An auto-framing method for stochastic process signals for fault detection by using a hidden Markov model based approach

There exist enormous amounts of newly information at each sampling time from processing equipment. Even though the information is mightily important to detect and diagnose the state of the equipment, their use is limited by the cost to gather, examine, and analyze them. Thus, there appears motivations to divide stochastic time-series signals into frames of different patterns and store only relevant statistical information for each frame. This so called “data framing” leads to significant data compression for easy storage and analysis. However, through visual inspection, the task for “data-framing” is inaccurate as well as cumbersome to perform it. In this work, stochastic signals are generalizaed using a hidden Markov model (HMM) and Markov Jump System (MJS), according to multiple models that switch randomly by underlying Markov chain. The most probable hidden path is reconstructed by using the recursive Expectation-Maximization (EM) algorithms. This optimal path can be one of the criteria for framing and statistical properties of each frame are analyzed and stored at the database. We have demonstrated the effectiveness of the HMM-based approach in auto-framing using realistic processing data from semiconductor industry.