Hypothesis testing of equality between exponential distributions with matched sets

In matched design, if the unit cost from one comparison group is higher than the unit cost from the other group, then one can consider matching each unit randomly selected from the former with more than one unit from the latter, to increase power of the test. This paper extends the discussion on testing equality between exponential distributions for one-to-one paired design to that for K-to-one matched design, where K can be any finite positive integer. This paper considers the asymptotic test procedure using the central limit and Fieller's theorems (CLFT), the asymptotic test procedure using the marginal likelihood ratio test (MLRT), an exact parametric test (EXPT) and applies Monte Carlo simulation to evaluate the performance of these procedures. When the number of matched sets, n, is as small as 10, the estimated type-I error for the two asymptotic procedures can still agree well with the nominal level. When the number of matched units, K, exceeds 4, the effect due to an increase in K on power generally becomes minimal. When the intra-class correlation between failure times within matched sets is small, using the CLFT generally has larger power than using either the MLRT or EXPT in one-to-one paired design. On the other hand, when the intra-class correlation between failure times within matched sets is large, the power for the MLRT is higher than the power for both the CLFT and EXPT in almost all the situations considered in this paper. Hence the author recommends the MLRT.