Critical Window Estimation Based On Triple Response

Critical window estimation is widely used in clinical experiments, industrial design and quality control. The test specimens may generate none response, success response and over response due to the change of stimulus level. Suppose the two critical points are independent and normal distributed, then based on triple response, we can transform the question of estimating the critical window under a given successful probability to estimating the generalized p quantile.In this paper, we proposed an experiment design procedure to estimate the parameters of the normal distribution with two critical points, and then estimate the critical window through computing the generalized p quantile. We testified that the estimation method was robust through Monte Carlo simulation, and compared with the current method of estimating critical window. It was turned out that our estimation method outperformed existing procedure when the required successful probability p is extremely high, such as p>0.999.