A Goodness of Fit Approach to NBURFR and NBARFR Classes

Most of the approaches suggested during the last decades for solving life testing problems are markedly different from those used in the related but wider area of goodness of fit problems. In this paper, it is demonstrated that applying the goodness of fit approach makes sense also for solving life testing problems and that it results in simpler procedures that are asymptotically equivalent or better than standard ones. They may also have superior finite sample behavior. Testing exponentiality against the class of “new better than used renewal failure rate” (NBURFR) or “new better than used average renewal failure rate” (NBARFR) as proposed by Abouammoh and Ahmed [Statistcs & Probability Letter 14: 211-217, 1992] are addressed here. The asymptotic properties are derived for these tests in the case of complete data. The censored data case is also studied. A practical application of the tests to data taken from medical sciences is presented.