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

Author

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  • Sudheesh K. Kattumannil

    (Indian Statistical Institute)

  • P. Anisha

    (Georgia Regents University)

Abstract

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.

Suggested Citation

  • Sudheesh K. Kattumannil & P. Anisha, 2019. "A simple non-parametric test for decreasing mean time to failure," Statistical Papers, Springer, vol. 60(1), pages 73-87, February.
    • Handle: RePEc:spr:stpapr:v:60:y:2019:i:1:d:10.1007_s00362-016-0827-y
    DOI: 10.1007/s00362-016-0827-y
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    References listed on IDEAS

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    1. Somnath Datta & Dipankar Bandyopadhyay & Glen A. Satten, 2010. "Inverse Probability of Censoring Weighted U‐statistics for Right‐Censored Data with an Application to Testing Hypotheses," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(4), pages 680-700, December.
    2. Xiaohu Li & Maochao Xu, 2008. "Reversed hazard rate order of equilibrium distributions and a related aging notion," Statistical Papers, Springer, vol. 49(4), pages 749-767, October.
    3. Norbert Henze & Simos G. Meintanis, 2005. "Recent and classical tests for exponentiality: a partial review with comparisons," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 61(1), pages 29-45, February.
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    Cited by:

    1. Ruhul Ali Khan & Dhrubasish Bhattacharyya & Murari Mitra, 2021. "Exact and asymptotic tests of exponentiality against nonmonotonic mean time to failure type alternatives," Statistical Papers, Springer, vol. 62(6), pages 3015-3045, December.
    2. Kanchan Jain & Sudheesh K. Kattumannil & Anjana Rajagopal, 2023. "Replacement model with random replacement time," Statistical Papers, Springer, vol. 64(1), pages 1-15, February.
    3. Marija Cuparić & Bojana Milošević, 2022. "New characterization-based exponentiality tests for randomly censored data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(2), pages 461-487, June.
    4. Bhattacharyya, Dhrubasish & Khan, Ruhul Ali & Mitra, Murari, 2020. "A test of exponentiality against DMTTF alternatives via L-statistics," Statistics & Probability Letters, Elsevier, vol. 165(C).

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