Optimum Burn-in Time for a Bathtub Shaped Failure Distribution |
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Authors: | Mark Bebbington Chin-Diew Lai Ri?ardas Zitikis |
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Institution: | (1) Institute of Information Sciences and Technology, Massey University, Private Bag 11222, Palmerston North, New Zealand;(2) Department of Statistical and Actuarial Sciences, University of Western Ontario, London, Ontario, Canada, N6A 5B7 |
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Abstract: | An important problem in reliability is to define and estimate the optimal burn-in time. For bathtub shaped failure-rate lifetime
distributions, the optimal burn-in time is frequently defined as the point where the corresponding mean residual life function
achieves its maximum. For this point, we construct an empirical estimator and develop the corresponding statistical inferential
theory. Theoretical results are accompanied with simulation studies and applications to real data. Furthermore, we develop
a statistical inferential theory for the difference between the minimum point of the corresponding failure rate function and
the aforementioned maximum point of the mean residual life function. The difference measures the length of the time interval
after the optimal burn-in time during which the failure rate function continues to decrease and thus the burn-in process can
be stopped.
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Keywords: | Mean residual life Inference Burn-in Modified Weibull distribution |
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