Software reliability stands as a cornerstone in the development and deployment of dependable applications, with the advent of AI intensifying its significance. The intricacies introduced by AI software demand tailored reliability frameworks, yet the existing research lacks a comprehensive engineering methodology for ensuring AI software reliability. This paper leverages the structural foundation provided by the IEEE 1633-2016 software reliability activities framework, offering a holistic review of current AI software reliability studies. Starting with a foundational understanding, the subsequent sections delve into extant reliability frameworks such as IEEE 1633-2016, followed by an exploration into AI-specific considerations in reliability planning, failure mode modeling, reliability application in development and testing phases, support for release decisions, and post-deployment monitoring. The study underscores the paramount importance of pioneering and adopting AI-specific reliability engineering practices.