With the rise in customized product demands, the production of small batches with a wide variety of products is becoming more common. A high degree of flexibility is required from operators to manage changes in volumes and products, which has led to the use of Human-Robot Collaboration (HRC) systems for custom manufacturing. However, this variety introduces complexity that affects production time, cost, and quality. To address this issue, multivariate control charts are used as diagnostic tools to evaluate the stability of several parameters related to both product/process and human well-being in HRC systems. These key parameters monitored include assembly time, quality control time, total defects, and operator stress, providing a more holistic view of system performance. Real-time monitoring of process performance along with human-related factors, which is rarely considered in statistical process control, provides comprehensive stability control over all customized product variants produced in the HRC system. The proposed approach includes defining the parameters to be monitored, constructing control charts, collecting data after product variant assembly, and verifying that the set of parameters is under control via control charts. This increases the system's responsiveness to both process inefficiencies and human well-being. The procedure can be automated by embedding control chart routines in the software of the HRC system or its digital twin, without adding additional tasks to the operator's workload. Its practicality and effectiveness are evidenced in custom electronic board assembly, highlighting its role in optimizing HRC system performance.