Bayesian robust parameter design for ordered response

Due to the nature of the quality characteristics, or there is no instrument available to measure the characteristics of interest, ordered data, e.g. 1 (poor), 2 (satisfactory), 3 (good), and 4 (excellent), often appears in industrial processes. Methods commonly used for continuous or categorical quality characteristics are not appropriate for modelling and optimising such quality characteristics. This motivated us to develop a more useful approach to address the variable selection, model construction, and process optimisation for the ordered response. Specifically, Bayesian Lasso is incorporated into the framework of the response surface model to simultaneously perform variable selection and model estimation. The relationship between the probability of the response falls into a specific category and significant factor effects are established by introducing a latent variable. The desirability function, which is commonly used for multi-objective optimisation for quantitative responses, is extended to process optimisation for the ordered response. A numerical example and an industrial case are used to validate the effectiveness of the proposed method. The performance studies of the proposed method show that our method is more competitive than existing methods.