As noted earlier, when performing reliability analysis, all failed states should be treated as absorbing states. Figure 8-10 shows a state transition diagram for a two-component parallel system without system repair.

Following the procedure mentioned earlier, the Laplace transformation of P3(t) can be shown as:

Where s1 and s2 are negative and are the roots of the equation s2+s(3λ+μ)+2λ2, where s1.s2=2λ2.

This means:

According to the above procedure:

Because state 3 is the only failed state and s1.s2=2λ2, then:

If μ>>λ, then s2 will be numerically very much greater than s1.

Specifically:

Therefore:

Considering the same procedure, the reliability as well as the approximation of any system can be found.