| Abstract: | We consider a model when a process involving the production of elements is under inspection. The elements have possible failures due to competing risks. We assume the availability of a data set of failure times, D1, obtained when the process is under control. Our main goal is to test if the failure rates in D1 are equal to or less than the failure rates in another data set D2, against undesirable neighbouring alternatives. A class of tests based on a two-dimensional vector statistic is obtained. Linear test statistics with weight functions giving optimal local asymptotic power are derived. Martingale techniques are used. An example illustrates the derivation of reasonable tests |
