Replicated Paired Comparisons Between Two Objects: The (k, r) - Series
Abstract The problem considered here is selecting the better of two objects based on a series of replicated paired comparisons between the objects. A (k, r)-series, a generalization of the ordinary k-series, is defined as a sequential selection procedure such that the object selected is the first one to win k comparisons, provided it is ahead by at least r comparisons. The relationship of a (k, r)-series to Wald's sequential probability ratio test (SPRT) is discussed and this relationship is exploited to derive formulas for the probability of correct selection and the expected number of comparisons required. The “optimal” (k, r)-series is derived with respect to two loss functions.