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Exact and asymptotic tests of exponentiality against nonmonotonic mean time to failure type alternatives

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  • Ruhul Ali Khan

    (Indian Institute of Engineering Science and Technology)

  • Dhrubasish Bhattacharyya

    (Indian Institute of Engineering Science and Technology)

  • Murari Mitra

    (Indian Institute of Engineering Science and Technology)

Abstract

The performance and effectiveness of an age replacement policy can be assessed by its mean time to failure (MTTF) function. In this paper we propose a class of tests to detect trend change in MTTF function. We develop test statistics utilising a measure of deviation based on a weighted integral approach. We derive the exact and asymptotic distributions of our test statistics exploiting L-statistic theory and also establish the consistency of the test as a consequence of our results. A Monte Carlo study is conducted to evaluate the performance of the proposed test. Finally, we apply our test to some real life data sets for illustrative purposes.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:stpapr:v:62:y:2021:i:6:d:10.1007_s00362-021-01226-3
    DOI: 10.1007/s00362-021-01226-3
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    2. Tommaso Lando, 2022. "Testing convexity of the generalised hazard function," Statistical Papers, Springer, vol. 63(4), pages 1271-1289, August.

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