Testing Whether New is Better Than Used
Abstract : A U-statistic J sub N is proposed for testing the hypothesis H sub O that a new item has stochastically the same life length as a used item of any age (i.e., the life distribution F is exponential), against the alternative hypothesis H sub 1 that a new item has stochastically greater life length (F(x) F(y) > or = F(x+y), for all x > or = 0, y > or = 0, where F = 1-F). J sub n is unbiased; in fact, under a partial ordering of H sub 1 distributions, J sub n is ordered stochastically in the same way. Consistency against H sub 1 alternatives is shown, and asymptotic relative efficiencies are computed. Small sample null tail probabilities are derived, and critical values are tabulated to permit application of the test. (Author)