Failure Rate & Probability Calculator
Calculate reliability, failure probability, and MTBF using the exponential distribution.
Mean Time Between Failures (MTBF)
Failure Rate (λ)
Enter the average time between system failures.
The time period over which you want to calculate the probability of failure.
Calculation Results
Probability of Failure F(t):
0.00%
Reliability / Survival R(t):
0.00%
Failure Rate (λ):
0
MTBF:
0
Understanding Failure Rate Probability
In reliability engineering, calculating the probability that a system or component will fail over a specific period is crucial for risk assessment, maintenance scheduling, and warranty planning. This calculator uses the Exponential Distribution, which assumes a constant failure rate over time—the most common assumption for electronic components and mechanical systems during their useful life phase.
Key Definitions
- MTBF (Mean Time Between Failures): The predicted elapsed time between inherent failures of a mechanical or electronic system during normal system operation. It is expressed in hours.
- Failure Rate (λ): The frequency with which an engineered system or component fails, expressed in failures per unit of time (usually failures per hour).
- Reliability R(t): The probability that a unit will function as intended for a specified duration.
- Probability of Failure F(t): The probability that the unit will fail before time t. Also known as Unreliability.
The Formulas
This calculator relies on the relationship between MTBF and Failure Rate (λ), and uses the exponential decay function to determine probability.
1. Converting MTBF to Failure Rate:
λ = 1 / MTBF
2. Reliability Formula:
R(t) = e-(λ * t)
Where 'e' is Euler's number (~2.71828) and 't' is the operation duration.
3. Probability of Failure Formula:
F(t) = 1 – R(t) = 1 – e-(λ * t)
Example Calculation
Imagine a hard drive with an MTBF of 500,000 hours. You want to know the probability of it failing within 1 year (8,760 hours).
- Calculate λ: 1 / 500,000 = 0.000002 failures/hour.
- Calculate exponent: -(0.000002 * 8760) = -0.01752.
- Calculate Reliability: e-0.01752 ≈ 0.9826 or 98.26%.
- Calculate Failure Probability: 1 – 0.9826 = 0.0174 or 1.74%.
This means that while the MTBF is very high, there is still a 1.74% chance of failure within the first year of operation for a single unit.