Testing for NBUL using goodness of fit approach with applications

Abstract

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 demonstrate that applying the goodness of fit approach makes sense also for solving life testing problems and that result in simpler procedures that are asymptotically equivalent or better than standard ones. They may have superior finite sample behavior. A U-statistic is obtained for testing exponentiality against the new better than used in the Laplace transform order aging class (NBUL). The pitman asymptotic efficiency of (NBUL) is studied. The power and the critical values of the proposed statistic are calculated. Real examples are given to elucidate the use of the proposed test statistic in the reliability analysis. Finally, the problem with the right censored data is also handled with some applications.