ABSTRACT
For a given USP test, under the specific sampling plan and acceptance criteria, it is of interest to evaluate the probability of passing the USP test for a given sample. Under underlying distribution assumptions of the test characteristics, the probability of passing a USP test can be evaluated based on the sampling plan and acceptance criteria. The probability of passing a USP test generally depends on the population mean and standard deviation of the test characteristics. In practice, it is desired to obtain acceptance limits which guarantee that future samples will pass the USP test with a high probability. Such acceptance limits are usually constructed based on the sample mean and standard
deviation of the test results. For a given sample, the idea is to construct a joint confidence region for the population mean and standard deviation. The probability of passing the USP test for each population mean and standard deviation in the confidence region can then be evaluated. The confidence region is obtained as the set of all possible sample means and standard deviations such that the probability of passing the USP test is greater than a prespecified probability for all points in the confidence region. The confidence region is usually referred to as the acceptance region.
