If a system comprised of two sub-systems in active redundancy (see Figure 4-3) is inspected every T time units and if, at the time of inspection, one of the sub-systems is discovered to have failed and is immediately replaced, then the system mean time to failure (MTTFS) instead of being given by equation (4.1) will be given by:

which, when both sub-systems have equal, constant failure rates, becomes:

If a plot is made of the variation of MTTFS with T, it is found that a graph of the following form is obtained:

From the above, the enormous benefit that can arise as the inspection interval is decreased can be seen. In fact, as T approaches zero, the value of MTTFS approaches infinity.

It should be noted that equation (4.7) is generally valid, but for the special case where RS(t)=exp(-λt) (no maintenance), MTTFS as given by equation (4.7) simplifies to 1/λ.