Calculate probability of failure over a mission time from MTBF or failure rate, or find failure rate, failure percentage and MTBF from observed failures.

Assumes a constant failure rate (exponential model).

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Failure Rate Formula

The following formula is used to calculate the (average) failure rate over an observation period.

ฮป = (n) / (t)

Variables:

  • ฮป is the failure rate (failures per unit time)
  • n is the number of failures
  • t is the total operating time summed across all observed units

To estimate the observed failure rate, divide the whole-number failure count by total unit operating time. The result has units of failures per time. Zero observed failures do not establish zero underlying risk or a finite MTBF estimate.

What is Failure Rate?

Failure rate is a measure of how frequently a system or component fails over time, commonly used in reliability engineering. It is not a probability by itself because it has units (1/time). If you need a failure probability over a time interval and can assume a constant failure rate (exponential/Poisson model), a common model is:

P(at least one failure in T) = 1 - e - ฮป T

How to Calculate Failure Rate?

The following steps outline how to calculate the failure rate.

  1. First, determine the number of failures (n) that have occurred.
  2. Next, determine the time period (t) over which the failures were observed.
  3. Next, gather the formula from above: ฮป = n / t.
  4. Finally, calculate the failure rate (ฮป) in failures per unit time.
  5. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

number of failures (n) = 5

time period (t) = 1 year

failure rate (ฮป) = n / t = 5 / 1 = 5 failures/year