How to Calculate Failure Rate from Reliability

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Failure Rate & MTBF Calculator

Enter as a decimal (0.95) or a percentage (95%).

Calculation Results:

Failure Rate (λ): failures/hour

MTBF (Mean Time Between Failures): hours

FIT (Failures In Time – per 10⁹ hrs):

Please enter valid numbers. Reliability must be between 0 and 100% (and not 100% for a finite failure rate). Time must be greater than zero.
function calculateFailureRate() { var relVal = parseFloat(document.getElementById('reliabilityInput').value); var timeVal = parseFloat(document.getElementById('timeInput').value); var resDiv = document.getElementById('calcResults'); var errDiv = document.getElementById('calcError'); // Reset displays resDiv.style.display = 'none'; errDiv.style.display = 'none'; // Basic validation if (isNaN(relVal) || isNaN(timeVal) || timeVal 1) { R = R / 100; } // Reliability cannot be = 1 for the math to produce a real failure rate if (R = 1) { errDiv.style.display = 'block'; return; } // Formula: R(t) = e^(-λt) // ln(R) = -λt // λ = -ln(R) / t var lambda = -Math.log(R) / timeVal; var mtbf = 1 / lambda; var fit = lambda * 1000000000; document.getElementById('resLambda').innerText = lambda.toExponential(6); document.getElementById('resMTBF').innerText = mtbf.toLocaleString(undefined, {maximumFractionDigits: 2}); document.getElementById('resFIT').innerText = fit.toLocaleString(undefined, {maximumFractionDigits: 0}); resDiv.style.display = 'block'; }

Understanding Reliability and Failure Rate

In reliability engineering, understanding the relationship between the probability of a system's survival (Reliability) and the frequency of its breakdown (Failure Rate) is critical for maintenance planning and product safety. This calculator uses the constant failure rate model, which is the industry standard for the "useful life" phase of most electronic and mechanical components.

The Mathematical Relationship

The core relationship follows the exponential distribution. The probability that a component will survive until time t is defined by the formula:

R(t) = e-λt

Where:

  • R(t) is the Reliability (probability of success).
  • λ (Lambda) is the Failure Rate (failures per unit time).
  • t is the operating time.
  • e is Euler's number (approx. 2.718).

How to Calculate Failure Rate from Reliability

If you know the reliability percentage and the time period, you can find the failure rate by rearranging the formula:

  1. Convert your Reliability percentage to a decimal (e.g., 90% = 0.90).
  2. Take the natural logarithm (ln) of the Reliability.
  3. Divide the result by the negative of the time period.

λ = -ln(R) / t

Key Metrics Explained

Once the Failure Rate (λ) is calculated, two other vital metrics can be derived:

  • MTBF (Mean Time Between Failures): This represents the average time elapsed between inherent failures of a system. It is simply the reciprocal of the failure rate (1/λ).
  • FIT (Failures In Time): This is a standard unit used especially in the electronics industry. 1 FIT represents 1 failure per 1 billion (10⁹) device-hours.

Real-World Example

Imagine a server power supply that has a measured reliability of 98% (0.98) after 5,000 hours of continuous operation. To find the failure rate:

  • Step 1: ln(0.98) ≈ -0.0202
  • Step 2: -(-0.0202) / 5000 = 0.00000404 failures per hour.
  • Step 3: MTBF = 1 / 0.00000404 ≈ 247,524 hours.
  • Step 4: FIT = 0.00000404 × 10⁹ = 4,040 FIT.

This data helps engineers decide if the component meets the required safety standards or if redundancy (like a second power supply) is needed to achieve higher system-level reliability.

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