Material sampling theory is well established in mineral process monitoring, improvement and control. It has been much enhanced by fundamental contributions due to Gy._x000D_
When Gy's sampling theory is applied to sampling inspection and monitoring, it provides estimates of average quality or extent of contamination. It also provides estimates of uncertainty, but these often ignore uncertainty in estimated variograms or other measures of variability._x000D_
Risk assessment is often an implied task in sampling inspection and quality monitoring. A valid technique of risk assessment needs to take into account the uncertainty in the variational measures themselves. Standard statistical tolerance limit calculations which do take such uncertainty into account can be adapted to develop a technique for handling uncertainty in variational measures such as the variogram. Data from a published example is used to illustrate the technique.