How much should we reweigh?

Abstract

Suppose that in the final stage of manufacturing of, for instance, chemical products, there is a process in which we weigh each product using a scale to obtain its exact weight, and then mark each product with its weight. In practice, such a weighing process is not necessarily carefully checked and its associated cost is reduced as much as possible since it does not affect the product quality itself. However, the scale occasionally becomes uncalibrated, that is, inaccurate, and hence will produce inaccurate weights for individual products. Particularly when the products are very heavy, a special scale is used and only qualified persons with licenses can inspect the scale to detect its inaccuracy and adjust it. We focus on a problem of this sort and propose a stochastic model aiming to control the volume of products shipped out with inaccurate marked weights.