A comment on consecutive-2-out-of-n systems

In 1986, Du and Hwang proved that the probability of failure in a cyclic double-loop system is always minimized by using some fixed arrangement σ* of the items. This arrangement σ* does not depend on the exact values of the failure probabilities of the items, but only on their relative ordering. In 1957, Supnick proved that the travelling salesman problem with certain specially structured distance matrices is always solved to optimality by the same permutation σ* of the cities. We show that the occurrence of the permutation σ* in the statement of both results is not a sheer coincidence: The result of Du and Hwang may be interpreted as a simple special case of Supnick's result.