Optimal Stopping With Exact Confidence on Remaining Defects
S. R Dalal, C. L. Mallows · Technometrics · 2008
We derive a new class of stopping rules which may be helpful to buyers of software, testing for faults, or to buyers of large lots screening for defectives, or to database engineers converting a database from one schema to another. Suppose that a fixed but unknown number n of faults or defectives remain before testing. In the testing phase, these are observed at random times which are assumed to be iid exponentials with an unknown mean. Under this assumption, we derive several stopping rules that guarantee, for any chosen level α and integer m, that no matter what n is (provided only that n > m), with probability exactly 1 − α, when testing stops, no more than m faults remain in the product. We further show that one specific rule is most economical in the class of all scale-equivariant rules that satisfy the exact confidence property. We propose another class of rules, based on gaps, that can satisfy the exact confidence property.