Mean Time Between Failures

In the software the occurance of Unplanned Downtimes are calculated based on a uniform probability distribution, where the mean is equal to the Mean Time Between Failures (MTBF).

MTBF represents the average amount of time a piece of equipment operates before experiencing a failure. To calculate the MTBF, both the Mean Time To Repair (MTTR) and availabilty of the equipment are needed.

Mean Time To Repair

Mean Time To Repair (MTTR) is a metric that measures the average time it takes to repair equipment after a failure has occurred. In the context of the simulator, this is the weighted average of the mean duration of potential downtime events that is specified in the Unplanned Downtime step.

Expanded Explanation:

1. The mean duration of each downtime event is specified individually (e.g., how long each type of downtime typically lasts).
2. Each event's duration is weighted by its likelihood (probability of occurrence).
3. The weighted average combines all these values to give a representative "average downtime duration," accounting for both how often each event happens and how long it lasts.

Availability

Availability represents the percentage of time that equipment is operational and ready for use, excluding planned maintenance. In the software, this value is provided as an input under the term Unplanned Availability. Availability can be expressed using the following equation:

$$\text{Availability} = \frac{\text{MTBF}}{\text{MTBF} \, + \, \text{MTTR}}$$

With both Availability and MTTR known, the equation can be rearranged to calculate the MTBF:

$$\text{MTBF} = \frac{\text{MTTR} \, \times \, A}{1 - A}$$

With the MTBF known, a uniform probability distribution is generated and sampled to determine when unplanned downtimes occur. The distribution is constrained with a minimum value of 0 and a maximum value of twice the mean.