Data-driven methods for fault detection and diagnostics (FDD) require a large amount of labeled data and knowledge about complete failure modes set to train a reliable classifier as well as require the same label space in an online testing phase. Typical supervised classifiers in FDD can only predict precedented faults, limiting their performance in identifying unprecedented failure modes in on-line testing data. In addition, in most applications, it may be expensive and time-consuming to obtain sufficient labeled samples. This study focuses on fault detection and diagnosis without sufficient labels or prior knowledge of the complete set of failure modes. This paper proposes a novel FDD framework using active learning and semi-supervised learning to detect both precedented and unprecedented failures with minimum labeling effort. The effectiveness of proposed approach is demonstrated and validated using a synthetic condition monitoring dataset.