Multivariate statistical modeling and robust optimization in quality engineering.

摘要

Multivariate statistical modeling and mathematical optimization method, used in combination, provide a powerful tool to solve real problems. This dissertation, motivated by a practical problem arising in the medical device industry, deploys this combination to address some significant applications in quality engineering.; The first application concerns the adjustment of the process settings in the startup stage of a batch process. The batch process is characterized by multiple, correlated process and product variables. The startup consists of a search for process settings that produce good product, and it often needs numerous iterations of adjustment and product testing to find the correct settings.; To make the adjustment more quickly, multivariate statistics and optimization are used together to address batch startup. Partial least squares (PLS), a multivariate statistical approach, is used to model the relationship between process and product variables for successful baseline batches. A goodness-of-fit measure is defined to indicate the distance between the process settings and the PLS baseline model; and the aim here is to find a set of process settings to minimize this distance measure. We develop a mixed-integer quadratic program (MIQP), by incorporating the statistical model, engineering constraints and operator input, to identify the optimal adjustment such that the recommended process settings are consistent with the PLS model.; The second application concerns robust optimization of a response function relating performance measures and design parameters. In product design, this response function is often estimated from designed experiments. In contrast to the usual approach where a single estimated response function is optimized, the robust optimization approach considers a family of estimated response functions. We construct a minimax deviation model to find a robust solution that works well for all of these estimated functions. We prove a reduction theorem to reduce the minimax deviation model to a tractable, finite, mathematical program. Simulation shows the robust solution is more insensitive to the noise in the experimental data than the usual approach.; To determine a reasonable number of experimental runs in deriving a robust solution, we develop a sequential experimentation method. Multiple imputation, a missing data analysis technique, is used to predict the quality of a robust solution assuming additional runs are performed. The sequential experiments continue as long as predicted improvement of the quality of the robust solution is evident.; Various extensions of the above problems are discussed in this dissertation to show the effectiveness of combining multivariate statistics and optimization methods.