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Reliability At Time T Calculator

Work out reliability at time t instantly with clear inputs, formula shown and shareable results.

About Reliability At Time T Calculator

For a constant failure rate, reliability decays exponentially: R(t) = e^(-t/MTBF). Failure rate lambda is the reciprocal of MTBF. Multiplying the complement of reliability by the fleet size gives the expected number of failures in the mission, and MTBF against MTTR gives inherent availability.

Formulas

Exponential reliability

R(t) = e^(-t / MTBF); failure rate = 1 / MTBF

Availability

Inherent availability = MTBF / (MTBF + MTTR)

Worked example

With the default values below, Reliability At Time T Calculator returns Reliability At Mission Time of 86.5888%. Change any input above and every figure here is recalculated in your browser.

Inputs used

Mean Time Between Failuresminimum 0.01 hours
5,000 hours
Mission Timeminimum 0.01 hours
720 hours
Units In Serviceminimum 1
40
Mean Time To Repairminimum 0.01 hours
6 hours

Results

Reliability At Mission Time
86.5888%
Failure Rate
0.00020000
Expected Failures In The Fleet
5.364
Inherent Availability
99.8801%

Step by step

  1. 1Values used
  2. 2Exponential reliability
  3. 3Availability
  4. 4Reliability At Mission Time= 86.5888
  5. 5Failure Rate= 0.00020000
  6. 6Expected Failures In The Fleet= 5.364
  7. 7Inherent Availability= 99.8801

Assumptions and limits

  • The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

When does the exponential model apply?

During the useful-life phase where failures are random. It does not describe infant mortality or wear-out, which need a Weibull model with shape parameter below or above 1.

Why is reliability at MTBF only 37%?

Because e^-1 = 0.368. MTBF is the mean, not a guarantee period; most items fail before reaching it under an exponential distribution.

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