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 - <p style="text-align: justify;">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.</p>