| Abstract: | This paper discusses interval estimation for the ratio of the mean failure times on the basis of paired exponential observations. This paper considers five interval estimators: the confidence interval using an idea similar to Fieller's theorem (CIFT), the confidence interval using an exact parametric test (CIEP), the confidence interval using the marginal likelihood ratio test (CILR), the confidence interval assuming no matching effect (CINM), and the confidence interval using a locally most powerful test (CIMP). To evaluate and compare the performance of these five interval estimators, this paper applies Monte Carlo simulation. This paper notes that with respect to the coverage probability, use of the CIFT, CILR, or CIMP, although which are all derived based on large sample theory, can perform well even when the number of pairs n is as small as 10. As compared with use of the CILR, this paper finds that use of the CIEP with equal tail probabilities is likely to lose efficiency. However, this loss can be reduced by using the optimal tail probabilities to minimize the average length when n is small (<20). This paper further notes that use of the CIMP is preferable to the CIEP in a variety of situations considered here. In fact, the average length of the CIMP with use of the optimal tail probabilities can even be shorter than that of the CILR. When the intraclass correlation between failure times within pairs is 0 (i.e., the failure times within the same pair are independent), the CINM, which is derived for two independent samples, is certainly the best one among the five interval estimators considered here. When there is an intraclass correlation but which is small (<0.10), the CIFT is recommended for obtaining a relatively short interval estimate without sacrificing the loss of the coverage probability. When the intraclass correlation is moderate or large, either the CILR or the CIMP with the optimal tail probabilities is preferable to the others. This paper also notes that if the intraclass correlation between failure times within pairs is large, use of the CINM can be misleading, especially when the number of pairs is large. |
