Consistency of FOSSA procedures

Establish consistency for the broad class of fragmented one-shot screening for acceptability (FOSSA) procedures, specifically showing that each FOSSA procedure asymptotically screens out every system whose true response configuration lies outside the closure of that system’s acceptable region, under suitable conditions on the confidence regions.

Background

The paper defines a screening procedure as consistent when, as the minimum sample size across systems tends to infinity, the probability of returning any system whose true response configuration is outside the closure of its acceptable region converges to zero. The authors explain that consistency is difficult to establish for OSSA procedures in full generality because it depends on the particular acceptability definition and on stronger properties of the confidence regions.

For FOSSA procedures, the relevant sufficient behavior is that the favorable configurations used for screening converge to a point or set outside the unacceptable system’s acceptable region. The paper reports that all FOSSA procedures evaluated numerically can be shown to be consistent, but explicitly presents consistency for the vast majority of FOSSA procedures as a conjecture rather than a general theorem.