Making Inferences about the Shipper's Variance in a Shipper-Receiver Difference Situation

There are a number of instances in safeguards in which the situation identified in the title as the "shipper-receiver difference situation" will arise. This is the situation in which two parties make independent measurements on the same items. This occurs for example whenever • The shipper and the receiver make measurements on the same items (hence the label). t An inspector, or more generally, an audit team makes measurements on samples of items and compares the results with those values assigned by the facility operator. • An operator compares measurement methods by measuring some items by both methods and compares results. t Two analytical laboratories are compared by sending the 'same items to both laboratories for measurement. In this article, some results are given that will enable the user to determine what statistical procedure to use in certain estimation and hypothesis-testing situations. The Model The mathematical model that applies is written in its simplest form. Since biases that may exist between the two sets of measurements do not affect inferences made about the variances, they are not included in this discussion. For simplicity in exposition, the model is written in the shipperreceiver notation framework, keeping in mind the more general applications. Let s. = shipper's reported value for item i ri = receiver's reported value for item i ui = true value for item i ej = random error of measurement for the shipper for item i ni = random error of measurement for the receiver for item i Then, the model is Si = PI + EI (1) ri = v\ + ni (2) where e^ and ni are normally distributed with zero means and variances denoted by from 1 to n, the sample size. a\ and on respectively. The index i runs