One-sided screening procedure using multiple normally distributed variables

Abstract

In the situations in which the proportion of acceptable products from the output of a production process is below the required level, it is essential to screen out the products of unacceptable quality. By eliminating the products of low quality, the proportion of products of the acceptable quality in the remaining population of products is raised.

In some instances it is not possible to make quality assessment by measuring directly on the variable of interest (performance variable). The measure is not possible because it destroys or degrades the product. In such cases, auxiliary variables which are correlated with the performance variable can be used to indirectly determine the quality of the product. These variables are called screening variables.

Under the assumption that the performance and the screening variables follow a multivariate normal distribution, a regression model is used to predict the value of the performance variable. Using Monte Carlo simulation, the performance of the regression model is evaluated. The evaluation is done for two cases: (1) the parameters of the underlying distribution are known, (2) the parameters are not known. The results show that the efficiency of the screening depends highly on the value of the correlation coefficient between the performance variable and a linear combination of the screening variables. Furthermore, the comparison with the previously developed models is performed.

Findings show that the regression model is very useful, especially in the cases in which multiple screening variables are available and the parameters of the underlying distribution are not known.