Calculate λ (Lambda), MTBF, and FITs without Excel formulas.
Please enter valid operating hours.
Please enter a valid number of failures.
Used to calculate the probability of survival for a specific duration.
Failure Rate (λ) per hour:–
MTBF (Mean Time Between Failures):–
FITs (Failures in Time – 10⁹ hours):–
Reliability (Probability of Survival):–
Understanding Excel Failure Rate Calculation
Calculating failure rates is a critical task in reliability engineering, quality assurance, and maintenance planning. While many professionals use Microsoft Excel to track data and compute these metrics, setting up the formulas manually can be prone to syntax errors. This tool automates the standard calculations used to determine the reliability of a system, component, or product.
What is Failure Rate (λ)?
The failure rate, denoted by the Greek letter Lambda (λ), represents the frequency with which an engineered system or component fails. It is typically expressed in failures per unit of time (usually hours).
λ = Number of Failures / Total Operating Hours
For example, if you test 10 units for 1,000 hours each (10,000 total hours) and observe 2 failures, your failure rate is 0.0002 failures per hour.
MTBF Calculation
Mean Time Between Failures (MTBF) is the inverse of the failure rate (assuming a constant failure rate during the useful life of the product). It predicts the average time elapsed between inherent failures of a mechanical or electronic system during normal system operation.
MTBF = 1 / λ
In Excel, this would be calculated as =1/(Failures/Hours) or simply =Hours/Failures.
What are FITs?
Because raw failure rates often result in very small numbers (e.g., 0.000005), the industry standard is to use FITs (Failures In Time). One FIT equals one failure per one billion (109) device hours.
Formula:FITs = λ × 1,000,000,000
Reliability Probability
This calculator also determines the Reliability, which is the probability that an item will perform its required function for a stated period of time under stated conditions. This uses the exponential distribution formula:
R(t) = e^(-λt)
Where t is the Mission Time you input above. The result is expressed as a percentage.
Why Use This Calculator vs. Excel?
While Excel is powerful, it requires manual entry of the EXP, SUM, and division functions. A manual spreadsheet failure rate calculation is susceptible to cell referencing errors. This tool provides an instant, error-free computation of the four primary reliability metrics used in engineering reports.
function calculateFailureRate() {
// 1. Get DOM elements
var inputHours = document.getElementById('totalHours');
var inputFailures = document.getElementById('failureCount');
var inputMission = document.getElementById('missionTime');
var errorHours = document.getElementById('errorHours');
var errorFailures = document.getElementById('errorFailures');
var resultDiv = document.getElementById('results');
var valLambda = document.getElementById('resLambda');
var valMTBF = document.getElementById('resMTBF');
var valFIT = document.getElementById('resFIT');
var valReliability = document.getElementById('resReliability');
// 2. Reset errors and display
errorHours.style.display = 'none';
errorFailures.style.display = 'none';
resultDiv.style.display = 'none';
// 3. Get values
var hours = parseFloat(inputHours.value);
var failures = parseFloat(inputFailures.value);
var mission = parseFloat(inputMission.value);
var isValid = true;
// 4. Validation
if (isNaN(hours) || hours <= 0) {
errorHours.style.display = 'block';
isValid = false;
}
if (isNaN(failures) || failures 0) {
lambda = failures / hours;
}
// MTBF is infinity if failures are 0, practically we handle it by checking failures
if (failures === 0) {
mtbf = "Infinite (No Failures)";
} else {
mtbf = hours / failures;
}
// FITs
fits = lambda * 1000000000;
// Reliability R(t) = e^(-lambda * t)
if (!isNaN(mission) && mission > 0) {
var prob = Math.exp(-(lambda * mission));
reliability = (prob * 100).toFixed(4) + "%";
} else {
reliability = "N/A (Enter Mission Time)";
}
// 6. Formatting Output
// Lambda in scientific notation if very small, or fixed
var lambdaDisplay = lambda === 0 ? "0" : lambda.toExponential(4);
// MTBF Formatting
var mtbfDisplay;
if (typeof mtbf === 'string') {
mtbfDisplay = mtbf;
} else {
mtbfDisplay = mtbf.toFixed(2) + " Hours";
}
// FITs Formatting
var fitsDisplay = fits.toFixed(2);
// 7. Update DOM
valLambda.textContent = lambdaDisplay;
valMTBF.textContent = mtbfDisplay;
valFIT.textContent = fitsDisplay;
valReliability.textContent = reliability;
resultDiv.style.display = 'block';
}