Abstract
This paper considers a problem where lots are coming independently and sequentially for testing their quality, and at each stage a lot is accepted as reliable if and only if the mean life 0 of items is at least 00, a specified standard required by the practitioner, and the penality for making an incorrect decision is taken as proportional to the distance the true 0 is away from 00. When the prior distribution of 0 remains unknown at each stage (hence the minimum risk Bayes optimal test procedure is not available for use at any stage), this paper provides asymptotically optimal empirical Bayes procedures for situations where life time distribution has negative exponential or gamma density and investigates the rates of convergence to optimality. We also consider the case where the life time distribution has density belonging to general exponential family, and the case where one has to deal with k varieties of lots simultaneously at each stage.
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© 1998 Springer Science+Business Media New York
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Singh, R.S. (1998). Empirical Bayes Procedures For Testing The Quality and Reliability With Respect To Mean Life. In: Abraham, B. (eds) Quality Improvement Through Statistical Methods. Statistics for Industry and Technology. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1776-3_30
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DOI: https://doi.org/10.1007/978-1-4612-1776-3_30
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-7277-9
Online ISBN: 978-1-4612-1776-3
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