Control Chart Based On 1-norm CRPS

Statistical process control are widely used in the industrial field,it aims to monitor quality issues in the production process.Control charts play a very important role.With the advancement of technology,more and more sensors are applied to the production process,making the process data richer and more complex,which brings great challenges to the traditional control chart,especially the Shewhart control chart that assumes the process obeys normal distribution.Since the process distribution is usually unknown and difficult to estimate in practice,the traditional control chart is more misjudged.In this thesis,the process of data-rich process is taken as the research object,and the control chart based on 1-norm continuous ranked probability score is proposed.Firstly,this thesis studies the basic theory and properties of 1-norm CRPS.Both theoretical proof and experimental simulation can show that the statistic subjects to normal distribution,especially when the sample size is large.Then,the CRPS₁ is combined with Shewhart control chart,and the construction method of the SRS chart and the determination of the control limit under different sample size are specifically explained.Both in-control and out-of-control performance of the SRS control chart are given by simulation,and the relevant parameters of the run length are discussed.At the same time,we compare SRS chart with Shewhart chart based on 2-norm CRPS.It shows that the proposed chart has more robust in-control performance.Secondly,this thesis combines the CRPS₁ with the EWMA control chart to further explore the ability of ERS chart to monitor small and medium shifts,and demonstrates the monitoring performance through simulation and actual cases.The simulation experiment uses the normal distribution and the Laplace distribution respectively.The simulation shows that ERS chart is superior to the other two control charts,especially the ability of monitoring scale parameter.Finally,the control chart is applied to the indoor noise case.The results show that ERS chart can quickly monitor the process shifts,which proves that ERS chart is of great significance in practice.