August 1980 SOME TESTS AGAINST AGING BASED ON THE TOTAL TIME ON TEST TRANSFORM by

Let F be a life distribution with survival function F = 1 F and 00 — finite mean y * j n F(x)dx. The scaled total time on test transform -1 F ( t ) — <P,,(t) = /n /F(x)dx/y was introduced by Barlow and Campo (1975) as a r U tool in the statistical analysis of life data. The properties IFR, IFRA, NBUE, DMRL and heavy-tailedness can be translated to properties of tp„(t). r We discuss the previously known of these relationships and present some new results. Guided by properties of <P„(t) we suggest some test statistics r for testing exponentiality against IFR, IFRA, NBUE, DMRL and heavy-tailedness, respectively. The asymptotic distributions of the statistics are derived and the asymptotic efficiencies of the tests are studied. The power for some of the tests is estimated by simulation for some alterna­ tives when the sample size is n = 10 or n = 20.