Multi-state systems have received considerable attention recently with regards to reliability and maintenance. Since most mechanical equipment operates under some sort of stress or load, it tends to deteriorate or degrade over time, thus possibly resulting in discrete degradation states (damage degrees), ranging from perfect functioning to complete failure. This multi-state deterioration is the motivation for using condition monitoring tools for the purpose of modeling, diagnosis, prognosis, and condition-based maintenance. Most mechanical equipment is subject to multiple independent failure modes and degradation processes. Rather than independently diagnosing and prognosing the health condition of the equipment for a single failure mode, it is important to investigate how multi-dimensional condition monitoring information can be used for recognition purposes of the state of the health of equipment with multiple independent failure modes. This paper focuses on a non-repairable piece of equipment with multiple independent failure modes, in which the state of the equipment for each single failure mode is not directly observable and only incomplete information is available through condition monitoring. The main objective of this paper is to develop a method to obtain an observation probability matrix which can be used as the main tool for damage degree classification of each failure mode. An observation probability matrix represents the statistical relationship between the actual health state (damage degree and failure mode) of the equipment and the condition monitoring information. This observation probability matrix is an input for such methods, as hidden Markov models, hidden Semi-Markov models, and Naive Bayes classifiers. We modify the Naive Bayes classifier to use this observation probability matrix for classification. The result of this paper is applied for damage degree classification of a planetary gearbox, which is subject to multiple failure modes.