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: letsplot 4.10.1 | Python 3.13.14
Quality: 91/100 | Updated: 2026-06-20
"""
import os
import numpy as np
import pandas as pd
from lets_plot import *
LetsPlot.setup_html()
# Theme tokens (Imprint palette — theme-adaptive chrome)
THEME = os.getenv("ANYPLOT_THEME", "light")
PAGE_BG = "#FAF8F1" if THEME == "light" else "#1A1A17"
ELEVATED_BG = "#FFFDF6" if THEME == "light" else "#242420"
INK = "#1A1A17" if THEME == "light" else "#F0EFE8"
INK_SOFT = "#4A4A44" if THEME == "light" else "#B8B7B0"
INK_MUTED = "#6B6A63" if THEME == "light" else "#A8A79F"
# Imprint palette — data colors (theme-independent)
DATA_COLOR = "#009E73" # Imprint position 1 — always first series
OOC_COLOR = "#AE3030" # Imprint position 5 — semantic red for out-of-control
# Data - CNC shaft diameter measurements (subgroups of n=5)
np.random.seed(42)
n_samples = 30
target_diameter = 25.0 # mm
process_std = 0.05 # mm
# Generate subgroup measurements
measurements = np.random.normal(target_diameter, process_std, (n_samples, 5))
# Inject mean shifts for X-bar out-of-control points
measurements[7] += 0.15 # sudden upward shift
measurements[18] -= 0.18 # sudden downward shift
measurements[24] += 0.12 # upward drift
# Inject extreme spread for R chart OOC at sample 12 (preserves mean, inflates range)
measurements[11, 0] -= 0.16
measurements[11, 4] += 0.16
sample_ids = np.arange(1, n_samples + 1)
sample_means = measurements.mean(axis=1)
sample_ranges = measurements.max(axis=1) - measurements.min(axis=1)
# Control chart constants for n=5 subgroups
A2 = 0.577
D3 = 0.0
D4 = 2.114
# X-bar chart limits
xbar_bar = sample_means.mean()
r_bar = sample_ranges.mean()
xbar_ucl = xbar_bar + A2 * r_bar
xbar_lcl = xbar_bar - A2 * r_bar
xbar_uwl = xbar_bar + (2 / 3) * A2 * r_bar
xbar_lwl = xbar_bar - (2 / 3) * A2 * r_bar
# R chart limits
r_ucl = D4 * r_bar
r_lcl = D3 * r_bar
r_uwl = r_bar + (2 / 3) * (r_ucl - r_bar)
# Classify in-control vs out-of-control
xbar_ooc = (sample_means > xbar_ucl) | (sample_means < xbar_lcl)
r_ooc = sample_ranges > r_ucl
# DataFrames
df_xbar = pd.DataFrame(
{"sample": sample_ids, "mean": sample_means, "status": np.where(xbar_ooc, "Out of Control", "In Control")}
)
df_r = pd.DataFrame(
{"sample": sample_ids, "range": sample_ranges, "status": np.where(r_ooc, "Out of Control", "In Control")}
)
# Limit line dataframes (each line = 2 rows: start and end sample)
xbar_limits = pd.DataFrame(
{
"sample": np.tile([1, n_samples], 5),
"y": ([xbar_ucl] * 2 + [xbar_lcl] * 2 + [xbar_bar] * 2 + [xbar_uwl] * 2 + [xbar_lwl] * 2),
"line": ["UCL"] * 2 + ["LCL"] * 2 + ["CL"] * 2 + ["UWL"] * 2 + ["LWL"] * 2,
}
)
r_limits = pd.DataFrame(
{
"sample": np.tile([1, n_samples], 4),
"y": [r_ucl] * 2 + [r_lcl] * 2 + [r_bar] * 2 + [r_uwl] * 2,
"line": ["UCL"] * 2 + ["LCL"] * 2 + ["CL"] * 2 + ["UWL"] * 2,
}
)
# Label annotations placed just past last data point (within x-axis range)
xbar_labels = pd.DataFrame(
{"sample": [n_samples + 0.5] * 3, "y": [xbar_ucl, xbar_bar, xbar_lcl], "label": ["UCL", "CL", "LCL"]}
)
r_labels = pd.DataFrame({"sample": [n_samples + 0.5] * 3, "y": [r_ucl, r_bar, r_lcl], "label": ["UCL", "R̄", "LCL"]})
# Theme for top panel (X-bar chart — title here, no x-axis labels)
theme_top = theme(
plot_title=element_text(size=16, color=INK, face="bold"),
axis_title_y=element_text(size=12, color=INK),
axis_text_y=element_text(size=10, color=INK_SOFT),
axis_text_x=element_blank(),
axis_title_x=element_blank(),
panel_grid_major_x=element_blank(),
panel_grid_minor=element_blank(),
panel_grid_major_y=element_line(color=INK_SOFT, size=0.25),
panel_background=element_rect(fill=PAGE_BG, color=PAGE_BG),
plot_background=element_rect(fill=PAGE_BG, color=PAGE_BG),
axis_line_x=element_line(color=INK_SOFT, size=0.6),
axis_line_y=element_line(color=INK_SOFT, size=0.6),
axis_ticks=element_line(color=INK_SOFT, size=0.3),
legend_position="none",
plot_margin=[20, 50, 5, 15],
)
# Theme for bottom panel (R chart — x-axis labels here)
theme_bottom = theme(
axis_title=element_text(size=12, color=INK),
axis_text=element_text(size=10, color=INK_SOFT),
panel_grid_major_x=element_blank(),
panel_grid_minor=element_blank(),
panel_grid_major_y=element_line(color=INK_SOFT, size=0.25),
panel_background=element_rect(fill=PAGE_BG, color=PAGE_BG),
plot_background=element_rect(fill=PAGE_BG, color=PAGE_BG),
axis_line_x=element_line(color=INK_SOFT, size=0.6),
axis_line_y=element_line(color=INK_SOFT, size=0.6),
axis_ticks=element_line(color=INK_SOFT, size=0.3),
legend_position="none",
plot_margin=[5, 50, 20, 15],
)
# X-bar chart
xbar_plot = (
ggplot()
+ geom_line(
data=xbar_limits[xbar_limits["line"].isin(["UWL", "LWL"])],
mapping=aes(x="sample", y="y", group="line"),
linetype="dotted",
color=INK_MUTED,
size=0.8,
)
+ geom_line(
data=xbar_limits[xbar_limits["line"].isin(["UCL", "LCL"])],
mapping=aes(x="sample", y="y", group="line"),
linetype="dashed",
color=INK_SOFT,
size=1.0,
)
+ geom_line(
data=xbar_limits[xbar_limits["line"] == "CL"],
mapping=aes(x="sample", y="y"),
linetype="solid",
color=INK,
size=0.9,
)
+ geom_line(data=df_xbar, mapping=aes(x="sample", y="mean"), color=DATA_COLOR, size=1.5)
+ geom_point(
data=df_xbar[df_xbar["status"] == "In Control"],
mapping=aes(x="sample", y="mean"),
color=DATA_COLOR,
fill=PAGE_BG,
size=5,
shape=21,
stroke=1.5,
)
+ geom_point(
data=df_xbar[df_xbar["status"] == "Out of Control"],
mapping=aes(x="sample", y="mean"),
color=OOC_COLOR,
fill=OOC_COLOR,
size=6,
shape=21,
stroke=1.5,
)
+ geom_text(
data=xbar_labels,
mapping=aes(x="sample", y="y", label="label"),
size=4,
color=INK_SOFT,
fontface="bold",
hjust=0,
)
+ scale_x_continuous(breaks=list(range(1, n_samples + 1, 5)) + [n_samples], limits=[0.5, n_samples + 4.5])
+ scale_y_continuous(expand=[0.12, 0])
+ labs(title="spc-xbar-r · python · letsplot · anyplot.ai", y="X̄ (Sample Mean, mm)", x="")
+ theme_top
+ ggsize(800, 260)
)
# R chart
r_plot = (
ggplot()
+ geom_line(
data=r_limits[r_limits["line"] == "UWL"],
mapping=aes(x="sample", y="y"),
linetype="dotted",
color=INK_MUTED,
size=0.8,
)
+ geom_line(
data=r_limits[r_limits["line"].isin(["UCL", "LCL"])],
mapping=aes(x="sample", y="y", group="line"),
linetype="dashed",
color=INK_SOFT,
size=1.0,
)
+ geom_line(
data=r_limits[r_limits["line"] == "CL"], mapping=aes(x="sample", y="y"), linetype="solid", color=INK, size=0.9
)
+ geom_line(data=df_r, mapping=aes(x="sample", y="range"), color=DATA_COLOR, size=1.5)
+ geom_point(
data=df_r[df_r["status"] == "In Control"],
mapping=aes(x="sample", y="range"),
color=DATA_COLOR,
fill=PAGE_BG,
size=5,
shape=21,
stroke=1.5,
)
+ geom_point(
data=df_r[df_r["status"] == "Out of Control"],
mapping=aes(x="sample", y="range"),
color=OOC_COLOR,
fill=OOC_COLOR,
size=6,
shape=21,
stroke=1.5,
)
+ geom_text(
data=r_labels, mapping=aes(x="sample", y="y", label="label"), size=4, color=INK_SOFT, fontface="bold", hjust=0
)
+ scale_x_continuous(breaks=list(range(1, n_samples + 1, 5)) + [n_samples], limits=[0.5, n_samples + 4.5])
+ scale_y_continuous(expand=[0.15, 0])
+ labs(x="Sample Number", y="R (Sample Range, mm)")
+ theme_bottom
+ ggsize(800, 190)
)
# Add tooltip layers for HTML interactivity (lets-plot distinctive feature)
xbar_interactive = xbar_plot + geom_point(
data=df_xbar,
mapping=aes(x="sample", y="mean"),
size=5,
alpha=0.01,
tooltips=layer_tooltips().line("Sample|@sample").line("X̄|@mean").line("Status|@status").format("mean", ".4f"),
)
r_interactive = r_plot + geom_point(
data=df_r,
mapping=aes(x="sample", y="range"),
size=5,
alpha=0.01,
tooltips=layer_tooltips().line("Sample|@sample").line("Range|@range").line("Status|@status").format("range", ".4f"),
)
# Combine top (X-bar, 260) + bottom (R, 190) = 800×450 logical → 3200×1800 at scale=4
combined = gggrid([xbar_plot, r_plot], ncol=1)
combined_interactive = gggrid([xbar_interactive, r_interactive], ncol=1)
# Save
ggsave(combined, f"plot-{THEME}.png", scale=4, path=".")
ggsave(combined_interactive, f"plot-{THEME}.html", path=".")
Part of Statistical Process Control Chart (X-bar/R) on anyplot.ai.