Efficient reliability approximation for large k-out-of-n cold standby systems with position-dependent component lifetime distributions

Many real-world systems are heterogeneous k-out-of-n cold standby systems, like unmanned aerial vehicles performing a reconnaissance mission along multiple routes exposed to different environmental conditions. Reliability analysis of such systems is difficult and complicated. In this paper, efficient complete and partial approximation methods based on the central limit theorem are proposed for reliability analysis of k-out-of-n cold standby systems with position-dependent component lifetime distributions. Particularly, there are k online positions in the considered system with varying operating conditions and stress levels. The time-to-failure distribution of a component depends on the online position at which the component is working. The system fails when more than (n − k) components have failed. Case studies are performed to demonstrate the efficiency and accuracy of the proposed complete and partial approximation methods as compared to the existing convolution method. Influences of system parameters k and n and the component time-to-failure distribution parameter on the accuracy of the proposed complete approximation method are also demonstrated through empirical studies. Practice guidelines are provided based on performance studies of the proposed methods. The proposed approximation methods are also generalized by considering imperfect switchover.