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font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif;
max-width: 800px;
margin: 0 auto;
padding: 20px;
line-height: 1.6;
color: #333;
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.calc-container {
background-color: #f8f9fa;
border: 1px solid #e9ecef;
border-radius: 8px;
padding: 30px;
margin-bottom: 40px;
box-shadow: 0 4px 6px rgba(0,0,0,0.05);
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.calc-title {
text-align: center;
margin-bottom: 25px;
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font-weight: 700;
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.form-group {
margin-bottom: 20px;
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.form-group label {
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line-height: 1.5;
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transition: border-color .15s ease-in-out;
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box-shadow: 0 0 0 0.2rem rgba(0,123,255,.25);
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.help-text {
font-size: 12px;
color: #6c757d;
margin-top: 5px;
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.btn-calc {
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width: 100%;
font-weight: 600;
text-align: center;
white-space: nowrap;
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transition: background-color 0.15s;
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.btn-calc:hover {
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.results-area {
margin-top: 30px;
padding-top: 20px;
border-top: 2px solid #e9ecef;
display: none;
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.result-row {
display: flex;
justify-content: space-between;
align-items: center;
padding: 10px 0;
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.result-row:last-child {
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.result-label {
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.result-value {
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.article-content ul, .article-content ol {
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.formula-box {
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function calculateFailureMetrics() {
// Get inputs
var failCountInput = document.getElementById('fail_count');
var totalHoursInput = document.getElementById('total_hours');
var missionTimeInput = document.getElementById('mission_time');
var failures = parseFloat(failCountInput.value);
var hours = parseFloat(totalHoursInput.value);
var missionTime = parseFloat(missionTimeInput.value);
// Validation
if (isNaN(failures) || failures < 0) {
alert("Please enter a valid non-negative number for failures.");
return;
}
if (isNaN(hours) || hours <= 0) {
alert("Please enter a valid positive number for total operating hours.");
return;
}
if (isNaN(missionTime) || missionTime 0, we calculate.
var reliability = 0;
if (missionTime > 0) {
reliability = Math.exp(-lambda * missionTime);
} else {
reliability = 1; // 100% at time 0
}
var probFailure = 1 – reliability;
// Display Results
document.getElementById('calc_results').style.display = 'block';
// Format numbers nicely
document.getElementById('res_lambda').innerHTML = lambda.toExponential(4) + " / hr";
document.getElementById('res_mtbf').innerHTML = mtbfText;
document.getElementById('res_fit').innerHTML = fit.toFixed(2);
// Show percentages
document.getElementById('res_reliability').innerHTML = (reliability * 100).toFixed(4) + "%";
document.getElementById('res_prob_fail').innerHTML = (probFailure * 100).toFixed(4) + "%";
}
Failure Rate & MTBF Calculator
Total count of component failures during the test period.
Sum of operating hours for all units (e.g., 10 units × 1000 hours = 10,000 hours).
Enter hours to calculate the probability of survival (Reliability) for that duration.
Failure Rate (λ):
MTBF (Mean Time Between Failures):
Failures in Time (FIT):
Reliability for Target Duration:
Probability of Failure:
Failure Rate Calculation Example and Guide
In reliability engineering, understanding how often a system is expected to fail is critical for maintenance planning, warranty estimation, and safety analysis. The failure rate, denoted by the Greek letter lambda (λ), represents the frequency of component failure per unit of time.
The Core Formulas
This calculator uses the constant failure rate model (the bottom of the "bathtub curve"), which is standard for electronic components and mechanical systems during their useful life phase.
λ (Failure Rate) = Number of Failures / Total Operating Hours
MTBF = 1 / λ
Reliability R(t) = e^(-λ * t)
MTBF = 1 / λ
Reliability R(t) = e^(-λ * t)
Step-by-Step Calculation Example
Let's look at a realistic scenario to understand how the numbers work.
Scenario: A manufacturer tests 50 hard drives. Each drive runs for 2,000 hours continuously. During this test, 4 drives fail.
- Calculate Total Operating Time:
First, determine the total exposure time. Even though the test lasted 2,000 hours, we had 50 units running.
50 units × 2,000 hours = 100,000 Total Unit-Hours. - Identify Number of Failures:
The observed count is 4. - Calculate Failure Rate (λ):
λ = 4 / 100,000 = 0.00004 failures per hour. - Calculate MTBF:
Mean Time Between Failures is the reciprocal of the failure rate.
MTBF = 1 / 0.00004 = 25,000 Hours.
Understanding the Metrics
- MTBF (Mean Time Between Failures): This is the average time expected between inherent failures of a mechanical or electronic system during normal system operation. It does not mean the unit is guaranteed to last that long. In fact, at time = MTBF, the reliability is approximately 36.8%.
- FIT (Failures In Time): Because failure rates per hour are often tiny numbers (like 0.00004), engineers often use FIT. One FIT equals one failure per billion (109) device hours.
- Reliability R(t): This is the probability that a unit will function without failure for a specific period (t).
Common Applications
These calculations are essential in:
- Electronics Manufacturing: Estimating warranty costs for SSDs, motherboards, and power supplies.
- Industrial Maintenance: Planning preventive maintenance schedules for pumps and motors.
- Software Engineering: Tracking crash rates per 1,000 active user hours.