Industrial problems frequently require estimates from various sources of information. For example, one may need to predict the tensile strength of a future bar from a particular casting based on limited data on other bars from that casting and extensive data on bars from other castings. Or one may wish to estimate the true viscosity of a batch of material based on a single measurement for the current batch, subject to appreciable measurement error, and similar readings on a large number of other batches. Simple weighting functions that use all of the data provide point estimates for these two problems, and a Bayesian framework yields associated interval estimates. Other applications and possible generalizations are also suggested.