Constructing tolerance intervals for the number of defectives using both high-and low-resolution data

Defect inspection is important in many industries, such as in the manufacturing and pharmaceutical industries. Existing methods usually use either low-resolution data, which are obtained from less precise measurements, or high-resolution data, which are obtained from more precise measurements, to estimate the number of defectives in a given amount of goods produced. In this study, a novel approach is proposed that combines the two types of data to construct tolerance intervals with a desired average coverage probability. A simulation study shows that the derived tolerance intervals can lead to better performance than a tolerance interval that is constructed based on only the low-resolution data. In addition, a real-data example shows that the tolerance interval based on only the low-resolution data is more conservative than the tolerance intervals based on both high-resolution and low-resolution data.