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: highcharts 12.6.0 | JavaScript 22.22.3
// Quality: 92/100 | Created: 2026-06-20
//# anyplot-orientation: landscape
const t = window.ANYPLOT_TOKENS;
// Binomial CDF in log-space PMF for numerical stability
function Pa(n, c, p) {
if (p <= 0) return 1;
if (p >= 1) return 0;
let lnN = 0;
for (let i = 2; i <= n; i++) lnN += Math.log(i);
let lnK = 0, lnNK = lnN, prob = 0;
for (let k = 0; k <= c; k++) {
if (k > 0) { lnK += Math.log(k); lnNK -= Math.log(n - k + 1); }
prob += Math.exp(lnN - lnK - lnNK + k * Math.log(p) + (n - k) * Math.log(1 - p));
}
return Math.min(1, Math.max(0, prob));
}
// --- Sampling plans ----------------------------------------------------------
const plans = [
{ n: 50, c: 1, label: "n=50, c=1" },
{ n: 100, c: 2, label: "n=100, c=2" },
{ n: 150, c: 3, label: "n=150, c=3" },
];
const AQL = 0.01; // Acceptable Quality Level
const LTPD = 0.08; // Lot Tolerance Percent Defective
const N_POINTS = 120;
const X_MAX = 0.15;
const xValues = Array.from({ length: N_POINTS }, (_, i) => i * X_MAX / (N_POINTS - 1));
// OC curves
const ocSeries = plans.map(({ n, c, label }) => ({
name: label,
type: "spline",
data: xValues.map(p => [p, Pa(n, c, p)]),
lineWidth: 2.5,
marker: { enabled: false },
}));
// Crossover points at AQL and LTPD for each plan (where curves meet the reference lines)
const crossoverSeries = plans.map(({ n, c }, i) => ({
type: "scatter",
name: "",
showInLegend: false,
color: t.palette[i],
marker: { symbol: "circle", radius: 5 },
data: [
[AQL, Pa(n, c, AQL)],
[LTPD, Pa(n, c, LTPD)],
],
}));
// --- Chart -------------------------------------------------------------------
Highcharts.chart("container", {
chart: {
backgroundColor: "transparent",
animation: false,
style: { fontFamily: "inherit" },
marginRight: 30,
},
credits: { enabled: false },
colors: t.palette,
title: {
text: "curve-oc · javascript · highcharts · anyplot.ai",
style: { color: t.ink, fontSize: "22px", fontWeight: "600" },
},
xAxis: {
title: {
text: "Fraction Defective (p)",
style: { color: t.inkSoft, fontSize: "16px" },
},
min: 0,
max: X_MAX,
tickAmount: 7,
lineColor: t.inkSoft,
tickColor: t.inkSoft,
gridLineWidth: 0,
labels: {
style: { color: t.inkSoft, fontSize: "14px" },
formatter: function () { return (this.value * 100).toFixed(0) + "%"; },
},
plotBands: [
{
from: AQL,
to: LTPD,
color: "rgba(0, 158, 115, 0.08)",
label: {
text: "Discrimination Zone",
style: { color: t.inkSoft, fontSize: "11px" },
align: "center",
verticalAlign: "bottom",
y: -8,
},
zIndex: 0,
},
],
plotLines: [
{
value: AQL,
color: t.inkSoft,
dashStyle: "Dash",
width: 1.5,
label: {
text: "AQL (1%)",
style: { color: t.inkSoft, fontSize: "13px" },
rotation: 0,
y: -6,
x: 4,
},
zIndex: 3,
},
{
value: LTPD,
color: t.inkSoft,
dashStyle: "Dash",
width: 1.5,
label: {
text: "LTPD (8%)",
style: { color: t.inkSoft, fontSize: "13px" },
rotation: 0,
y: -6,
x: 4,
},
zIndex: 3,
},
],
},
yAxis: {
title: {
text: "Probability of Acceptance",
style: { color: t.inkSoft, fontSize: "16px" },
},
min: 0,
max: 1,
tickAmount: 6,
gridLineColor: t.grid,
lineColor: t.inkSoft,
tickColor: t.inkSoft,
labels: {
style: { color: t.inkSoft, fontSize: "14px" },
formatter: function () { return (this.value * 100).toFixed(0) + "%"; },
},
plotLines: [
{
value: 0.95,
color: t.inkSoft,
dashStyle: "ShortDot",
width: 1,
label: {
text: "α = 5% (producer's risk)",
align: "right",
style: { color: t.inkSoft, fontSize: "13px" },
x: -6,
},
zIndex: 3,
},
{
value: 0.10,
color: t.inkSoft,
dashStyle: "ShortDot",
width: 1,
label: {
text: "β = 10% (consumer's risk)",
align: "right",
style: { color: t.inkSoft, fontSize: "13px" },
x: -6,
},
zIndex: 3,
},
],
},
legend: {
enabled: true,
align: "right",
verticalAlign: "middle",
layout: "vertical",
itemStyle: { color: t.inkSoft, fontSize: "14px", fontWeight: "normal" },
itemHoverStyle: { color: t.ink },
title: {
text: "Sampling Plan",
style: { color: t.inkSoft, fontSize: "12px", fontWeight: "normal" },
},
},
plotOptions: {
series: { animation: false },
spline: {
lineWidth: 2.5,
states: { hover: { lineWidth: 2.5 } },
},
},
series: [...ocSeries, ...crossoverSeries],
});
Part of Operating Characteristic (OC) Curve on anyplot.ai.