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

Ruhul Ali Khan (), Dhrubasish Bhattacharyya () and Murari Mitra ()
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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

Statistical Papers, 2021, vol. 62, issue 6, No 20, 3015-3045

Abstract: 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.

Keywords: Life distribution; Nonmonotonic ageing; Age replacement policy; Turning point; IDMTTF class; L-statistic; Asymptotic normality.; 62G10; 90B25; 62N05 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s00362-021-01226-3

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