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max-width: 800px;
margin: 0 auto;
background: #fff;
padding: 20px;
border-radius: 8px;
box-shadow: 0 2px 10px rgba(0,0,0,0.1);
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padding: 25px;
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padding: 14px 20px;
font-size: 16px;
font-weight: 600;
border-radius: 4px;
cursor: pointer;
width: 100%;
transition: background-color 0.2s;
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.calc-btn:hover {
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.results-box {
display: none;
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function toggleLabel() {
var mode = document.getElementById('inputType').value;
var label = document.getElementById('inputLabel');
var input = document.getElementById('rateValue');
if (mode === 'lambda') {
label.innerText = "Failure Rate (λ) – e.g., failures per hour";
input.placeholder = "Enter Failure Rate (e.g., 0.001)";
} else {
label.innerText = "Mean Time Between Failures (MTBF) – e.g., hours";
input.placeholder = "Enter MTBF (e.g., 1000)";
}
}
function calculateReliability() {
// Get inputs
var mode = document.getElementById('inputType').value;
var val = parseFloat(document.getElementById('rateValue').value);
var time = parseFloat(document.getElementById('timeDuration').value);
var errorDiv = document.getElementById('errorDisplay');
var resultsDiv = document.getElementById('resultsArea');
// Reset UI
errorDiv.style.display = "none";
resultsDiv.style.display = "none";
// Validation
if (isNaN(val) || val <= 0) {
errorDiv.innerText = "Please enter a valid positive number for the Rate or MTBF.";
errorDiv.style.display = "block";
return;
}
if (isNaN(time) || time < 0) {
errorDiv.innerText = "Please enter a valid non-negative number for Time.";
errorDiv.style.display = "block";
return;
}
// Calculation Logic
var lambda, mtbf;
if (mode === 'lambda') {
lambda = val;
mtbf = 1 / lambda;
} else {
mtbf = val;
lambda = 1 / mtbf;
}
// Exponential Reliability Formula: R(t) = e^(-λt)
var reliability = Math.exp(-1 * lambda * time);
var unreliability = 1 – reliability;
// Formatting Results
var rPercent = (reliability * 100).toFixed(4) + "%";
var fPercent = (unreliability * 100).toFixed(4) + "%";
// Display Results
document.getElementById('resReliability').innerText = rPercent + " (" + reliability.toFixed(6) + ")";
document.getElementById('resUnreliability').innerText = fPercent + " (" + unreliability.toFixed(6) + ")";
document.getElementById('resMTBF').innerText = mtbf.toFixed(2) + " hours";
document.getElementById('resLambda').innerText = lambda.toExponential(4);
resultsDiv.style.display = "block";
}
Understanding Reliability Calculation from Failure Rate
Reliability Engineering is a sub-discipline of systems engineering that emphasizes the ability of equipment to function without failure. This calculator helps determine the probability that a system or component will perform its required function under stated conditions for a specified period of time.
The calculation assumes the Exponential Distribution model, which describes the "useful life" phase of a product where the failure rate is considered constant. This is often visualized as the flat bottom portion of the "Bathtub Curve."
The Reliability Formula
The mathematical relationship between Reliability ($R$), Failure Rate ($\lambda$), and Time ($t$) is expressed as:
R(t) = e-λt
Where:
- R(t): Reliability (Probability of survival at time $t$).
- e: Euler's number (approximately 2.71828).
- λ (Lambda): Constant Failure Rate (failures per unit of time).
- t: Time duration of operation.
Failure Rate vs. MTBF
In reliability engineering, you will often encounter two different ways to describe how often a system fails: Failure Rate ($\lambda$) and Mean Time Between Failures (MTBF). They are mathematically the inverse of one another.
MTBF = 1 / λ
λ = 1 / MTBF
Therefore, the reliability formula can also be written using MTBF:
R(t) = e-t / MTBF
Example Calculation
Suppose you have a hard drive with a specified MTBF of 1,000,000 hours. You want to know the probability that this hard drive will survive for 5 years (43,800 hours) of continuous operation.
- Determine λ: λ = 1 / 1,000,000 = 0.000001 failures/hour.
- Set Time (t): 43,800 hours.
- Calculate Exponent: -0.000001 × 43,800 = -0.0438.
- Calculate R(t): R = e-0.0438 ≈ 0.9571.
The reliability is approximately 95.71%. This means there is a 95.71% chance the drive lasts 5 years without failure, and a 4.29% chance it fails within that period.
Unreliability (Probability of Failure)
Unreliability, denoted as $F(t)$, represents the probability that the system will fail before time $t$. Since the system must either survive or fail:
F(t) = 1 – R(t)
Limitations
This calculator relies on the constant failure rate assumption. It does not apply to:
- Infant Mortality: Early failures caused by manufacturing defects (decreasing failure rate).
- Wear-out: End-of-life failures caused by fatigue or aging (increasing failure rate).
For these phases, more complex distributions like the Weibull distribution are required.