Consider a special -out-of- system, where k=n-1. Examples of this system include 2-out-of-3 and 3-out-of-4 systems. Figure 8-11 shows a state transition diagram for such a system. It has only three states (versus n states because all failed states have been merged into a single state.) In other words, once the system reaches a failed state where there are exactly two failed components, it cannot be repaired. Because the system has already failed, it is not necessary to consider the events that can occur in that state and hence the states that follow it.

Following the previous procedures:

The reliability expression for this system is similar to the reliability expression for the two-component parallel system. The only difference is that here, s1 and s2 are the roots of the equation s2+s{(2n-1)(λ+μ)}+n(n-1)λ2.

As in the case of the parallel system, the approximation to reliability is:

Therefore: