Nonparametric Change Point Control Chart Based On Data Depth

For its quick quality diagnostics of using change-point theory to construct the control chart, lots of people have involved this philosophy in their studies to conduct statistical process control. However, most of them put attentions on the single variant control problem and the multivariate control problem under normal distribution. Nearly have someone study the multivariate control problem under non-normal distribution with change-point theory even it is very significant.Firstly, we give a brief introduction to the development of control chart from single variant, multivariate, change-point and data depth aspect respectively. Then the principle and core contains of SPC, control chart, change-point theory and data depth were explained. Especially for the development of change-point control chart, we describe them from stage I and stage II aspects.To construct our control chart, we use simplex data depth to descent the dimension of the observation. The standardized WM statistics was adapt to construct our change-point testing statistic. We also give the detailed description to the reference sample training, the reasonable time to begin testing, the scale of calculation and the way to set the control-limit sequence. Then Large-scale simulation was used to test its performance and compare it with exist way performance.Finally the sample under binary Gamma-distribution was used to test its performance. We studied every situation with settings, that location parameter shift range from 0.2 to 1.0, change point equals to 14, 24, 34. The simulation results show that, more shift and longer time before change point occurred, lead to better performance of control chart, especially when the shift below 0.7, or it has opposite effect. If the shift range from 0.1 to 0.4, the change point works in the same way, but the marginal effect will be reducing.