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Bathtub failure rates of mixtures in reliability and the Simes inequality under dependence in multiple testing

Wang, Jie (2008) Bathtub failure rates of mixtures in reliability and the Simes inequality under dependence in multiple testing. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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Two topics are presented in this dissertation: (1) obtaining bathtub-shaped failure rates from mixture models; and (2) the Simes inequality under dependence. The first topic is in the area of reliability theory. Bathtub-shaped failure rates are well-known in reliability due to their extensive applications for many electronic components, systems, products and even biological organisms. Here we derive some the conditions for obtaining bathtub-shaped failure rates distributions from mixtures, which have been utilized to model heterogeneous populations. In particular, we show that the mixtures of a family of exponential distributions and an IFR gamma distribution can yield distributions with bathtub-shaped failure rates.The second topic is concerned with the area of multiple testing, but uses dependence concepts important in reliability. Simes(1986) considered an improved Bonferroni test procedure based on the so-called Simes inequality. It has been proved that this inequality holds for independent multivariate distributions and a wide class of positively dependent distributions. However, as we show in this dissertation, the inequality reverses for a broad class of negatively dependent distributions. We also make some comments with regard to the Simes inequality and positive dependence.


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Item Type: University of Pittsburgh ETD
Status: Unpublished
CreatorsEmailPitt UsernameORCID
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee CoChairBlock, Henry W.hwb@pitt.eduHWB
Committee CoChairSavits, Thomas H.savits@pitt.eduSAVITS
Committee MemberTang, Gonggot1@pitt.eduGOT1
Committee MemberGleser, Leon J.gleser@pitt.eduGLESER
Date: 5 November 2008
Date Type: Completion
Defense Date: 2 June 2008
Approval Date: 5 November 2008
Submission Date: 25 June 2008
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Institution: University of Pittsburgh
Schools and Programs: Dietrich School of Arts and Sciences > Statistics
Degree: PhD - Doctor of Philosophy
Thesis Type: Doctoral Dissertation
Refereed: Yes
Uncontrolled Keywords: bathtub failure rate; mixtures; multiple testing procedures; Simes inequality
Other ID:, etd-06252008-105045
Date Deposited: 10 Nov 2011 19:48
Last Modified: 15 Nov 2016 13:45


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