Cloud computing has brought about new service models and research opportunities in the manufacturing and service industries with advantages in ubiquitous accessibility, convenient scalability, and mobility. With the emerging industrial big data prompted by the advent of the internet of things and the wide implementation of sensor networks, the cloud computing paradigm can be utilized as a hosting platform for autonomous data mining and cognitive learning algorithms. For machine health monitoring and prognostics, we investigate the challenges imposed by industrial big data such as heterogeneous data format and complex machine working conditions and further propose a systematically designed framework as a guideline for implementing cloud-based machine health prognostics. Specifically, to ensure the effectiveness and adaptability of the cloud platform for machines under complex working conditions, two key design methodologies are presented which include the standardized feature extraction scheme and an adaptive prognostics algorithm. The proposed strategy is further demonstrated using a case study of machining processes.