This paper presents the 'Subset Complement Addition Upper Bound' (SCAUB) procedure which produces upper bounds for probabilities of unions of n events given that probabilities of unions and/or intersections of subsets including up to k events are known. The SCAUB method is an extension of Hunter's (1976) improved Bonferroni bounds. The SCAUB inequality is much simplier to calculate than are other distribution free upper bounds proposed in the past. It is also a distribution free analog of Glaz and Johnson's (1984) product type bounds. We prove that for any fixed n events, the SCAUB inequality monotonically decreases with k. SCAUB upper bounds are applied to the multivariate normal (or t) simultaneous inference interval problem. © 1990.
Hoover, D. R. (1990). Subset complement addition upper bounds - an improved inclusion-exclusion method. Journal of Statistical Planning and Inference, 24(2), 195–202. https://doi.org/10.1016/0378-3758(90)90041-R