Degradation modeling and classification of mixed populations using segmental continuous hidden Markov models.

With the market demands, the classification for highly reliable products becomes more and more significant. The degradation data can provide information about the degradation states and can be used to classify products to various classes according to the reliability attribute. In this paper, a temporal probabilistic approach, named segmental continuous hidden Markov model (SCHMM), is proposed to tackle the problem of degradation modeling and classification for mixed populations. Separate SCHMMs are built for each class of the mixed populations. The SCHMMs can directly depict the correspondence between actual degradation and the hidden states. A novel method called self-training algorithm for the preprocessing of the original data from the mixed populations is proposed. Furthermore, the unknown parameters of the SCHMMs are estimated by the maximum likelihood method with the complete degradation data. The root mean square error of the estimated degradation value compared with the actual physical degradation value, as well as Akaike information criterion and Bayesian information criterion, is used for the evolution of the fitting accuracy and the selection of model topologies and discretization methods. Then the maximum posterior probability-based classification criteria are developed. Degradation tests are designed for the data collection. To obtain the optimal classification policies, a cost function that consists of the degradation test cost and misclassification cost is constructed. A numerical example is used to illustrate the proposed method and demonstrate its advantages by comparing with other classification methods.