Stat Papers DOI 10.1007/s00362-016-0827-y REGULAR ARTICLE A simple non-parametric test for decreasing mean time to failure Sudheesh K. Kattumannil 1 · P. Anisha 2 Received: 3 September 2015 / Revised: 27 July 2016 © Springer-Verlag Berlin Heidelberg 2016 Abstract In this paper, we develop a simple non-parametric test for testing exponen- tiality against decreasing mean time to failure class alternatives. We derive the exact null distribution of the test statistic and find the critical values for different sample sizes. Asymptotic properties of the test statistics are studied. The test is compared with some other test by evaluating Pitman’s asymptotic efficacy. We also discuss how the proposed method takes the censoring information into consideration. Finally, some numerical results are presented and the test procedure is illustrated using a real data. Keywords Exponential distribution · Mean time to failure · Pitman’s asymptotic efficacy · Replacement model · U-statistics 1 Introduction Many results in life testing are based on the assumption that the lifetime of a product is described through exponential distribution. This assumption implies that a used item is stochastically as good as a new one and hence no need for replacing a working unit. However, this is not always a realistic assumption and it is important to know which life distribution deserves membership benefits of an ageing class. In this scenario, tests for exponentiality designed to detect the appropriate alternative hypothesis have This work was initiated while Sudheesh K. Kattumannil was visiting Prof. Hira L Koul, Department of Statistics and Probability, Michigan State University, under IUSSTF Fellowship. B Sudheesh K. Kattumannil skkattu@isichennai.res.in 1 Indian Statistical Institute, Chennai, India 2 Department of Biostatistics and Epidemiology, Georgia Regents University, Augusta, USA 123