Calculate failure rate, MTBF, and FIT from failures and total operating time, or convert directly between MTBF and failure rate.

Divide the whole number of observed failures by combined operating exposure.

Use total accumulated operating time across all tested devices. Reciprocal MTBF and FIT conversions assume a compatible constant-rate model; they do not predict when an individual device will fail.

Add actual operating exposure across devices; exclude downtime.

Failure Rate Formula

The basic failure rate formula is:

λ = F / T
  • λ = failure rate
  • F = number of failures
  • T = total operating time

Under a constant-rate model, failure rate times operating exposure gives the expected number of failures:

F = λ × T

Under a constant-rate model, the exposure associated with an expected failure count is shown below. This is not a guaranteed time to failure:

T = F / λ

For a compatible constant-rate model, the reciprocal relationship is:

MTBF = 1 / λ
λ = 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

Choose failure rate from observed data, failure rate from MTBF, or MTBF from failure rate. Enter the fields shown; no blank-field solving or separate fleet tab is used. For a fleet, add actual device operating times before entering combined exposure. The rearranged formulas above may be used separately to calculate expected counts or required exposure.

Time Unit Conversions Used

The calculator converts time to hours first. Day and week are fixed operating durations; month means 730 hours and year means 365 days. A FIT is one failure per billion device-hours.

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 No finite estimate from zero observed failures 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.

λ = 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
λ = 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 operating exposure. Under a compatible constant-rate model, MTBF is its reciprocal: 0.005 failures/hour corresponds to 200 hours. MTBF is not a guaranteed lifetime. Zero observed failures over finite exposure does not establish infinite MTBF.

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.