Features extraction and analysis for classifying causable patterns in control charts

Obtaining adequate features is a critical step in classifying causable patterns in control charts. Various methods were developed to extract features that maximize the inter-class variability while minimizing the intra-class variations. Most of these methods are based on either time or frequency domain analysis. As a multi-resolution analysis approach, wavelet transform was considered to exploit the joint time-frequency characteristics of the patterns. However, the effectiveness of the features obtained by multi-resolution wavelet analysis (MRWA) suffers from the frequency leakage among the different spectral bands. This phenomenon is inherent in wavelet analysis regardless of the choice of the mother wavelet. Cross-band frequency leakage smears the band-specific information, which may yield less distinguishing features, especially for short-time observation patterns. In this work we introduce a multi-resolution analysis approach based on discrete cosine transform (DCT) that overcomes the problems associated with MRWA. We also verify that the classification rates of shift, trend, and cyclic causable patterns using multi-resolution DCT (MRDCT) features are higher than those obtained using MRWA features. Furthermore, the computational requirements for MRDCT are notably less than those needed for MRWA. Artificial neural network (ANN) classifier was used with both feature extraction methods.