Availability
Consider a two-component repairable system in which the two components are identical. Initially, assume that both of the components are working (state 1). Either of the components leads the system to a state where there is only one working component (state 2). Because each component can fail with failure rate , failure of any one of the components is 2λ. (This is similar to the failure rate of a series system with two identical components.) This technique is known as state merging.
In state 2, two events can exist:
• The working component can fail, which causes the system to reach a failed state (state 3) where both components are failed.
• The failed component can be repaired, and the system returns to state 1.
In state 3, both the components are under repair. If either of the components is repaired, then the system reaches state 2. As in the case of failure rate, here, the effective transition rate is 2μ. Figure 8-9 shows the state transition diagram for the two-component parallel system.
 | Although the availability of this system can be found using combinatorial models, the exact reliability cannot. |
Using the previous procedures results in:
Because state 3 is the only failed state:
If μ>>λ, then:
Using the previous procedures, the availability of any system can be found. However, it is advisable to use combinatorial models whenever possible.