Abstract
Defect rate control is crucial in industries. When binary response is considered, the defect rate is the average of these binary responses. In this study, with logistic regression model and sparsity assumption, the feedback control problem is expressed as an optimization problem which solves a hinge loss with an L 1 penalty. Here the hinge loss function is substituted for the Huberized hinge loss to avoid discontinuity caused by the L 1 penalty, and the majorization-minimization principle is applied to enhance computing efficiency. Then the coordinate descent algorithm is implemented for sparse estimation. Several examples and a real data example are used to illustrate the performance of the proposed feedback control procedure.