Truncation and acceptance rules for sequential tests of a Bernoulli parameter.

• Main Author: Petersen, Jurgen
• Other Authors: Lindsay, Glenn F.
• Language: en_US
• Published: Monterey, California. Naval Postgraduate School 2014
• Online Access: http://hdl.handle.net/10945/41078

Approved for public release, distribution unlimited === All original copies missing. Best digital copy available. === In the paper, Wald's Sequential Probability Ratio test for a Bernoulli parameter is studied to assess the influence of truncation on the tree probabilities of error of the first and second kind. It is shown that a natural truncation point exists for every SPR test such that the desired error probabilities are not exceeded. Extended acceptance rules were described whose use allows truncation comparatively early when certain sample sizes are picked. The true error probabilities achieved are either both smaller or equal to the desired ones or one is smaller or equal and the other is exceeded. In the latter case, that probability of error that shall not be exceeded can be chosen and the other will be as small as possible. A listing of 126 SPR plans useful in quality control applications has been included which gives all described truncation points with the applicable acceptance rules and the values for the true probabilities of error.