Reliability computing method for generalized k-out-of-n system

The generalized k-out-of-n: F system (G(k,n:F)) consists of N modules ordered in a line or circle. The ith module is composed of ni components in parallel (ni⩾1,i=1,2,…,N). The G(k,n:F) fails if and only if there exist at least f failed components or if there exist at least k consecutive failed modules. To evaluate the reliability of G(k,n:F), we introduce the concept of a generalized sequence of multivariate Bernoulli trials (GMVBT) and define the bivariate run statistic based on this sequence. We bring out the relation between the probability distribution of the bivariate run statistic and the reliability of G(k,n:F). We demonstrate the evaluation of reliability of G(k,n:F) and some other related systems through a numerical example.