Optimization problems and methods in quality control and improvement

The connection between optimization methods and statistics dates back at least to the early part of the 19th century and encompasses many aspects of applied and theoretical statistics, including hypothesis testing, parameter estimation, model selection, design of experiments, and process control. This paper is an overview of some of the more frequently encountered optimization problems in statistics, with a focus on quality control and improvement. Descriptions of a variety of optimization procedures are given, including direct search methods, mathematical programming algorithms such as the generalized reduced gradient method, and heuristic approaches such as simulated annealing and genetic algorithms. We hope both to stimulate more interaction between the statistics and optimization methodology communities and to create more awareness of the important role that optimization methods play in quality control and improvement.