBAf(INK.r, INK.g, INK.b, 0.12f0)
# Figure — landscape 3200 × 1800 (resolution × px_per_unit = 2)
fig = Figure(
size = (1600, 900),
fontsize = 14,
backgroundcolor = PAGE_BG,
)
Label(fig[0, 1],
title_str;
fontsize = title_fs,
color = INK,
font = :bold,
halign = :center,
tellwidth = false,
)
# X-bar Axis (top panel — x tick labels hidden; shared via linkxaxes!)
ax_xbar = Axis(fig[1, 1];
backgroundcolor = PAGE_BG,
ylabel = "Sample Mean (mm)",
ylabelcolor = INK,
ylabelsize = 14,
xticklabelsvisible = false,
xticksize = 0,
yticklabelcolor = INK_SOFT,
yticklabelsize = 12,
topspinevisible = false,
rightspinevisible = false,
leftspinecolor = INK_SOFT,
bottomspinecolor = INK_SOFT,
xgridcolor = grid_c,
ygridcolor = grid_c,
xminorgridvisible = false,
yminorgridvisible = false,
xticks = collect(5:5:n_samples),
)
# R Axis (bottom panel — carries x-axis labels)
ax_r = Axis(fig[2, 1];
backgroundcolor = PAGE_BG,
xlabel = "Sample Number",
xlabelcolor = INK,
xlabelsize = 14,
ylabel = "Sample Range (mm)",
ylabelcolor = INK,
ylabelsize = 14,
xticklabelcolor = INK_SOFT,
yticklabelcolor = INK_SOFT,
xticklabelsize = 12,
yticklabelsize = 12,
topspinevisible = false,
rightspinevisible = false,
leftspinecolor = INK_SOFT,
bottomspinecolor = INK_SOFT,
xgridcolor = grid_c,
ygridcolor = grid_c,
xminorgridvisible = false,
yminorgridvisible = false,
xticks = collect(5:5:n_samples),
)
linkxaxes!(ax_xbar, ax_r)
xlims!(ax_xbar, 0.5, n_samples + 4.0)
xlims!(ax_r, 0.5, n_samples + 4.0)
# --- X-bar chart ---
# Warning limits (±2σ) — amber dashed
lines!(ax_xbar, [1.0, Float64(n_samples)], [uwl_xbar, uwl_xbar];
color=ANYPLOT_AMBER, linewidth=1.4, linestyle=:dash)
lines!(ax_xbar, [1.0, Float64(n_samples)], [lwl_xbar, lwl_xbar];
color=ANYPLOT_AMBER, linewidth=1.4, linestyle=:dash)
# Control limits (±3σ) — red dashed
lines!(ax_xbar, [1.0, Float64(n_samples)], [ucl_xbar, ucl_xbar];
color=IMPRINT_PALETTE[5], linewidth=2.2, linestyle=:dash)
lines!(ax_xbar, [1.0, Float64(n_samples)], [lcl_xbar, lcl_xbar];
color=IMPRINT_PALETTE[5], linewidth=2.2, linestyle=:dash)
# Center line (X̄-bar) — solid ink
lines!(ax_xbar, [1.0, Float64(n_samples)], [x_bar_bar, x_bar_bar];
color=INK, linewidth=1.8)
# Data line and markers
lines!(ax_xbar, xs, sample_means; color=IMPRINT_PALETTE[1], linewidth=2.2)
scatter!(ax_xbar, in_ctrl_xbar, sample_means[in_ctrl_xbar];
color=IMPRINT_PALETTE[1], markersize=10, strokewidth=0)
if !isempty(ooc_xbar)
scatter!(ax_xbar, ooc_xbar, sample_means[ooc_xbar];
color=IMPRINT_PALETTE[5], markersize=14, marker=:diamond,
strokewidth=1, strokecolor=PAGE_BG)
end
# Right-edge limit labels
text!(ax_xbar, x_right, ucl_xbar;
text="UCL", fontsize=11, color=IMPRINT_PALETTE[5], align=(:left, :center))
text!(ax_xbar, x_right, x_bar_bar;
text="X̄", fontsize=11, color=INK, align=(:left, :center))
text!(ax_xbar, x_right, lcl_xbar;
text="LCL", fontsize=11, color=IMPRINT_PALETTE[5], align=(:left, :center))
# --- R chart ---
# Warning limit — amber dashed
lines!(ax_r, [1.0, Float64(n_samples)], [uwl_r, uwl_r];
color=ANYPLOT_AMBER, linewidth=1.4, linestyle=:dash)
# UCL — red dashed
lines!(ax_r, [1.0, Float64(n_samples)], [ucl_r, ucl_r];
color=IMPRINT_PALETTE[5], linewidth=2.2, linestyle=:dash)
# Center line (R̄) — solid ink
lines!(ax_r, [1.0, Float64(n_samples)], [r_bar, r_bar];
color=INK, linewidth=1.8)
# Data line and markers
lines!(ax_r, xs, sample_ranges; color=IMPRINT_PALETTE[1], linewidth=2.2)
scatter!(ax_r, in_ctrl_r, sample_ranges[in_ctrl_r];
color=IMPRINT_PALETTE[1], markersize=10, strokewidth=0)
if !isempty(ooc_r)
scatter!(ax_r, ooc_r, sample_ranges[ooc_r];
color=IMPRINT_PALETTE[5], markersize=14, marker=:diamond,
strokewidth=1, strokecolor=PAGE_BG)
end
# Right-edge limit labels
text!(ax_r, x_right, ucl_r;
text="UCL", fontsize=11, color=IMPRINT_PALETTE[5], align=(:left, :center))
text!(ax_r, x_right, r_bar;
text="R̄", fontsize=11, color=INK, align=(:left, :center))
rowgap!(fig.layout, 1, 16)
save("plot-$(THEME).png", fig; px_per_unit=2)
Part of Statistical Process Control Chart (X-bar/R) on anyplot.ai.