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: plotly 6.8.0 | Python 3.13.14
Quality: 92/100 | Updated: 2026-06-20
"""
import os
import sys
# Prevent self-import: remove this script's directory from sys.path so that
# "import plotly" resolves to the installed package, not this file.
_here = os.path.dirname(os.path.abspath(__file__))
sys.path = [p for p in sys.path if os.path.abspath(p) != _here]
import numpy as np
import plotly.graph_objects as go
from scipy.stats import binom
# Theme
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"
GRID = "rgba(26,26,23,0.15)" if THEME == "light" else "rgba(240,239,232,0.15)"
# Imprint categorical palette
IMPRINT_PALETTE = ["#009E73", "#C475FD", "#4467A3", "#BD8233", "#AE3030", "#2ABCCD", "#954477", "#99B314"]
# Data
fraction_defective = np.linspace(0, 0.20, 200)
sampling_plans = [
{"n": 50, "c": 1, "label": "n=50, c=1", "dash": "solid"},
{"n": 100, "c": 2, "label": "n=100, c=2", "dash": "dash"},
{"n": 150, "c": 3, "label": "n=150, c=3", "dash": "dot"},
]
colors = [IMPRINT_PALETTE[0], IMPRINT_PALETTE[1], IMPRINT_PALETTE[2]] # green, lavender, blue
aql = 0.02
ltpd = 0.08
# Compute acceptance probabilities
oc_curves = {}
for plan in sampling_plans:
prob_accept = binom.cdf(plan["c"], plan["n"], fraction_defective)
oc_curves[plan["label"]] = prob_accept
# Plot
fig = go.Figure()
# OC curves with distinct line styles for redundant encoding
for i, plan in enumerate(sampling_plans):
label = plan["label"]
fig.add_trace(
go.Scatter(
x=fraction_defective,
y=oc_curves[label],
mode="lines",
name=label,
line={"color": colors[i], "width": 3, "dash": plan["dash"]},
hovertemplate=(f"<b>{label}</b><br>Fraction defective: %{{x:.3f}}<br>P(accept): %{{y:.3f}}<extra></extra>"),
)
)
# Risk calculations on the first plan
alpha_plan = sampling_plans[0]
prob_accept_aql = binom.cdf(alpha_plan["c"], alpha_plan["n"], aql)
alpha = 1 - prob_accept_aql
beta = binom.cdf(alpha_plan["c"], alpha_plan["n"], ltpd)
# Producer's risk shading (area between P(accept) and 1.0 near AQL)
p_region_x = fraction_defective[fraction_defective <= aql]
p_region_oc = binom.cdf(alpha_plan["c"], alpha_plan["n"], p_region_x)
fig.add_trace(
go.Scatter(
x=np.concatenate([p_region_x, p_region_x[::-1]]),
y=np.concatenate([p_region_oc, np.ones(len(p_region_x))]),
fill="toself",
fillcolor="rgba(0,158,115,0.15)",
line={"width": 0},
name=f"Producer's risk α = {alpha:.3f}",
hoverinfo="skip",
showlegend=True,
)
)
# Consumer's risk shading (area from 0 to OC curve beyond LTPD)
c_region_x = fraction_defective[fraction_defective >= ltpd]
c_region_oc = binom.cdf(alpha_plan["c"], alpha_plan["n"], c_region_x)
fig.add_trace(
go.Scatter(
x=np.concatenate([c_region_x, c_region_x[::-1]]),
y=np.concatenate([np.zeros(len(c_region_x)), c_region_oc[::-1]]),
fill="toself",
fillcolor="rgba(174,48,48,0.15)",
line={"width": 0},
name=f"Consumer's risk β = {beta:.3f}",
hoverinfo="skip",
showlegend=True,
)
)
# Producer's risk diamond marker at AQL
fig.add_trace(
go.Scatter(
x=[aql],
y=[prob_accept_aql],
mode="markers+text",
marker={"size": 14, "color": colors[0], "symbol": "diamond", "line": {"color": PAGE_BG, "width": 2}},
text=[f"α={alpha:.3f}"],
textposition="bottom right",
textfont={"size": 10, "color": colors[0]},
showlegend=False,
hovertemplate=(
f"<b>Producer's Risk (α)</b><br>"
f"At AQL = {aql}<br>"
f"P(accept) = {prob_accept_aql:.3f}<br>"
f"α = {alpha:.3f}<extra></extra>"
),
)
)
# Consumer's risk diamond marker at LTPD — matte red for semantic "bad lot accepted"
fig.add_trace(
go.Scatter(
x=[ltpd],
y=[beta],
mode="markers+text",
marker={"size": 14, "color": IMPRINT_PALETTE[4], "symbol": "diamond", "line": {"color": PAGE_BG, "width": 2}},
text=[f"β={beta:.3f}"],
textposition="top right",
textfont={"size": 10, "color": IMPRINT_PALETTE[4]},
showlegend=False,
hovertemplate=(f"<b>Consumer's Risk (β)</b><br>At LTPD = {ltpd}<br>P(accept) = {beta:.3f}<extra></extra>"),
)
)
# AQL reference line
fig.add_shape(type="line", x0=aql, x1=aql, y0=0, y1=1, line={"color": INK_MUTED, "width": 1.5, "dash": "dash"})
fig.add_annotation(
x=aql, y=1.05, text=f"<b>AQL={aql}</b>", showarrow=False, font={"size": 10, "color": INK_SOFT}, yref="y"
)
# LTPD reference line
fig.add_shape(type="line", x0=ltpd, x1=ltpd, y0=0, y1=1, line={"color": INK_MUTED, "width": 1.5, "dash": "dash"})
fig.add_annotation(
x=ltpd, y=1.05, text=f"<b>LTPD={ltpd}</b>", showarrow=False, font={"size": 10, "color": INK_SOFT}, yref="y"
)
# Layout
fig.update_layout(
autosize=False,
title={
"text": "curve-oc · python · plotly · anyplot.ai",
"font": {"size": 16, "color": INK, "family": "Arial, Helvetica, sans-serif"},
"x": 0.5,
"y": 0.97,
"xanchor": "center",
},
xaxis={
"title": {"text": "Fraction Defective (p)", "font": {"size": 12, "color": INK}},
"tickfont": {"size": 10, "color": INK_SOFT},
"showgrid": False,
"showline": True,
"linewidth": 1,
"linecolor": INK_SOFT,
"range": [0, 0.20],
"dtick": 0.02,
"tickformat": ".2f",
"spikemode": "across",
"spikethickness": 1,
"spikecolor": INK_MUTED,
"spikedash": "dot",
},
yaxis={
"title": {"text": "Probability of Acceptance", "font": {"size": 12, "color": INK}},
"tickfont": {"size": 10, "color": INK_SOFT},
"showgrid": True,
"gridcolor": GRID,
"gridwidth": 0.5,
"range": [-0.02, 1.12],
"zeroline": False,
"showline": True,
"linewidth": 1,
"linecolor": INK_SOFT,
"dtick": 0.2,
"spikemode": "across",
"spikethickness": 1,
"spikecolor": INK_MUTED,
"spikedash": "dot",
},
legend={
"title": {"text": "Sampling Plans", "font": {"size": 10, "color": INK_SOFT}},
"font": {"size": 10, "color": INK_SOFT},
"x": 0.99,
"y": 0.98,
"xanchor": "right",
"bgcolor": ELEVATED_BG,
"bordercolor": INK_SOFT,
"borderwidth": 1,
},
hovermode="x unified",
paper_bgcolor=PAGE_BG,
plot_bgcolor=PAGE_BG,
margin={"l": 80, "r": 40, "t": 80, "b": 60},
width=800,
height=450,
)
# Save
fig.write_image(f"plot-{THEME}.png", width=800, height=450, scale=4)
fig.write_html(f"plot-{THEME}.html", include_plotlyjs="cdn")
Part of Operating Characteristic (OC) Curve on anyplot.ai.