Fully PCA-based approach to optimization of multiresponse-multistage problems with stochastic considerations

- Developing the stochastic programming model for the quality chain design problem.
- Proposing the scenario construction method based on Nataf transformation.
- Analyzing location, dispersion, and correlation effects of factors and covariates.
- Working with random samples instead of considering only some measures such as mean.
- Reaching more precise estimation of regression coefficients by applying PCA method.

Manufacturing systems have several stages of operations in which different quality characteristics are formed so it is an important objective to ensure that the final products meet the predefined specification limits. Due to the stream of variations in such systems, controlling and improving the product quality level becomes more complicated rather than the single stage ones. To deal with such problems, Response Surface Methodology has received much more attention in recent years. In the context of quality engineering, these problems usually include correlated response variables as well as correlated covariates. This study presents a new framework for product quality improvement in multistage manufacturing systems with multiple correlated responses and covariates in each stage. Stochastic aspects of this model include probabilistic covariates and statistical distributions of estimated parameters in the response surfaces. To cover these considerations, multistage stochastic programming is used together with the Principal Component Analysis technique to make the responses as well as the covariates uncorrelated at each stage of the operations. At the end, a numerical example has been analyzed by the proposed approach and for large-scale cases some meta-heuristic algorithms have been applied to solve the model.