The number of failed components in a k-out-of-n system consisting of multiple types of components

Highlights: • k-out-of-n system consists of multiple types of components. • Mean number of failed components is studied. • Optimal number of components of each type are computed. • Optimal replacement time is computed. The number of failed components in a failed or operating system is a very useful quantity in terms of replacement and maintenance strategies. These quantities have been studied in several papers for a system consisting of identical components. In this paper, the number of failed components at the time when the system fails and the number of failed components when the system is working are considered for a well-known and widely applicable k-out-of-n structure. The system is assumed to have multiple types of components. That is, the system consists of components having nonidentical failure time distributions. Optimization problems are also formulated to find optimal values of the number of components of each type, and the optimal replacement time.