Research On Some Issues In Statistical Process Control

Statistical process control(SPC)chart has been widely applied in the fields of in-dustrial engineering,disease prevention,environment monitoring,etc.In recent years,with the rapid development of automatic sensor technology and large-scale data storage technology,various types of complex data with complicated structure are collected and saved,posing great challenges to the flexibility and efficiency of control charts.In such a situation,conventional control charts in the literature are no longer applicable.There-fore,it is desirable to develop some new methods for these complex data.In this thesis.we mainly focus on one-dimensional correlated data with unknown distribution,high-dimensional data streams,dynamic system with semi-parametric longitudinal behaviour and profile data with jumps,and propose some novel methods for online monitoring and fault diagnosisWhen the one-dimensional process distribution is unknown and the process obser-vations are serially correlated,we propose a nonparametric self-starting cumulative sum(CUSUM)control chart for online monitoring.The proposed control chart does not re-quire any parametric form for describing the IC distribution.Besides,through a Cholesky-decomposition-based decorrelation procedure,parametric time series model assumption is no longer required for describing serial correlation.All the control chart needs is a small-to-moderate IC historical dataset so that initial estimates of the IC parameters can be provided.Then,the estimates of these IC parameters are updated recursively using a self-starting scheme for improving their accuracy.Compared to existing methods,the proposed control chart has significant advantages.Then we focus on the fault diagnosis problem of high-dimensional data streams(HDS).We first formulate the fault diagnosis problem of HDS as a large-scale multiple testing problem,and then propose a novel weighted missed discovery rate(wMDR)-control procedure to find the diagnosis subset with the smallest expected number of false positives(EFP)while controlling the wMDR at given level a.We systematically investigate the theoretical properties of the proposed procedure,and establish its validity and optimal-ity for wMDR-control.Numerical results show that the proposed diagnostic procedure outperform conventional methods significantly.Then,we extend dynamic screening system(DySS)to semi-parametric.When the longitudinal behaviour of dynamic system is semi-parametric,we integrates semi-parametric longitudinal data analysis with an exponentially weighted moving average(EWMA)charting scheme,and propose a novel semi-parametric dynamic screening sys-tem for monitoring subjects with irregular semi-parametric longitudinal pattern.Exten-sive simulation results and a real data example about the total cholesterol level of patients show that the proposed method works well in practice.Finally,when jumps exist in profile data,we first propose a novel iterative jump detection procedure to estimate the positions and sizes of the jumps.After the jumps are detected,a piecewise profile registration procedure is proposed for eliminating phase variability.By integrating the key information on jumps,profile registration and the registered profiles into an EWMA charting scheme,we propose a control chart for mon-itoring profiles with jumps.We use simulation studies and a real-data analysis to show the efficiency of the proposed control chart.