Non-minimal sums of disjoint products

We refine a conjecture of M.O. Locks and J.M. Wilson [Reliab Eng Syst Saf 1994;46:283–286] regarding disjoint forms of the Abraham reliability problem. We also present other examples of reliability problems with the interesting property that their minimal disjoint forms do not arise from the familiar tautology M 1 + ⋯ + M n ≡ M 1 + ( M 2 M ¯ 1 ) + ( M 3 M ¯ 2 M ¯ 1 ) + ⋯ + ( M n M ¯ n − 1 ⋯ M ¯ 1 ) .