A Solution Framework to Address Model Parameter Uncertainties in ANN-Based Response Surface Models for Multivariate Process Quality Control

Multivariate manufacturing process output involves multiple correlated critical quality characteristics called ‘responses.’ These responses must be monitored, controlled, and optimised simultaneously to maintain the desired overall product quality. Due to dynamic and complex behaviour in multivariate manufacturing processes, researchers and practitioners prefer data-driven empirical models, so-called response surface (RS) models. An empirical RS model provides a mapping function(s) between dependent responses and independent controllable variables. RS models are developed based on offline experimentation or real-time ‘as-is’ process data, or a combination of both. In this context, due to inherent sampling or process uncertainties, the estimated parameters of the RS model can deviate from their actual values. Thus, such uncertainties in model parameters need to be quantified while developing the RS model(s). Due to the influence of outliers and complex nonlinear relationships between independent and dependent variables, many researchers recommend artificial neural networks (ANN) to generate the RS. However, no specific research considered model parameter uncertainties to develop the RS, using ANN, for multivariate manufacturing processes. Thus, this study attempts to demonstrate and compare three popular approaches, viz. Approximate Bayesian Ensembling (ABE), Monte Carlo Dropout (MCD), and Bayes by Backprop (BBB) to address model parameter uncertainties for ANN-based RS models. The performance of these approaches is evaluated using simulated, real-life manufacturing and experimental case data. The key metrics used for performance assessment are average test mean square error and signal-to-noise (S/N) ratio. A multi-criteria decision-making (MCDM) technique is further used to rank the approaches. The results indicate the superiority of Approximate Bayesian Ensembling in providing credible confidence intervals.