An Operating Characteristic (OC) curve shows the probability of accepting a lot as a function of the true fraction defective in that lot. It is the primary tool for evaluating and comparing acceptance sampling plans, revealing how well an inspection plan discriminates between good and bad lots. The S-shaped curve highlights producer's risk (rejecting good lots) and consumer's risk (accepting bad lots), making it essential for designing effective quality inspection strategies.
""" anyplot.ai
curve-oc: Operating Characteristic (OC) Curve
Library: plotnine 0.15.7 | Python 3.13.14
Quality: 91/100 | Updated: 2026-06-20
"""
import os
import numpy as np
import pandas as pd
from plotnine import (
aes,
annotate,
element_blank,
element_line,
element_rect,
element_text,
geom_line,
geom_point,
geom_ribbon,
geom_vline,
ggplot,
guide_legend,
guides,
labs,
scale_color_manual,
scale_linetype_manual,
scale_x_continuous,
scale_y_continuous,
theme,
theme_minimal,
)
from scipy.stats import binom
# Theme tokens — Imprint palette
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 = ["#009E73", "#C475FD", "#4467A3", "#BD8233", "#AE3030"]
ZONE_ALPHA = 0.09 if THEME == "light" else 0.15
# Data
fraction_defective = np.linspace(0, 0.15, 200)
sampling_plans = [
{"n": 75, "c": 2, "label": "n=75, c=2"},
{"n": 120, "c": 1, "label": "n=120, c=1"},
{"n": 200, "c": 2, "label": "n=200, c=2"},
]
rows = []
for plan in sampling_plans:
prob_accept = binom.cdf(plan["c"], plan["n"], fraction_defective)
for i, p in enumerate(fraction_defective):
rows.append({"fraction_defective": p, "probability_acceptance": prob_accept[i], "plan": plan["label"]})
df = pd.DataFrame(rows)
plan_order = [p["label"] for p in sampling_plans]
df["plan"] = pd.Categorical(df["plan"], categories=plan_order, ordered=True)
# Discrimination envelope between most lenient (n=75,c=2) and most strict (n=200,c=2)
envelope_df = df.pivot(index="fraction_defective", columns="plan", values="probability_acceptance").reset_index()
envelope = pd.DataFrame(
{
"fraction_defective": envelope_df["fraction_defective"],
"ymin": envelope_df["n=200, c=2"],
"ymax": envelope_df["n=75, c=2"],
}
)
# AQL and LTPD reference points
aql = 0.01
ltpd = 0.08
# Risk metrics for reference plan (n=75, c=2)
plan_ref = sampling_plans[0]
alpha_risk = 1 - binom.cdf(plan_ref["c"], plan_ref["n"], aql)
beta_risk = binom.cdf(plan_ref["c"], plan_ref["n"], ltpd)
risk_points = pd.DataFrame(
[
{"fraction_defective": aql, "probability_acceptance": 1 - alpha_risk},
{"fraction_defective": ltpd, "probability_acceptance": beta_risk},
]
)
colors = {p["label"]: c for p, c in zip(sampling_plans, IMPRINT[:3], strict=False)}
linetypes = {"n=75, c=2": "solid", "n=120, c=1": "dashed", "n=200, c=2": "dashdot"}
# Plot
plot = (
ggplot(df, aes(x="fraction_defective", y="probability_acceptance", color="plan", linetype="plan"))
# Shaded quality zones
+ annotate("rect", xmin=0, xmax=aql, ymin=0, ymax=1.05, fill=IMPRINT[0], alpha=ZONE_ALPHA)
+ annotate("rect", xmin=ltpd, xmax=0.15, ymin=0, ymax=1.05, fill=IMPRINT[4], alpha=ZONE_ALPHA)
# Discrimination envelope ribbon — shows range of plan discrimination power
+ geom_ribbon(
aes(x="fraction_defective", ymin="ymin", ymax="ymax"),
data=envelope,
inherit_aes=False,
fill=INK_MUTED,
alpha=0.06,
)
# AQL / LTPD reference lines
+ geom_vline(xintercept=aql, linetype="dashed", color=INK_SOFT, size=0.5, alpha=0.8)
+ geom_vline(xintercept=ltpd, linetype="dashed", color=INK_SOFT, size=0.5, alpha=0.8)
# OC curves
+ geom_line(size=1.0, alpha=0.9)
# Producer's and consumer's risk markers on reference plan
+ geom_point(
aes(x="fraction_defective", y="probability_acceptance"),
data=risk_points,
inherit_aes=False,
size=3,
color=IMPRINT[0],
fill=PAGE_BG,
stroke=1,
shape="o",
)
# AQL / LTPD axis labels
+ annotate("text", x=aql + 0.002, y=0.05, label="AQL", size=3.5, color=INK_MUTED, fontstyle="italic")
+ annotate("text", x=ltpd + 0.002, y=0.11, label="LTPD", size=3.5, color=INK_MUTED, fontstyle="italic")
# Risk annotations
+ annotate(
"text",
x=aql + 0.012,
y=1 - alpha_risk - 0.07,
label=f"α = {alpha_risk:.2f}",
size=3.2,
color=IMPRINT[0],
fontweight="bold",
)
+ annotate(
"text",
x=ltpd + 0.007,
y=beta_risk + 0.06,
label=f"β = {beta_risk:.2f}",
size=3.2,
color=IMPRINT[0],
fontweight="bold",
)
+ scale_color_manual(values=colors)
+ scale_linetype_manual(values=linetypes)
+ scale_x_continuous(
breaks=np.arange(0, 0.16, 0.02), labels=lambda lst: [f"{v:.0%}" for v in lst], limits=(0, 0.15)
)
+ scale_y_continuous(breaks=np.arange(0, 1.1, 0.2), limits=(0, 1.05))
+ labs(
x="Fraction Defective (p)",
y="Probability of Acceptance P(a)",
title="curve-oc · python · plotnine · anyplot.ai",
color="Sampling Plan",
linetype="Sampling Plan",
)
+ guides(color=guide_legend(override_aes={"size": 4, "alpha": 1}))
+ theme_minimal()
+ theme(
figure_size=(8, 4.5),
text=element_text(size=7, color=INK_SOFT),
axis_title=element_text(size=10, color=INK),
axis_text=element_text(size=8, color=INK_SOFT),
plot_title=element_text(size=12, color=INK),
legend_title=element_text(size=8, color=INK),
legend_text=element_text(size=8, color=INK_SOFT),
legend_position=(0.78, 0.78),
legend_background=element_rect(fill=ELEVATED_BG, color=INK_SOFT),
panel_grid_major_x=element_blank(),
panel_grid_minor=element_blank(),
panel_grid_major_y=element_line(color=INK, size=0.3, alpha=0.15),
axis_line=element_line(color=INK_SOFT, size=0.5),
plot_background=element_rect(fill=PAGE_BG, color=PAGE_BG),
panel_background=element_rect(fill=PAGE_BG),
)
)
# Save
plot.save(f"plot-{THEME}.png", dpi=400, width=8, height=4.5, units="in", verbose=False)
Part of Operating Characteristic (OC) Curve on anyplot.ai.