Simultaneous outer and inner tolerance limits for screening and descriptive purposes

A restricted version of the familiar outer tolerance limits for a normal distribution is defined and developed with particular emphasis on screening in addition to the usual descriptive applications. It is seen that the related concepts of precision and sample size determination are central issues for employing these new tolerance limits. Applications include the familiar quality control context where one may wish to protect against reporting unnecessarily wide tolerance intervals and clinical normal ranges used for screening purposes where it is desirable to protect against an overly large rate of false positives.