Sample sizes for batch acceptance from single- and multistage designs using two-sided normal tolerance intervals with specified content.

One quality control test in the pharmaceutical industry is a test for uniformity of content of a batch prior to release of the batch to market. For batch acceptance by this or other quantitative tests of batch quality, one approach uses two-sided tolerance intervals of specified content. If the tolerance interval falls entirely within an acceptance interval, the batch is accepted. This has the form of a statistical hypothesis test. Once we recognize this approach as a statistical test, we can ask what sample size is required to be able to accept the batch with a desired power. The power for a single-stage design is a bivariate noncentral t probability and can be determined using previously published algorithms. Using standard methods for interim analyses, the approach is extended to multistage designs. Power and sample size for multistage designs are validated with simulations. We demonstrate it is possible to design one- and two-stage designs for batch acceptance with desired power and specified type I level.