As a new maintenance method, CBM (condition based maintenance) is becoming more and more important for the health management of complicated and costly equipment. A prerequisite to widespread deployment of CBM technology and practice in industry is effective diagnostics and prognostics. Recently, a pattern recognition technique called HMM (hidden Markov model) was widely used in many fields. However, due to some unrealistic assumptions, diagnositic results from HMM were not so good, and it was difficult to use HMM directly for prognosis. By relaxing the unrealistic assumptions in HMM, this paper presents a novel approach to equipment health management based on auto-regressive hidden semi-Markov model (AR-HSMM). Compared with HMM, AR-HSMM has three advantages: 1) It allows explicitly modeling the time duration of the hidden states and therefore is capable of prognosis. 2) It can relax observations’ independence assumption by accommodating a link between consecutive observations. 3) It does not follow the unrealistic Markov chain's memoryless assumption and therefore provides more powerful modeling and analysis capability for real problems. To facilitate the computation in the proposed AR-HSMM-based diagnostics and prognostics, new forwardbackward variables are defined and a modified forward-backward algorithm is developed. The evaluation of the proposed methodology was carried out through a real world application case study: health diagnosis and prognosis of hydraulic pumps in Caterpillar Inc. The testing results show that the proposed new approach based on AR-HSMM is effective and can provide useful support for the decisionmaking in equipment health management.