Geodesic
On reliability analysis of consecutive $k$-out-of-$n$ systems with arbitrarily dependent components
Applications of Mathematics, Tome 61 (2016) no. 5, pp. 565-584.

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In this paper, we consider the linear and circular consecutive $k$-out-of-$n$ systems consisting of arbitrarily dependent components. Under the condition that at least $n-r+1$ components ($r\leq n$) of the system are working at time $t$, we study the reliability properties of the residual lifetime of such systems. Also, we present some stochastic ordering properties of residual lifetime of consecutive $k$-out-of-$n$ systems. In the following, we investigate the inactivity time of the component with lifetime $T_{r:n}$ at the system level for the consecutive $k$-out-of-$n$ systems under the condition that the system is not working at time $t>0$, and obtain some stochastic properties of this conditional random variable.
DOI : 10.1007/s10492-016-0147-5
Classification : 60E05, 60E15, 60K10, 62N05
Keywords: residual lifetime; inactivity time; stochastic order; dependence; reliability 
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Salehi, Ebrahim. On reliability analysis of consecutive $k$-out-of-$n$ systems with arbitrarily dependent components. Applications of Mathematics, Tome 61 (2016) no. 5, pp. 565-584. doi : 10.1007/s10492-016-0147-5. http://geodesic.mathdoc.fr/articles/10.1007/s10492-016-0147-5/

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