A life distribution F is an increasing failure rate average (IFRA) ifFor testing H0: F is exponential, versus H1F is IFRA, but not exponential based on randomly censored data, we propose a test statistics whereis the KAPLAN–MIEER Product limit estimator of F. The asymptotic normality of Jnc(b) is established and an asymptotically distribution – free test is obtained. /The efficiency loss due to ocensoring is studied compared to DESHPANDE'S (1983) test uncensored case. The asymptotic relati ve efficiency with respect to CHEN,HOLLANDER AND LANGBERG'S (1983) test is shoen to be reasonably high