Unilateral Conformance Proportions under Simple Linear Regression Models

In this study, we investigate the construction of lower confidence limit for unilateral conformance proportions under a simple linear regression model. Let a quality characteristic of interest be denoted by Y, then P(Y≥A) or P(Y≤B) are called the unilateral conformance proportions, where A and B denote the specification acceptance limits. We consider the situation that Y is fitted by the simple linear regression model, and develop an approach for constructing lower confidence limits for the unilateral conformance proportions based on the concept of a generalized pivotal quantity (GPQ). The performance of the proposed method is evaluated through detailed simulation studies and real data analysis. It is shown that the proposed method is easy to implement and reasonably satisfactory for practical use.