Providing Open Architecture High Availability Solutions

Equation 2.

Where C is the number of components in the system, and π is the average proportion of time

component i is under execution. It is the sum of each of the components failure rates, with a

compensator for its actual sojourn time.

Equation 2 may be used for both hardware and software system failure rate analysis. When just

hardware components are considered it is generally accepted that all components are running all

the time. All the π

terms equal 1 and Equation 2 simply becomes the sum of the failure rates of

each of the components, shown in Equation 3.

Equation 3.

For software systems and their components, the most challenging problem is how to estimate the

failure rates of each of the components.

In the previous section, the interaction between components was considered with an interpretive

view. Revisiting this model [Lyu96] shows that the failure rate at any of the interpreters, or

components can be derived via some vector arithmetic. Perhaps most importantly, the failure rate

of the system, also considered being the first layer interpreter, can be derived. In the simplest case

of a single software interpreter and a single hardware interpreter, and using the same assumptions

made above with regard to hardware components always running, the system failure rate can then

be approximated by:

Equation 4.

Where i is an iterator across all of the software components and j is an iterator across all the

hardware components.

λπ

i 1=

∑

λλ

i 1=

∑

λπ

i 1=

∑

j 1=

∑