In quality control applications, the most basic tasks are monitoring and fault diagnosis. Monitoring results determines if diagnosis is required, and conversely, diagnostic results aids better monitoring design. Quality monitoring and fault diagnosis are closely related but also have significant difference. Essentially. monitoring focus on online changepoint detection, whilst the primary objective of diagnosis is to identify fault root causes as an offline method. Several critical problems arise in the research of quality control: firstly, whether process monitoring is able to distinguish systematic or assignable faults and occasional deviation; secondly, how to diagnose faults with coupled root causes in complex manufacturing systems; thirdly, if the changepoint and root causes of faults can be diagnosed simultaneously.
In Chapter 2, we propose a novel Bayesian statistical process control method for count data in the presence of outliers. That is, we discuss how to discern out of control status and temporary abnormal process behaviors in practice, which is incapable for current SPC methodologies. In this work, process states are modeled as latent variables and inferred by the sequential Monte Carlo method. The idea of Rao-Blackwellization is employed in the approach to control detection error and computational cost. Another contribution of this work is that our method possesses self-starting characteristics, which makes the method a more robust SPC tool for discrete data. Sensitivity analysis on monitoring parameter settings is also implemented to provide practical guidelines.
In Chapter 3, we study the diagnosis of dimensional faults in manufacturing. A novel Bayesian variable selection oriented diagnostic framework is proposed. Dimensional fault sources are not explicitly measurable; instead, they are connected with dimensional measurements by a generalized linear mixed effect model, based on which we further construct a hierarchical quality-fault model to conduct Bayesian inference. A reversible jump Markov Chain Monte Carlo algorithm is developed to estimate the approximate posterior probability of fault patterns. Such diagnostic procedure is superior over previous studies since no numeric regularization is required for decision making. The proposed Bayesian diagnosis can further lean towards sparse fault patterns by choosing suitable priors, in order to handle the challenge from the diagnosability of faults. Our work considers the diagnosability in building dimensional diagnostic methodologies. We explain that the diagnostic result is trustworthy for most manufacturing systems in practice. The convergence analysis is also implemented, considering the trans-dimensional nature of the diagnostic method.
In Chapter 4 of the thesis, we consider the diagnosis of multivariate linear profile models. We assume liner profiles as piece-wise constant. We propose an integrated Bayesian diagnostic method to answer two problems: firstly, whether and when the process is shifted, and secondly, in which pattern the shift occurs. The method can be applied for both Phase I and Phase II needs. For Phase I diagnosis, the method is implemented with no knowledge of in control profiles, whereas in Phase II diagnosis, the method only requires partial observations. To identify exactly which profile components deviate from nominal value, the variability of the value of profile components is marginalized out through a fully Bayesian approach. To address computational difficulty, we implement Monte Carlo Method to alternatively inspect between spaces of changepoint positions and fault patterns. The diagnostic method is capable to be applied under multiple scenarios.