12. The system of claim 9 , wherein: the training module applies a metric to the Markov model for determining goodness of the Markov model; and training the Markov model for trend prediction comprises adjusting the state probabilities and transition probabilities to obtain substantially optimal performance of the Markov model according to the metric.
9. A system for identifying trends of fault occurrences in a manufacturing process with a Markov model, the system comprising: a plurality of modules wherein each module includes non-transitory computer-readable medium with an executable program stored thereon, the plurality of modules including: an input module configured to receive a plurality of data series and input parameters; a sort module configured to sort the plurality of data series to form a sorted plurality of data series, said data series including discrete data elements that identify the fault occurrences in the manufacturing process; a selection module configured to select data series from the sorted plurality of data series to form selected data series; a class development module configured to develop a plurality of classes from the selected data series and input parameters; and a binning and classification module configured to bin and classify the selected data series according to an input parameter and the plurality of classes, where the discrete data elements in each of the data series are classified into a particular bin depending on when they occurred, wherein the binning and classification module clusters the classified data series to iteratively arrange the data elements into clusters to meet a predetermined criteria, and wherein classifying the selected data series includes identifying the fault occurrences according to frequency of occurrence, mean time to repair and/or duration of downtime and selecting the most frequently occurring fault occurrences and/or the fault occurrences resulting in the longest downtime duration; a Markov model initialization module configured to initialize the Markov model for trend prediction including determining the number of known states in the Markov model based on the data series and associating a state of the Markov model for each class of data determined by the binned and classified data series; a Markov model training module configured to train the Markov model for trend prediction of the binned and classified data series to form a trained Markov model, said Markov model being trained to predict trends of the data series by determining the probability of states of the data as classified and binned and the probability of the transition of data from state to state where the state probabilities are calculated for the data series by evaluating a probability in a training window, wherein training the Markov model includes training the model to predict the frequency of occurrence, the mean time to repair and/or the downtime duration of the fault occurrences, using the model to predict frequency and/or duration of the fault occurrences during a testing period immediately succeeding a training period of the model, and evaluating the accuracy of the trend predictions by comparing the trend predictions during the testing period with actual data obtained during the testing period; an output module configured to output trend predictions upon deployment of the trained Markov model that identify predictions of fault occurrences that may occur during the manufacturing process; and updating the training of the model when new data is obtained during the manufacturing process.