Publications Details
Multiple weight stepwise regression
In many science and engineering applications, there is an interest in predicting the outputs of a process for given levels of inputs. In order to develop a model, one could run the process (or a simulation of the process) at a number of points (a point would be one run at one set of possible input values) and observe the values of the outputs at those points. There observations can be used to predict the values of the outputs for other values of the inputs. Since the outputs are a function of the inputs, we can generate a surface in the space of possible inputs and outputs. This surface is called a response surface. In some cases, collecting data needed to generate a response surface can e very expensive. Thus, in these cases, there is a powerful incentive to minimize the sample size while building better response surfaces. One such case is the semiconductor equipment manufacturing industry. Semiconductor manufacturing equipment is complex and expensive. Depending upon the type of equipment, the number of control parameters may range from 10 to 30 with perhaps 5 to 10 being important. Since a single run can cost hundreds or thousands of dollars, it is very important to have efficient methods for building response surfaces. A current approach to this problem is to do the experiment in two stages. First, a traditional design (such as fractional factorial) is used to screen variables. After deciding which variables are significant, additional runs of the experiment are conducted. The original runs and the new runs are used to build a model with the significant variables. However, the original (screening) runs are not as helpful for building the model as some other points might have been. This paper presents a point selection scheme that is more efficient than traditional designs.