Failure Rate Calculator
Failure rate (lambda) is the fundamental parameter for reliability analysis, expressing how frequently failures occur per unit of operating time. Reliability engineers compute failure rate from observed test or field data to verify component specifications, update system reliability models, and support warranty cost forecasting. This calculator converts between failure count and operating hours to produce the failure rate in failures per hour, the equivalent FIT rating used in electronic component specifications, and the implied MTBF and expected annual failure count per deployed unit.
Failure rate formula
lambda = failures / total_unit_hours
FIT = lambda * 10^9
MTBF = 1 / lambda
annual_failures_per_unit = lambda * 8,760
Understanding FIT ratings
- FIT 1 = 1 failure per billion hours; MTBF = 1,000,000,000 hours (extremely reliable).
- FIT 100 = MTBF of 10,000,000 hours (typical for high-quality electronics).
- FIT 1,000 = MTBF of 1,000,000 hours (standard commercial electronics).
- FIT 10,000 = MTBF of 100,000 hours (consumer-grade or high-stress components).
- For a system with 1,000 units deployed, annual_failures = total_FIT/10^9 * 8,760 * 1,000.
Frequently asked questions
What is failure rate (lambda) and what are its units?
Failure rate (lambda) is the number of failures per unit of time for a population of items. Units are failures/hour, failures/year, or FIT (failures per 10^9 hours). Lambda = number_of_failures / total_operating_hours. A lower lambda means higher reliability. For most electronic components in normal operating life, lambda is approximately constant (exponential failure distribution).
What is a FIT rating?
FIT (Failures In Time) = failures per 10^9 device-hours. FIT = lambda * 10^9. A component with a FIT rating of 100 has 100 failures per billion device-hours, or equivalently, lambda = 0.0000001 failures/hour and MTBF = 10,000,000 hours. FIT ratings are used extensively for electronic components where MTBF values run into millions of hours.
How do I calculate the failure rate for a system with multiple components?
For a series system where all components must work, the system failure rate = sum of all individual failure rates: lambda_sys = lambda_1 + lambda_2 + ... + lambda_n. The system MTBF = 1 / lambda_sys. Adding more components always increases the system failure rate and decreases system MTBF. This is why reliability engineers minimize the number of serial components.
How does confidence interval affect failure rate calculations?
A point estimate of failure rate from a limited sample has uncertainty. The 90% upper confidence limit on lambda is calculated using the chi-squared distribution: lambda_upper = chi2(0.90, 2r+2) / (2 * T), where r = number of failures and T = total test time. Using the upper confidence limit gives a conservative (pessimistic) reliability estimate for safety analysis.
What is the difference between observed failure rate and predicted failure rate?
Observed (empirical) failure rate is calculated from actual field data or test results. Predicted failure rate comes from reliability prediction models like MIL-HDBK-217 or Telcordia SR-332, which estimate failure rate based on component type, quality level, and stress factors. Predicted rates are used during design; observed rates refine reliability estimates during product life.
Official sources
- IEEE: IEEE 610.12 - Standard Glossary of Software Engineering Terminology.
- DLA: DLA - MIL-HDBK-217 Electronic Reliability Prediction.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.