Question

Show mathematically using failure distribution how reliability, maintainability and availability are related?

Answer 1

Relationship Between Availability and Reliability

Availability is defined as the probability that the system is operating properly when it is requested for use. In other words, availability is the probability that a system is not failed or undergoing a repair action when it needs to be used. At first glance, it might seem that if a system has a high availability then it should also have a high reliability. However, this is not necessarily the case. This article will explore the relationship between availability and reliability and will also present some of the specified classifications of availability.

Availability and Reliability

Reliability represents the probability of components, parts and systems to perform their required functions for a desired period of time without failure in specified environments with a desired confidence. Reliability, in itself, does not account for any repair actions that may take place. Reliability accounts for the time that it will take the component, part or system to fail while it is operating. It does not reflect how long it will take to get the unit under repair back into working condition.

As stated earlier, availability represents the probability that the system is capable of conducting its required function when it is called upon given that it is not failed or undergoing a repair action. Therefore, not only is availability a function of reliability, but it is also a function of maintainability. Table 1 below displays the relationship between reliability, maintainability and availability. Please note that in this table, an increase in maintainability implies a decrease in the time it takes to perform maintenance actions

reliability	Maintainbility	Availability
Constant	decreases	decreases
Constant	increases	increases
Increases	constant	increases

Decreases	constant	decreases

Table 1: Relationship between reliability, maintainability and availability.

As you can see from the table, if the reliability is held constant, even at a high value, this does not directly imply a high availability. As the time to repair increases, the availability decreases. Even a system with a low reliability could have a high availability if the time to repair is short.

Availability Classifications

The definition of availability is somewhat flexible, depending on what types of downtimes are considered in the analysis. As a result, there are a number of different classifications of availability. In BlockSim 6, the following availabilities can be obtained directly from simulation or can be indirectly calculated with values returned from analysis:

Point (instantaneous) availability

Average up-time availability (mean availability)

Steady state availability

Operational availability