I created this post from one of my blogs on Availability, as per the suggestions that calculating Availability is tricky and a separate blog should be there for calculating or predicting the availability.

Consider a System with 3 subsystems/components A, B, and C. The component B is a combination of components B1 and B2. Here A, B, and C are in series and component B1 and B2 are in Parallel.

Components of a sub system, are called operating in series if failure of any of the components causes failure of the sub system. In such case, multiply the availability (A) of components, to find availability of the Sub system. A_{substem}= A_{component_1} x A_{component_2}

In this case, component A, B, C are working in series. Hence the availability of complete system will be

A_{system} = A_{A} x A_{B} x A_{C}

Components of a sub system, are called operating in parallel if failure of ALL components causes failure of the sub system. In such cases if a components fails, other components take over. In such case, multiply the Unavailability (UA) of components, to find availability of the Sub system.

A_{substem}= 1- (UA_{component_1} x UA_{component_2 x ………} UA_{component_n)}

_{ }Where UA_{component}= 1-A_{component}

Now let’s use the above formula to find the availability of component B, which is set of two components.

A_{B} = 1- (1-A_{B1}) x (1-A_{B2})

Hence to calculate the Availability of above sample system, following are the steps.

Availability = A_{A} x A_{B} x A_{C }

= A_{A} x {1- (1-A_{B1}) x (1-A_{B2})} x A_{C}

= 99.00% x {1- (1-99.00%) x (1-99.99%)} x 99.99%

= 99.00% x 99.9999% x 99.99%

= 98.99%