SUMMARYScalograms provide measures of signal energy at various frequency bands and are commonly used in decision making in many fields including signal and image processing, astronomy and metrology. This article extends the scalogram's ability for handling noisy and possibly massive data. The proposed thresholded scalogram is built on the fast wavelet transform, which can capture non-stationary changes in data patterns effectively and efficiently. The asymptotic distribution of the thresholded scalogram is derived. This leads to large sample confidence intervals that are useful in detecting process faults statistically, based on scalogram signatures. Application of the scalogram-based data mining procedure (mainly, classification and regression trees) demonstrates the potential of the proposed methods for analysing complicated signals for making engineering decisions.
A method is provided and demonstrated for robust design of the batch dyeing process. This method is used to identify optimal batch dyeing process parameter settings which produce target color with the least color variation within and among dyed fabric pieces. The robust design problem is defined in terms of the design objectives, control factors and noise factors. Performance measures are presented to evaluate mean and dispersion characteristics of the dyeing output. Design and conduct of experiments are discussed for developing empirical models of the performance measures, and these models are developed for the study case. The robust design problem is formulated and solved as a nonlinear programming problem. Confirmation of results and iterative use of the proposed design method are discussed.
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