One-Sided Intervals for at Least p of m Observations from a Normal Population on Each of r Future Occasions

Abstract

In environmental monitoring, one must often use background data obtained before an installation begins operation to produce prediction intervals for future sets of m observations to be taken on each of r future occasions spanning the anticipated lifetime of the installation. A future observation falling outside of its interval will be taken as evidence of a change in the process being monitored; one would like to control the overall risk of false detection of change while maintaining an adequate sensitivity to real changes. Toward this end, the procedure of Fertig and Mann (1977) is extended to produce simultaneous prediction intervals for at least p of m observations to be obtained on each of r future occasions. Tables with superior choices of p for selected m, r, and background sample size are provided; these choices of p provide the best power given the other parameters, where power is defined in terms of the chance of quick detection of a future shift in the process being monitored.