A Weibull probability plot displays failure or lifetime data on Weibull probability paper (logarithmic x-axis for time/cycles, linearized Weibull CDF on y-axis) with a fitted straight line. It is the standard tool in reliability engineering for estimating Weibull distribution parameters (shape and scale), assessing whether data follow a Weibull distribution, and extrapolating failure probabilities. The slope of the fitted line gives the shape parameter (beta), while the characteristic life (eta) is read at the 63.2% failure probability crossing.
// anyplot.ai
// probability-weibull: Weibull Probability Plot for Reliability Analysis
// Library: echarts 5.5.1 | JavaScript 22.22.3
// Quality: 90/100 | Created: 2026-06-07
//# anyplot-orientation: landscape
// anyplot.ai
// probability-weibull: Weibull Probability Plot for Reliability Analysis
// Library: echarts 5.5.1 | JavaScript 22
// Quality: pending | Created: 2026-06-07
const t = window.ANYPLOT_TOKENS;
// --- Data: hydraulic pump service-life study (hours, n=20) ---
// 14 failures, 6 right-censored (still running at inspection end)
// Already sorted ascending by time — required for rank assignment
const observations = [
{ time: 620, fail: true },
{ time: 890, fail: true },
{ time: 1100, fail: false },
{ time: 1340, fail: true },
{ time: 1580, fail: true },
{ time: 1920, fail: false },
{ time: 2200, fail: true },
{ time: 2550, fail: true },
{ time: 2900, fail: false },
{ time: 3300, fail: true },
{ time: 3750, fail: true },
{ time: 4100, fail: true },
{ time: 4600, fail: false },
{ time: 5200, fail: true },
{ time: 5900, fail: true },
{ time: 6700, fail: true },
{ time: 7800, fail: false },
{ time: 9200, fail: true },
{ time: 11000, fail: true },
{ time: 13500, fail: false },
];
const n = observations.length;
// Median rank (i - 0.3) / (n + 0.4) where i = 1-based rank among ALL observations
const failurePoints = [];
const censoredTimes = [];
observations.forEach((obs, idx) => {
const i = idx + 1;
if (obs.fail) {
const F = (i - 0.3) / (n + 0.4);
const yW = Math.log(-Math.log(1 - F));
failurePoints.push({ time: obs.time, F, yW });
} else {
censoredTimes.push(obs.time);
}
});
// Linear regression: log10(time) vs Weibull y → estimates beta (shape) and eta (scale)
const logT = failurePoints.map(p => Math.log10(p.time));
const yVals = failurePoints.map(p => p.yW);
const nF = failurePoints.length;
const mLogT = logT.reduce((a, b) => a + b, 0) / nF;
const mY = yVals.reduce((a, b) => a + b, 0) / nF;
let ssXX = 0, ssXY = 0;
for (let i = 0; i < nF; i++) {
ssXX += (logT[i] - mLogT) ** 2;
ssXY += (logT[i] - mLogT) * (yVals[i] - mY);
}
const beta = ssXY / ssXX; // shape parameter β
const intercept = mY - beta * mLogT;
const eta = Math.pow(10, -intercept / beta); // characteristic life η (hours)
// Fitted line spanning the full x range
const tMin = 350, tMax = 22000;
const fitData = [
[tMin, beta * Math.log10(tMin) + intercept],
[tMax, beta * Math.log10(tMax) + intercept],
];
// Censored markers: project each suspended time onto the fitted line for y-position
const censoredData = censoredTimes.map(time => [
time,
beta * Math.log10(time) + intercept,
]);
// Parameter labels
const betaStr = beta.toFixed(2);
const etaStr = Math.round(eta).toLocaleString();
// --- Init ---
const chart = echarts.init(document.getElementById("container"));
// --- Option ---
chart.setOption({
animation: false,
color: t.palette,
backgroundColor: "transparent",
title: {
text: "probability-weibull · javascript · echarts · anyplot.ai",
left: "center",
top: 24,
textStyle: { color: t.ink, fontSize: 22, fontWeight: "bold" },
},
legend: {
top: 65,
left: "center",
textStyle: { color: t.inkSoft, fontSize: 14 },
itemGap: 32,
data: [
{ name: "Failure", icon: "circle" },
{ name: "Censored (suspended)", icon: "circle" },
{ name: "Weibull Fit" },
{ name: "63.2% Reference" },
],
},
grid: { left: 115, right: 70, top: 110, bottom: 90 },
xAxis: {
type: "log",
name: "Time to Failure (hours)",
nameLocation: "middle",
nameGap: 52,
nameTextStyle: { color: t.inkSoft, fontSize: 16 },
min: tMin,
max: tMax,
axisLabel: {
color: t.inkSoft,
fontSize: 13,
formatter: val => {
if (val >= 10000) return (val / 1000).toFixed(0) + "k";
if (val >= 1000) return (val / 1000).toFixed(0) + "k";
return String(val);
},
},
axisLine: { lineStyle: { color: t.inkSoft } },
splitLine: { lineStyle: { color: t.grid, type: "dashed" } },
minorSplitLine: { show: true, lineStyle: { color: t.grid, opacity: 0.45 } },
},
yAxis: {
type: "value",
name: "Cumulative Failure Probability",
nameLocation: "middle",
nameGap: 88,
nameTextStyle: { color: t.inkSoft, fontSize: 16 },
min: -4.5,
max: 2.0,
interval: 1,
axisLabel: {
color: t.inkSoft,
fontSize: 13,
// Convert Weibull y-value back to a readable probability percentage
formatter: val => {
if (val < -4.3 || val > 1.85) return "";
const F = 1 - Math.exp(-Math.exp(val));
const pct = F * 100;
return pct < 1 ? pct.toFixed(1) + "%" : Math.round(pct) + "%";
},
},
axisLine: { lineStyle: { color: t.inkSoft } },
splitLine: { lineStyle: { color: t.grid } },
},
series: [
// Weibull fitted line
{
name: "Weibull Fit",
type: "line",
data: fitData,
symbol: "none",
lineStyle: { color: t.palette[2], width: 3 },
z: 2,
},
// Horizontal reference at 63.2% cumulative probability (y = 0)
{
name: "63.2% Reference",
type: "line",
data: [[tMin, 0], [tMax, 0]],
symbol: "none",
lineStyle: { color: t.palette[3], width: 2, type: "dashed" },
z: 1,
},
// Failure observations — filled circles
{
name: "Failure",
type: "scatter",
data: failurePoints.map(p => [p.time, p.yW]),
symbolSize: 16,
itemStyle: {
color: t.palette[0],
borderColor: t.pageBg,
borderWidth: 1.5,
},
z: 3,
},
// Censored (suspended) observations — hollow circles at projected y position
{
name: "Censored (suspended)",
type: "scatter",
data: censoredData,
symbolSize: 16,
itemStyle: {
color: "transparent",
borderColor: t.inkSoft,
borderWidth: 2,
},
z: 3,
},
],
// Weibull parameter annotation
graphic: [
{
type: "group",
left: "66%",
top: "18%",
children: [
{
type: "rect",
shape: { width: 200, height: 66, r: 4 },
style: { fill: t.elevatedBg, stroke: t.grid, lineWidth: 1 },
},
{
type: "text",
style: {
text: `β (shape) = ${betaStr}`,
fill: t.ink,
fontSize: 15,
fontWeight: "bold",
x: 14,
y: 14,
},
},
{
type: "text",
style: {
text: `η (char. life) = ${etaStr} h`,
fill: t.ink,
fontSize: 15,
fontWeight: "bold",
x: 14,
y: 38,
},
},
],
},
],
});
Runnable source as JSON, for any HTTP client: https://api.anyplot.ai/specs/probability-weibull/echarts/code. Any spec id and library id listed in llms-full.txt fit the same URL shape; every URL below is complete and callable.
{
"spec_id": "probability-weibull",
"language": "javascript",
"library": "echarts",
"page": "https://anyplot.ai/probability-weibull/javascript/echarts",
"hub": "https://anyplot.ai/probability-weibull",
"code_json": "https://api.anyplot.ai/specs/probability-weibull/echarts/code",
"spec_json": "https://api.anyplot.ai/specs/probability-weibull",
"render_light_png": "https://storage.googleapis.com/anyplot-images/plots/probability-weibull/javascript/echarts/plot-light.png",
"render_dark_png": "https://storage.googleapis.com/anyplot-images/plots/probability-weibull/javascript/echarts/plot-dark.png",
"interactive_light_html": "https://storage.googleapis.com/anyplot-images/plots/probability-weibull/javascript/echarts/plot-light.html",
"interactive_dark_html": "https://storage.googleapis.com/anyplot-images/plots/probability-weibull/javascript/echarts/plot-dark.html",
"quality_score": 90.0,
"license": "MIT",
"guide": "https://anyplot.ai/llms.txt"
}Part of Weibull Probability Plot for Reliability Analysis on anyplot.ai.