Non-minimal sums of disjoint products

摘要

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 notarise from the familiar tautology M_1 + … + M_n ≡ M_1 + (M_2M_1) + (M_3M_2M_1) + … + (M_nM_(n-1) …M_1).