Purpose: Many organizations report difficulties in integrating lean. A possible cause could be that methods and tools do not support each other. The purpose of this research is, therefore, to explore the nature of the connections within the system. Understanding these provides practitioners with a better way of defining their system and offers researchers a conceptual model with a new way of understanding a company-specific production system (XPS). Design/methodology/approach: The study is designed as a multiple case study with three organizations and, in total, 25 lean experts serving as respondents. Findings: The connections between the elements of an XPS act as a duality based on a problem–solution (P–S) relation. These are categorized according to complexity and can be mapped into a conceptual model, where the connections can be either symmetrical or asymmetrical. Research limitations/implications: The results provide a method to analyze causes and effects in an XPS and a conceptual model. Given the limitations of a multiple case study, future research should explore connections depending on a broader variety of contextual conditions. Practical implications: The results present a way to avoid a cherry-picking problem through understanding connections between elements in an XPS. This provides a new way to understand the weaknesses of an XPS. Originality/value: The research provides a new approach with insights on how to conduct research in lean production by facilitating how to understand and interpret connections between elements in a system.