In this paper, system reliability is determined based on a K-map (Karnaugh map) and the Boolean algebra theory.  The proposed methodology incorporates the K-map technique for system level reliability, and Boolean analysis for interactions.  It considers not only the configuration of the production line, but also effectively incorporates the interactions between the machines composing the line.  Through the K-map, a binary argument is used for considering the interactions between the machines and a probability expression is found to assess the reliability of a bufferless production system.  The paper covers three main system design configurations: series, parallel and hybrid (mix of series and parallel).  In the parallel production system section, three strategies or methods are presented to find the system reliability.  These are the Split, the Overlap, and the Zeros methods.  A real-world case study from the automotive industry is presented to demonstrate the applicability of the approach used in this research work.