Reliability Failure Rate Calculation Example – Cost Calculator

Reliability & Failure Rate (λ) Calculator

Number of Failures (n):

Operating Time per Unit (hours):

Number of Units in Population:

Results:

Failure Rate (λ): failures/hour

Mean Time Between Failures (MTBF): hours

Probability of Success (for 1000h): %

Understanding Reliability Failure Rate Calculation

Reliability engineering focuses on the ability of a system or component to perform its required functions under stated conditions for a specified period. The primary metric used to quantify this is the Failure Rate (λ).

The Failure Rate Formula

The standard formula for calculating the constant failure rate during the "useful life" phase (the flat part of the bathtub curve) is:

            λ = Total Number of Failures / (Total Number of Units × Operating Time)
        

What is MTBF?

Mean Time Between Failures (MTBF) is the reciprocal of the failure rate. It represents the average time elapsed between inherent failures of a mechanical or electronic system during normal system operation.

MTBF = 1 / λ

Real-World Example Calculation

Suppose a data center operates 100 server power supplies. Over a period of 2,000 hours, exactly 4 units fail. Let's calculate the reliability metrics:

Total Exposure Time: 100 units × 2,000 hours = 200,000 unit-hours.
Failure Rate (λ): 4 failures / 200,000 hours = 0.00002 failures per hour.
MTBF: 1 / 0.00002 = 50,000 hours.

This means that on average, you can expect one power supply failure every 50,000 hours of cumulative operation across your fleet.

Calculating Reliability over Time

To determine the probability that a specific unit will survive for a certain duration (t), we use the exponential distribution formula:

R(t) = e^(-λt)

Where e is the base of natural logarithms (~2.718). If our failure rate is 0.00002 and we want to know the chance of a unit surviving 10,000 hours, we calculate e^(-0.00002 * 10000), which results in approximately 81.87% reliability.

function calculateReliabilityMetrics() { var failures = parseFloat(document.getElementById('totalFailures').value); var timePerUnit = parseFloat(document.getElementById('operatingHours').value); var units = parseFloat(document.getElementById('unitPopulation').value); var displayArea = document.getElementById('reliabilityResults'); if (isNaN(failures) || isNaN(timePerUnit) || isNaN(units) || timePerUnit <= 0 || units <= 0) { alert("Please enter valid positive numbers for all fields."); return; } // Total operating time (T) var totalTime = units * timePerUnit; // Failure Rate (Lambda) var lambda = failures / totalTime; // MTBF var mtbf = (lambda === 0) ? "Infinity" : (1 / lambda).toFixed(2); // Reliability for 1000 hours as a benchmark var tBenchmark = 1000; var reliability = (Math.exp(-lambda * tBenchmark) * 100).toFixed(2); // Display Results document.getElementById('lambdaResult').innerHTML = lambda.toFixed(8); document.getElementById('mtbfResult').innerHTML = mtbf; document.getElementById('reliabilityResult').innerHTML = reliability; displayArea.style.display = 'block'; }