Some Statistical Problems in Relating Experimental Data to Predicting Performance of a Production Process

Abstract

Abstract The performance of a production process is characterized by the quantity and quality of the output; it is affected by factors of production, such as conditions of the process and quantities of inputs. In experimentation where the factors are controlled, we assume a bivariate linear regression model with quantity and quality of output as dependent variates. In operation where quality of output is controlled by adjusting one of the factors, another regression model is used in which quantity of output and the one factor are dependent variates. The second model is derived from the first. It is shown how to use experimental data to estimate the coefficients of the regression of quantity of output in the second model; this regression function is desired for predicting performance in operation. Confidence regions and tests of hypotheses are treated. The exposition is in the form of an analysis of a particular problem met by a chemical engineering firm.