Rotary Indexing Machines (RIMs) are widely used in manufacturing due to their ability to perform multiple production steps on a single product without manual repositioning, reducing production time and improving accuracy and consistency. Despite their advantages, little research has been done on diagnosing faults in RIMs, especially from the perspective of the actual production steps carried out on these machines. Long downtimes due to failures are problematic, especially for smaller companies employing these machines. To address this gap, we propose a diagnosis algorithm based on the product perspective, which focuses on the product being processed by RIMs. The algorithm traces the steps that a product takes through the machine and is able to diagnose possible causes in case of failure. We also analyze the properties of RIMs and how these influence the diagnosis of faults in these machines. Our contributions are three-fold. Firstly, we provide an analysis of the properties of RIMs and how they influence the diagnosis of faults in these machines. Secondly, we suggest a diagnosis algorithm based on the product perspective capable of diagnosing faults in such a machine. Finally, we test this algorithm on a model of a rotary indexing machine, demonstrating its effectiveness in identifying faults and their root causes.