The purpose of this study was to compare the effectiveness of the classical estimator with that of a supplementary sample non-parametric empirical Bayes estimator in detecting an out-of-control situation arising in statistical quality control work. The investigation was accomplished through Monte Carlo simulation on the IBM-7040/1401 system at the Virginia Polytechnic Institute Computing Center, Blacksburg, Virginia. In most cases considered in this study, the sole criterion for accepting or rejecting the hypothesis that the industrial process is in control was the location of the estimate on the control chart for fraction defectives. If an estimate fell outside the 30 control limits, that particular batch was said to have been produced by an out-of-control system. In other cases the concept of "runs" was included as an additional criterion for acceptance or rejection. Also considered were various parameters, such as the mean in-control fraction defectives, the mean out-of-control fraction defectives, the~first sample size, the standard deviation of the supplementary sample estimates, and the number of past experiences used in computing the empirical Bayes estimator. The Monte Carlo studies showed that, for almost any set of parameter values, the empirical Bayes estimator is much more effective in detecting an out-of-control situation than is the classical estimator. The most notable advantage gained by using the empirical Bayes estimator is that long-range lack of detection is virtually impossible. / M.S.