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A simple non-parametric test for decreasing mean time to failure


In this paper, we develop a simple non-parametric test for testing exponentiality 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.

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The author Sudheesh K. Kattumannil is thankful to Indo-US Science and Technology Forum and Department of Science and Technology, Government of India for the financial assistant provided to carry out this research work at Michigan State University. We also thank anonymous referees for their constructive suggestions.

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Correspondence to Sudheesh K. Kattumannil.

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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.

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Kattumannil, S.K., Anisha, P. A simple non-parametric test for decreasing mean time to failure. Stat Papers 60, 73–87 (2019).

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  • Exponential distribution
  • Mean time to failure
  • Pitman’s asymptotic efficacy
  • Replacement model
  • U-statistics