[1] Wang Guanjun,. The NBEE and NWEE classes of lifetime distributionsand their properties [J]. Journal of Southeast University (English Edition), 2012, 28 (2): 251-255. [doi:10.3969/j.issn.1003-7985.2012.02.021]

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The NBEE and NWEE classes of lifetime distributionsand their properties()

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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:

28

Issue:

2012 2

Page:

251-255

Research Field:

Mathematics, Physics, Mechanics

Publishing date:

2012-06-30

Info

Title:

The NBEE and NWEE classes of lifetime distributionsand their properties

Author(s):

Wang Guanjun

Department of Mathematics, Southeast University, Nanjing 211189, China

Keywords:

lifetime distribution;  survival function;  closure property;  new better than equilibrium in expectation(NBEE);  equilibrium distribution;  shock model;  cumulative damage model

PACS:

O212.2

DOI:

10.3969/j.issn.1003-7985.2012.02.021

Abstract:

A class of lifetime distributions, new better than equilibrium in expectation(NBEE), and its dual, new worse than equilibrium in expectation(NWEE), are studied based on the comparison of the expectations of lifetime X and its equilibrium X_e. The relationships of the NBEE(NWEE)and other lifetime distribution classes are discussed. It is proved that the NBEE is very large, and increasing failure rate(IFR), new better than used(NBU)and the L class are its subclasses. The closure properties under two kinds of reliability operations, namely, convolution and mixture, are investigated. Furthermore, a Poisson shock model and a special cumulative model are also studied, in which the necessary and sufficient conditions for the NBEE(NWEE)lifetime distribution of the systems are established. In the homogenous Poisson shock model, the system lifetime belongs to NBEE(NWEE)if and only if the corresponding discrete failure distribution belongs to the discrete NBEE(NWEE). While in the cumulative model, the system has an NBEE lifetime if and only if the stochastic threshold of accumulated damage is NBEE.

References:

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Memo

Memo:

Biography: Wang Guanjun(1974—), male, doctor, associate professor, wgjmath@gmail.com.
Foundation item: The National Natural Science Foundation of China(No.10801032).
Citation: Wang Guanjun.The NBEE and NWEE classes of lifetime distributions and their properties[J].Journal of Southeast University(English Edition), 2012, 28(2):251-255.[doi:10.3969/j.issn.1003-7985.2012.02.021]

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