TESTING NEW BETTER THAN RENEWAL USED LIFE DISTRIBUTIONS BASED ON U-TEST

Abstract

In this paper, the problem of testing exponentiality against new better (worse) than renewal used in expectation is investigated and similarly for the case of nuharmonic new better than renewal used in expectation. For each of these two aging properties, a nonparametric procedure (U-statistic) is presented. Selected critical values are tabulated for sample sizes n = 5(1)30(10)50. The Pitman asymptotic relative efficiency to the test relative to other classes are studied. A real example is given to elucidate the use of the proposed test statistics for the reliability analysis.

Keywords:

• Efficiency
• Exponentiality
• Asymptotic normality
• U-test
• NBRUE
• HNBRUE

ACKNOWLEDGMENTS

The authors are greatly indebted to the referees and the editor for their constructive comments on the earlier version of the paper.