Uncertainty of measurement for summed masses: Application to controlled substances

Because sentences for drug possession depend on the mass of the seized drug, testing laboratories must often determine the summed mass of numerous items submitted under a single case. One common practice for this purpose is to continue analyzing and weighing samples until a legal threshold is passed, at which point it is important to inform the court whether the summed mass is significantly above the threshold, or only marginally so. This paper develops a means for estimating the uncertainty of the summed mass for the common situation where the readability, d, of the balance dominates the uncertainty. It is seen that for all sample sizes the uncertainty, UM, is given by the remarkable simple expression UM = (d/2) × [N + SQRT(3N)] + N × CCE, where N is the number of items and CCE is the absolute value of the calibration check error. In most instances, this can be further simplified to UM = N × d.