How to Use This Calculator
- Enter the failure rate (λ) per hour. This is the average number of failures that occur in one hour. For example, if a system fails once every 10,000 hours, the failure rate would be 0.0001 failures/hour.
- Specify the average annual operating hours. This is the number of hours the system is expected to operate per year.
- Select the confidence level for your calculation. A 95% confidence level means you can be 95% confident that the actual failure rate falls within the calculated interval.
- Click the "Calculate" button to compute the MTTF and its confidence interval.
Understanding the Results
The calculator provides two key results:
- MTTF (Mean Time to Failure): This is the average time between failures of the system, expressed in hours. A higher MTTF indicates a more reliable system.
- 95% Confidence Interval: This shows a range within which the actual failure rate is likely to fall with 95% confidence. The confidence interval accounts for uncertainties in the failure rate estimation.
Principle of Calculation
The calculator uses statistical reliability engineering principles:
For a system with a constant failure rate (Poisson process), the Mean Time to Failure (MTTF) is calculated as the reciprocal of the failure rate (λ). The confidence interval is calculated using the normal approximation to the binomial distribution, which is appropriate for systems with a low failure rate but high operating hours.
Example Application
This calculator can be used in various fields including:
- Manufacturing quality control
- Aviation system reliability analysis
- Software system stability testing
- Infrastructure maintenance planning
- Electronics product life expectancy estimation