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dido:public:ra:1.4_req:2_nonfunc:14_reliability:02_availability

# 4.3.2.2 Availability

Availability in this context is System Availability. System Availability is the probability the system will function as designed for a particular duration. The duration could be a fixed time period (i.e., 24 hours a day, 7 days a week, or 364.9 days a year) or it could be over a particular mission (i.e., a flying mission, a patient stay, or a growing season). The ability of an item to be in a state to perform a required function under given conditions at a given instant of time or over a time interval, assuming the required external resources are provided. 1)

It is important to remember that Availability is expressed as a probability expressed in terms of Five Nines, and therefore, the Multiplication Rule of Probability needs to be considered when thinking about a system comprised of parts. Each part has its own probability of success (or failure). The Multiplication Rule of Probability means that to find the probability of the intersection of two events, multiply the two probabilities. The intersection of the events occurs when the probability of two events occurring is known. The Multiplication Rule of Probability determines the intersection of two different sets of events, called independent and dependent events.

• An Independent Event is when the probability of an event is not affected by a previous event.
• A Dependent Event is when one event influences the outcome of another event in a probability scenario. To find the intersection of two events, whether they are independent or dependent, multiply the two probabilities together. 2)

Mission Duration (Tm) is the time the system needs to be operational. Tm can be expressed as a fixed time period (i.e., 24 hours a day, 7 days a week, or 365 days a year) or it could be over a particular mission (i.e., a flying mission, a patient stay, peak energy demand, or a growing season)

Mean Time Between Failure (MTBF) is a calculation of the arithmetic mean (average) time between failures of a system.

• Note: If a system is designed with both redundancy and automatic fault bypass, then MTBF is the anticipated lifespan of the system if these features cover all possible failure modes (infinity for all practical purposes). Such systems will continue without noticeable interruption when these conditions are satisfied unless there are secondary failures. This is called active redundancy and requires no maintenance to prevent mission failure. Active redundancy is required for systems that cannot be maintained, such as satellites. See: Wikipedia, Mean Time Between Failure (MTBF), Accessed 3 July 2020, https://en.wikipedia.org/wiki/Availability_(system)
• Note: The term is used for repairable systems3)

Downtime (Td) is the Mission Duration times the sum of all of the different kinds of time required to transition from being down to the time to be fully operational, divided by the Mean Time Between Failure.

## DIDO Specifics

2)
The Multiplication Rule of Probability: Definition & Examples, Chapter 4, lesson 11, Accessed 3 July 2020, https://study.com/academy/lesson/the-multiplication-rule-of-probability-definition-examples-quiz.html