Operational metrics for Machine Learning Systems (MLSystems) are crucial for maintaining consistent performance in real-world applications. However, achieving this reliability is challenging due to the need for standardized metrics designed for MLSystems functioning in dynamic and uncertain conditions. This literature survey explores reliable MLSystems, aiming to unify the current advancements, highlight knowledge gaps, and suggest future research paths for reliable MLSystems. Our research highlights significant advancements in developing Self-Adaptive System (SAS) architectures focused on MLSystem applications. The survey underscores the importance of contemporary software engineering standards, SAS architectures, and N-Version Programming (NVP) in attaining reliable MLSystems. However, more attention is required on operational metrics that capture upstream stimuli and downstream responses. Thus, a major challenge lies in creating a reliable MLSystem that operates independently of the Machine Learning (ML) artifact, ensuring that upstream sources produce expected downstream responses, even in a changing environment. The paper advocates for architectural focus, ensuring reliable MLSystem metrics from real-world case studies. This research trajectory lays a foundation for future reliable MLSystem studies, aiming to improve the Technology Readiness Level (TRL) for predictive manufacturing, diagnostics, and electricity grid management applications.