Statistical methods for heterogeneous profile data analytics in quality engineering applications

Abstract

Statistical process control (SPC) is an important and popular set of techniques for quality improvement in various engineering applications. With the recent development of production processes and sensing technologies, in an increasing number of modern industrial cases, the quality characteristics of a process or product can be well summarized by a profile which is defined as a relationship or function between a response variable and one or a few explanatory variables. Compared to univarite scalars and multivariate vectors, profile data convey much more complete and detailed quality information, and have evolved to be one of the most active research areas in SPC. This thesis is devoted to developing new SPC methodologies for profile data analytics. Particularly, an wide array of heterogeneous profile data of unique and complicated structures are systematically considered. Due to complex process mechanisms or diverse measurement capabilities in modern quality applications, the profile data may be of multiple functional forms or be collected at distinct accuracy levels. This heterogeneity of profile data results in a broad class of new challenges which have been successfully addressed in this thesis by the proposed novel statistical modeling and monitoring methods. Specifically, this thesis consists of four original research essays which belong to two categories and divide the thesis into two parts. The first part concerns the profile data generated in the heterogeneous production processes that have multiple operating conditions. To monitor multi-type shape profiles in the first essay, a registration-free approach is proposed to effectively extract features from each shape type, and a Gaussian mixture model is used to capture the heterogeneity of feature vectors. An adaptive control chart is developed to monitor the multi-modal density functions in the second essay, where the likelihood function is incorporated with two penalties to infer the subpopulation parameters and the number of subpopulations simultaneously. In this way, the process changes in the model parameters as well as in the model order can be both quickly detected. In the second part, the heterogeneous profile data result from the diverse or inconsistent measuring capabilities of measurement systems. To cheaply and reliably collect shape profile or surface data when both the high-end and low-end measurement devices are available, the third essay proposes a Bayesian generative model which parameterizes the two-resolution measurement data, based on which the accuracy of a new profile of low-resolution can be greatly improved. In the final essay, a fast in computation and robust to outliers kernel smoothing method is designed, and then a control chart is developed to monitor the free-form complex surface scanning data. The four essays above provide feasible and novel solutions to offline modeling and online monitoring of the heterogeneous profile data, the superiority of which is verified in extensive numerical Monte Carlo simulations as well as in real example studies.

Date of Award	2018
Original language	English
Awarding Institution	The Hong Kong University of Science and Technology