ABSTRACT

Statistical tolerance limits are the tool for making statistical inference on an unknown population. As opposed to a confidence limit that provides information concerning an unknown population parameter, a tolerance limit provides information on the entire population. The new technique given and illustrated in this chapter is offered as a conceptually simple, efficient, and useful method for constructing exact statistical tolerance limits on future outcomes under parametric uncertainty of underlying models. It is based on the idea of invariant embedding of a sufficient statistic in the underlying model in order to construct pivotal quantities and to eliminate the unknown parameters from the problem via pivotal quantity averaging. Using the proposed technique, the exact statistical tolerance limits on future order statistics associated with sampling from corresponding distributions can be found easily and quickly making tables, simulation, and special computer programs unnecessary.