A nonparametric change-point model for Phase II analysis.

Abstract

In statistical process control, the control chart based on the change-point model does not require prior knowledge about the parameters, making it an attractive technique. So far, change-point control charts are only developed under a normal assumption. But when the underlying distribution is not normal or unclear, this may not be appropriate. In this thesis, we propose a nonparametric change-point model based on the Mann-Whitney statistic for ongoing Phase II analysis, which has essentially the same computational complexity as the parametric. The simulated out-of-control ARL shows that this nonparametric model outperforms the parametric for small to moderate shifts, although loses for large shifts, even for data from normal distribution. And we show that modifying the parametric procedure to prohibit very short segments largely equalizes the performance of the parametric and nonparametric methods. Finally, an asymptotic limit of the control limit in parametric change-point model is proposed.