Availability Calculations
Availability calculations are more complex than reliability without repair calculations. However, availability calculations are comparatively simple compared to reliability when the effects of repairs are considered in the calculations.
System availability is calculated using either an analytical method or simulation. The calculations for the analytical method are similar to the calculations of reliability without repair; the only difference is that the inputs for these calculations are the availabilities of the components, whereas the inputs for the reliability calculations are the reliabilities of the components.
The availability of a single unit having exponential failure and repair distributions that correspond to the constant failure and repair rates is calculated at each time point with the following equation:
Where:
A(t) =The availability of the unit at time t.
λ = The constant failure rate.
μ = The constant repair rate.
The procedure for simulations is more complex than the case for reliability, even without considering the effects of repair. The failure and repair time histories of the components are calculated from the failure and repair information. When a simulation is performed, the failure and repair times of a component are determined by generating random numbers derived from the distribution of these random variables (failure time and repair time).
The random variables that correspond to a particular distribution are determined from the uniform random numbers by comparing them with the survival function (reliability of a component in case of failure times) of the distribution. The time of operation of the unit is estimated from the inverse probability density function (pdf) of the failure distribution. If the unit is repairable, the repair time is estimated from the inverse pdf of the repair distribution.
For example, in the case of a unit without repair, the survival function at the time of interest, which is the compliment of the distribution function or reliability, is compared with a random number. If the random number is less than the function evaluated at that time, the unit is assumed to be in the failed state. The availability values are incremented during the operational time of the unit and are not incremented during the repair times.
The following table describes the different types of availability results that are calculated. Additionally, mean availability can be calculated. For more information, see Mean Availability Calculations.
Result | Description |
|---|---|
Availability | The availability at a specific time. This calculation does not consider logistic delay times in the downtime; hence it is the inherent availability of the system/component. When availability is calculated, all results calculated, including cost-related results for the system, ignore logistic delay times. |
Steady state availability | The steady state availability is the inherent availability as time tends to infinity. This calculation takes into account corrective repair times. When operational availability is calculated, it also includes logistic delay times. |
Operational availability | The operational availability takes into account corrective repair times and the mean logistics downtime (or logistics time and administrative downtime for maintenance). When operational availability is calculated, all results calculated, including cost-related results for the system, take logistic delay times into consideration. |
Achieved availability | An achieved availability value is calculated only when spares optimization calculations run. Based on a stated mission time, achieved availability takes into account corrective repair times. When operational availability is calculated, it also takes into account logistic delay times. |