Research On Time-between-events Control Charts For High-quality Processes

As one of the most influential tools in data-driven fault detection methods,statistical process monitoring(SPM)have been extensively used in various fields,such as manufacturing industry,health surveillance,reliability analysis,and natural disaster prediction.With the improvement of manufacturing capacity,the occurrence rate of non-conformities(or defects,failures)in manufacturing processes can be maintained at a very low level,and these processes are usually named "high-quality processes" or "low failure rate process".Meanwhile,with the rapid development of the advanced computer system,the automatic sensor technology,and the large-scale data storage technology,massive amounts of complex production data in the manufacturing process can be collected and stored,and the complexity of the corresponding data is also increased.As one of the most effective tools,both the flexibility and efficiency of traditional attribute control charts in monitoring data from high-quality processes are facing significant challenges.In this context,it is desirable to develop some new methods for control charts in monitoring high-quality processes data.More specifically,focusing on the monitoring of univariate and multivariate data in high-quality processes,both the univariate Time-Between-Events(TBE)control chart and the multivariate TBE control chart are designed and studied in this thesis.For high-quality processes with univariate TBE data,a new one-sided exponentially weighted moving average(EWMA)TBE scheme using a new truncation method is developed here for monitoring data from high-quality processes with a known shift direction.Since the process parameters are rarely known in advance,the one-sided EWMA TBE scheme with unknown parameter(i.e.estimated parameter)is also studied in this thesis.In order to evaluate the run length(RL)properties of the proposed control chart,the average run length(ARL)performance of the one-sided EWMA TBE scheme with known and estimated parameters is studied using the corresponding Markov chain method,respectively.Meanwhile,to search the optimal parameters of the proposed one-sided EWMA TBE scheme,an optimal design procedure is developed in this thesis based on ARL criteria.Numerical results show that the proposed one-sided EWMA TBE control chart is more sensitive than the one-sided REWMA TBE chart in monitoring both upward and downward mean shifts.If the magnitude of the potential mean shift is unknown,it is desired to design a control chart to perform well over a wide range of shifts instead of only optimizing its performance in monitoring a particular mean shift level.In this study,a new one-sided adaptive EWMA(AEWMA)TBE control chart with known and estimated parameters is proposed to provide good performance in detecting both small and large shifts simultaneously.A discrete-state Markov chain model is established to evaluate the RL properties of the one-sided AEWMA TBE scheme with both known and estimated parameters.Furthermore,based on the ARL criteria,a two-stage optimal design procedure of the suggested scheme is developed for searching the optimal parameter combination.Numerical results show that,in the case of mean shift monitoring,the one-sided AEWMA TBE scheme is uniformly more sensitive than the one-sided REWMA TBE chart and the one-sided AREWMA TBE chart.In addition,the one-sided AEWMA TBE scheme with estimated parameters performs better than the two comparative schemes in compensating the adverse effect of parameter estimation.For high-quality processes with TBE data and event amplitude data,it is necessary to model such processes with Smith-Adelfang-Tubbs(SAT)models.Compared with the other bivariate Gamma distributions,SAT models can fully consider the dependency between TBE data and event amplitude data.In this study,a synthetic multivariate EWMA(SMEWMA)type scheme,which consists of a conventional multivariate EWMA(MEWMA)sub-chart and a conforming run length(CRL)sub-chart,is proposed to monitor bivariate Gamma distributed(BGD)vectors generated from the SAT model.Different from the one-sided AEWMA TBE chart,the corresponding Monte Carlo simulation methods are developed to evaluate the ARL performance of the SMEWMA BGD scheme in both zero-state and steady-state cases.Simulation results suggest that,irrespective of the zero-state or the steady-state case,the overall ARL performance of the proposed SMEWMA BGD scheme is superior to the conventional MEWMA control chart and the individual Gamma control chart.For high-quality processes with multivariate TBE data,we develop a multivariate cumulative sum(MCUSUM)control chart for monitoring Gumbel’s multivariate exponential(GME)distributed data.The corresponding Monte Carlo simulation methods are detailed in this study for the computation of both zero-state and steady-state ARL values.Moreover,based on the ARL performance,several guidelines for constructing the MCUSUM GME control chart are also provided.Simulation results show that,irrespective of the zero-state or the steady-state case,the proposed MCUSUM GME control chart outperforms the conventional MEWMA control chart and the individual CUSUM control chart for most shift domains.