Calculate failure rate, MTBF, and operating time from failures and total operating time, with fleet asset comparisons and benchmark checks.
- All Statistics Calculators
- Sigma Level Calculator
- DPMO Calculator (Defects Per Million Opportunities)
- Rate Per 1000 Calculator
- System Reliability Calculator
- Defect Density Calculator
Failure Rate Formula
The basic failure rate formula is:
\lambda = F/T
- λ = failure rate
- F = number of failures
- T = total operating time
If you know the failure rate and total operating time, the number of failures is:
F = \lambda*T
If you know the number of failures and the failure rate, the operating time is:
T = F/\lambda
For mean time between failures, the relationship is:
MTBF = 1/\lambda
\lambda = 1/MTBF
For a fleet or group of assets, total operating time can be found from:
T = A*t
- A = number of assets
- t = operating time per asset
- T = combined operating time for all assets
The Failure Rate tab solves for the blank value when you provide two of these three values: failures, total operating time, and failure rate. The MTBF Converter tab converts between failure rate and mean time between failures. The Fleet / Assets tab calculates a group failure rate from total failures and combined operating time. If you enter total operating time in the fleet tab, it overrides assets multiplied by time per asset.
Time Unit Conversions Used
The calculator converts time to hours first, then converts the result back to the unit you selected.
| Unit | Hours Used | Example Rate Meaning |
|---|---|---|
| Hour | 1 | Failures per operating hour |
| Day | 24 | Failures per 24 operating hours |
| Week | 168 | Failures per 168 operating hours |
| Month | 730 | Failures per average month |
| Year | 8,760 | Failures per 365-day year |
Common Failure Rate Interpretations
| Result | Equivalent MTBF | Plain Meaning |
|---|---|---|
| 0.1 failures/hour | 10 hours | About 1 failure every 10 operating hours |
| 0.01 failures/hour | 100 hours | About 1 failure every 100 operating hours |
| 0.001 failures/hour | 1,000 hours | About 1 failure every 1,000 operating hours |
| 0 failures/hour | Not finite | No failures were observed during the measured time |
Example Problems
Example 1: Calculate failure rate from failures and time
You observed 6 failures over 2,000 operating hours.
\lambda = 6/2000 = 0.003
The failure rate is 0.003 failures/hour. The MTBF is:
MTBF = 1/0.003 = 333.3333 hours
Example 2: Calculate fleet failure rate
A fleet has 25 assets. Each asset ran for 400 hours. There were 10 failures.
T = 25*400 = 10000 hours
\lambda = 10/10000 = 0.001
The fleet failure rate is 0.001 failures/hour. The MTBF is 1,000 hours.
FAQs
What is a failure rate?
Failure rate is the number of failures divided by the amount of operating time. A lower failure rate means failures happen less often. For example, 0.002 failures/hour means an average of 1 failure every 500 operating hours.
How is failure rate different from MTBF?
Failure rate measures failures per unit of time. MTBF measures average time between failures. They are inverse values. If the failure rate is 0.005 failures/hour, the MTBF is 1 ÷ 0.005, or 200 hours.
What counts as total operating time for multiple assets?
Use combined operating time. If 10 assets each run for 100 hours, the total operating time is 1,000 asset-hours. Do not use calendar time unless every asset was operating for that full period.
