Reliability and Failure Probability Functions of the Consecutive-k-out-of-m-from-n: F System with Multiple Failure Criteria

Abstract

The consecutive-k-out-of-m-from-n: F system with multiple failure criteria consists of n sequentially ordered components (K= (k1, k2,..., kH), m = (m1, m2,..., mH)). The system fails if among any m1, m2,..., mH consecutive components there are at least k1, k2,..., kH components in the failed state. In this paper, the ordinary consecutive-k-out-of-m-from-n: F system played a pivotal role in achieving the reliability and failure probability functions of the consecutive-k-out-of-m-from-n: F linear and circular system with multiple failure criteria. We proved that the failure states of the multiple failure criteria system is a union of all failure state of the consecutive-ki-out-of-mi-from-n: F system, while the functioning state is an intersection of the functioning states of the consecutive-ki-out-of-mi-from-n: F system for . The maximum number of failed components of the functioning consecutive k-out-of-m-from-n: F system with multiple failure criteria is computed.