Three-phase Sequential Design for Sensitivity Experiments

In some experimental investigations each experimental unit has a critical stimulus level that cannot be observed directly. The distribution of these critical levels (or thresholds) over test specimens is of primary interest. In pyrotechnics applications the stimulus (or stress) level, denoted by x, may be the drop height of an explosive, or the pressure on a pile of ammunition, and the response, denoted by y, is binary (e.g., explosion/non-explosion). In industrial applications, x may be the wind speed in a wind-tunnel experiment or the dosage of a compound in a toxicity study. Sensitivity tests are commonly used to estimate some aspects of this distribution. Numerous methods have been proposed for conducting sequential sensitivity testing. But there remains the outstanding question of finding a sequential procedure that works well when the test sample size is small, especially for estimating extreme quantiles. For example, there is no clear winner among the competing methods in a comprehensive simulation study by Young and Easterling (1994). The median is considered because it is easier to estimate (i.e., more information in the data). And engineers often use it as a benchmark, especially during product development. However, to assess the reliability of a product for field use, the interest and focus is often on the extreme percentiles with p ≥ 0.9 or even p ≥ 0.99.