DEVELOPING WAVELET-BASED METHODS FOR MONITORING IMAGES}

Statistical process control plays an impressive role in industries due to the growing complicated products and processes. This tool helps practitioners prevent the production of defected products and waste of money and time. Due to the importance of processes and inefficiency of methods based on human inspection, the use of image data for statistical process control has gained great attention among researchers in recent years. Image data have been applied by industries for many years for separating defected products and preventing them to get to customers. In recent years, some methods are proposed by researchers in the area of applying statistical features of image data in statistical process control. Image data analysis is decomposed into two categories: spatial domain and frequency domain. The main concentration of previous research studies in the area of process monitoring using image data is in the area of spatial domain analysis. This study has proposed three methods based on one-dimensional wavelet decomposition for monitoring image data with respect to frequency domain features. At each level of decomposition, wavelet transformation decomposes each signal into two elements including an approximation part (which is similar to the main signal and is performed as a low-pass filter) and a detail element (which is performed as a high-pass filter). The first method proposed in this paper only applies approximation coefficient for process monitoring. The second and third methods consider the detail coefficient by using hard thresholding and soft thresholding, respectively. These methods use a likelihood ratio-based statistic for process monitoring. Hence, they can show an out-of-control status and estimate the change point that is one of the most important diagnostic information. The performance of these methods is evaluated and compared with respect to the average run length and the difference between real and estimated changepoint criteria. Simulation studies are performed by using a textile image. Results showed a suitable degree of accuracy in detecting out of control status and estimating change points.