2k-q Experiments with Binary Response Sampling Until a Fixed Number of Defects

Abstract

In this article we will discuss the use of two-level factorial and fractional factorial experiments with binary responses (defectives/non-defectives) where the purpose is to reduce the rate of defectives. Contrary to a traditional fixed sample size scheme, we will consider one where each factorial combination is sampled until a fixed number of defectives is observed. The total number of items until that occurs is then used as the response. Such an Inverse Binomial sampling scheme has many practical and economical benefits that will be discussed. For the design of experiments based on this idea, we provide a methodology for choosing the necessary number of defectives r, to detect a given change in the probability of producing a defective unit with fixed levels of type I and type II errors.