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Ao Calculator

Given inputs of operational availability (Ao) and mean restoration time (MRT), this tool generates a plot to show the combinations of possible mean time between failure (MTBF) and MRT values that will result in the required Ao. Enter the required Ao, and either a system MTBF, or an upper bound MRT value to generate a plot showing the combinations of MTBFs and MRTs that will meet the required Ao.

Equation for calculating operational availability


MTBF is the mean time between failure, also referred to as mean time between critical failure (MTBCF).
MRT is the mean restoration time. This typically consists of mean logistics delay time (MLDT), plus mean time to repair (MTTR).

Note, some organizations use different terminology than shown above, such as mean time between maintenance (MTBM) instead of MTBF, or mean down time (MDT) instead of MRT. Ultimately, availability is uptime divided by total time. Specific time categories (and terminology) included in uptime and total time for computing "operational" availability may be organizational dependent. See this blog post for a more comprehensive description of various factors that may, or may not, be included in "uptime" and "downtime."

To model operational availability in greater detail, see the discrete event simulation tool and this blog post.

Calculation Inputs:


Ao sensivity +/- for last significant digit

Enter one of the following inputs (leave one blank):

MTBF (hours):
MRT (hours):

Featured Reference:

Practical Reliability Engineering
Practical Reliability Engineering

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  1. MIL-HDBK-338, Electronic Reliability Design Handbook.