Abstract
Most practical systems consist of multiple types of components although the components perform the same task within the system. The analysis of such systems is more challenging than the systems with single type of components. In this paper, we present expressions for the survival function of the failure time, and mean time to failure of the system under the general case when the random failure times of components of the same type are exchangeable dependent and the random failure times of components of different type are dependent. As a case study, we apply our results to linear consecutive- $k$ -out-of- $n$ :F systems consisting of three different types of dependent components.
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