arXiv:1503.08452v3 [math.ST] 2 Sep 2016 AN EXACT TEST FOR RENEWAL INCREASING MEAN RESIDUAL LIFE Sudheesh K Kattumannil Indian Statistical Institute, Chennai, India Abstract. In this paper, we develop an exact test for testing exponentiality against renewal increasing mean residual life class. Pitman’s asymptotic efficacy value shows that our test perform well. Some numerical results are presented to demonstrate the performance of the testing method. We also discuss how the pro- posed method incorporates the right censored observations. Keywords: Exponential distribution; Renewal increasing mean resid- ual life; Replacement model; Shock Model; U-statistics. 1. Introduction When a device is experiencing random number of shocks governed by a homogeneous Poisson process, the concept of renewal increasing mean residual life is very much useful to study the properties of age replace- ment model. In this context, test for exponentiality against renewal increasing mean residual life class is used to determine whether to adopt a planned replace model over unscheduled one. Sepehrifar et al. (2015) developed a non-parametric test against RIMRL shock class and obtained a critical region based on the asymptotic theory of U- statistics. We noted that the critical region developed by Sepehrifar et al. (2015) is incorrect (see Remark 2.1). Motivated by Sepehrifar et 1