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Volume 50, Issue 1
Conditional Residual Lifetimes of $(n-k+1)$-out-of-$n$ Systems with Mixed Erlang Components

Wenyong Gui, Rongtan Huang, Jianhua Lin & X. Sheldon Lin

DOI: 10.4208/jms.v50n1.17.01

J. Math. Study, 50 (2017), pp. 1-16.

Published online: 2017-03

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  • Abstract

We consider an $(n-k+1)$-out-of-$n$ system with component lifetimes being correlated. The main objective of this paper is to study the conditional residual lifetime of an $(n-k+1)$-out-of-$n$ system, given that at a fixed time a certain number of components have failed, assuming that the component lifetimes follow a multivariate Erlang mixture. Comparison studies of the stochastic ordering of the $(n-k+1)$-out-of-$n$ system are presented. Several examples are presented to illustrate and confirm our results.

  • Keywords

Conditional mean residual lifetime, multivariate Erlang mixture, $(n-k+1)$-out-of-$n$ system, dependence structure, exchangeable variables.

  • AMS Subject Headings

62G03, 62P30, 62H20

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

19020130154168@stu.xmu.edu.cn (Wenyong Gui)

rthuang@xmu.edu.cn (Rongtan Huang)

jianhualin@xmu.edu.cn (Jianhua Lin)

sheldon@utstat.utoronto.ca (X. Sheldon Lin)

  • BibTex
  • RIS
  • TXT
@Article{JMS-50-1, author = {Gui , WenyongHuang , RongtanLin , Jianhua and Lin , X. Sheldon}, title = {Conditional Residual Lifetimes of $(n-k+1)$-out-of-$n$ Systems with Mixed Erlang Components}, journal = {Journal of Mathematical Study}, year = {2017}, volume = {50}, number = {1}, pages = {1--16}, abstract = {

We consider an $(n-k+1)$-out-of-$n$ system with component lifetimes being correlated. The main objective of this paper is to study the conditional residual lifetime of an $(n-k+1)$-out-of-$n$ system, given that at a fixed time a certain number of components have failed, assuming that the component lifetimes follow a multivariate Erlang mixture. Comparison studies of the stochastic ordering of the $(n-k+1)$-out-of-$n$ system are presented. Several examples are presented to illustrate and confirm our results.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v50n1.17.01}, url = {http://global-sci.org/intro/article_detail/jms/976.html} }
TY - JOUR T1 - Conditional Residual Lifetimes of $(n-k+1)$-out-of-$n$ Systems with Mixed Erlang Components AU - Gui , Wenyong AU - Huang , Rongtan AU - Lin , Jianhua AU - Lin , X. Sheldon JO - Journal of Mathematical Study VL - 1 SP - 1 EP - 16 PY - 2017 DA - 2017/03 SN - 50 DO - http://doi.org/10.4208/jms.v50n1.17.01 UR - https://global-sci.org/intro/article_detail/jms/976.html KW - Conditional mean residual lifetime, multivariate Erlang mixture, $(n-k+1)$-out-of-$n$ system, dependence structure, exchangeable variables. AB -

We consider an $(n-k+1)$-out-of-$n$ system with component lifetimes being correlated. The main objective of this paper is to study the conditional residual lifetime of an $(n-k+1)$-out-of-$n$ system, given that at a fixed time a certain number of components have failed, assuming that the component lifetimes follow a multivariate Erlang mixture. Comparison studies of the stochastic ordering of the $(n-k+1)$-out-of-$n$ system are presented. Several examples are presented to illustrate and confirm our results.

Gui , WenyongHuang , RongtanLin , Jianhua and Lin , X. Sheldon. (2017). Conditional Residual Lifetimes of $(n-k+1)$-out-of-$n$ Systems with Mixed Erlang Components. Journal of Mathematical Study. 50 (1). 1-16. doi:10.4208/jms.v50n1.17.01
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