Research On Design Methods Of Robust Control Charts

Traditional control charts are constructed under the assumption of known process distribution.Such control charts are known as the parametric control charts.In various applications,most of the data streams follow complex processes and their exact distributions are often untraceable.When a parametric distribution specified beforehand is invalid,some articles argue that results from such conventional parametric monitoring schemes would no longer be reliable.To address this problem,the nonparametric or robust control chart is often considered.Nonparametric control charts are very effective in monitoring various non-normal and complex processes.Research on nonparametric control charts has increased in recent years.Nevertheless,there is one disadvantage of the existing nonparametric schemes.We often lose some information during scoring or ranking.For example,we sometimes ignore the information related to the shape or tail-weights of the underlying process distribution.Qiu(2018)pointed out that “the loss of information is just the price to pay for the nonparametric control charts to be robust without specifying a parametric form for describing the in-control process distribution.One important future research topic is to minimize the lost information while keeping the favorable properties of the nonparametric control charts.”Most existing multivariate control charts in the literature are designed to detect either mean or variation shifts rather than both.However,in practice,the process location vector and the scale matrix may change simultaneously in many cases.To this end,jointly monitoring both the location vector and the scale matrix is essential in the course of surveillance and control of a process.If a univariate monitoring scheme gives an out-of-control(OOC)signal,then one can quickly detect the problem and find a solution since a univariate charting procedure is associated with a single variable.However,this is not straightforward in multivariate processes as many variables are involved and correlations exist among them.The identification of an OOC variable or variables followed by a signal in a multivariate monitoring scheme rather complicated and,there is still a lack of useful diagnostic tools that can provide detailed diagnostic information when a process is OOC.In this dissertation,we aim to address the problems with the nature mentioned above through taking advantage of modern resources.We focus on the research on the univariate and bivariate nonparametric or robust control charts for a continuous process,the main contribution including a nonparametric Shewhart control chart for monitoring the scale parameter of a univariate continuous process based on asymptotically locally most powerful test for the scale problem if the underlying density is logistic;a class of nonparametric exponentially weighted moving average(EWMA)schemes for joint monitoring of location and scale parameters of a univariate continuous process;two approaches for improving detection efficiency of univariate nonparametric control charts: one is optimal design of distribution-free EWMA schemes with dynamic fast initial response(FIR)and the other is a new adaptive distribution-free approach with minimal loss of information,and finally a new approach for bivariate process monitoring and diagnosis which can be easily extended to multivariate cases.The full text is divided into seven parts.The first chapter is the introduction part,which mainly includes the research background,purpose and significance,literature review,research content and methods,and innovation of thesis.In Chapter2,we propose a new Shewhart-type distribution-free control chart(named as LOG chart)for monitoring of unknown scale parameter of continuous distributions.Numerical results based on Monte-Carlo analysis show that the proposed LOG chart provides quite a satisfactory performance for a class of location-scale models.There are many situations in practice in which process location and scale may change simultaneously.To this end,jointly monitoring both the location and scale parameters is essential in the course of surveillance and control of a continuous process.In Chapter 3,we investigate and compare six distribution-free EWMA schemes for simultaneously monitoring the location and scale parameters of an univariate continuous process.More precisely,we consider two existing distribution-free EWMA schemes based on the Lepage and Cucconi statistics,respectively,and we propose four new EWMA schemes for the same purpose.One of the four new schemes is based on the maximum of EWMA of two individual components,one for the location parameter and the other for the scale parameter,of the Lepage statistic.Such a component-wise combined EWMA is referred to as the cEWMA.Further,we show that the Cucconi statistic can also be expressed as a quadratic combination of two orthogonal statistics,one of which is ideal for monitoring location parameter and the other is suitable for scale parameter.Such decomposition of the Cucconi statistic is not unique and it can be done in three different ways.Therefore,we design three more cEWMA schemes based on the two components of the Cucconi statistic.We observe that the three cEWMA schemes based on the two components of the Cucconi statistic perform very well in many cases.Qiu(2018)noted that the IC performance of nonparametric schemes is robust,but the performance in the OOC state is inefficient in some cases.In order to improve the efficiency of univariate nonparametric control charts,two methods are proposed as follows: one method is optimal design of distribution-free EWMA schemes with dynamic FIR for joint monitoring of location and scale in Chapter 4.Our proposed approach restricts probability of an early false alarm to a prefixed value at any situation,while optimizes the early detection of true signal by setting an optimal(dynamic)head start value in presence of the FIR feature;There is one disadvantage of the traditional nonparametric schemes.We often lose some information during scoring or ranking,which often results in the loss of the efficiency of the schemes(cf.Qiu 2018).To this end,we propose a new adaptive distribution-free approach with minimal loss of information in Chapter 5.In adaptive inference,we first use the available data to estimate the tail-weight and skewness of the underlying distribution.Thereafter,an appropriate test is selected for the classified type of distribution.Clearly,an adaptive test does not completely overlook the information about the tail-weights or the degree of asymmetry in the original data.Consequently,the adaptive approach corrects the disadvantage of the traditional distribution-free schemes to a great extent.Motivated by this,we introduce distribution-free adaptive Shewhart-Lepage(SL)type schemes for simultaneous monitoring of location and scale parameters using information about symmetry and tail-weights of the process distribution.We consider an adaptive SL type scheme,referred to as the LPA scheme,based on the three modified Lepagetype statistics.Using numerical results obtained via Monte-Carlo,we also propose a new adaptive SL type scheme,referred to as the MLPA scheme,with finite sample correction.Numerical results establish that the MLPA scheme is superior for jointly monitoring the parameters of a broad class of process distributions belong to the location-scale family.Monitoring and diagnosis of multivariate data have become a statistical process control problem of key importance.In practice,most of the data steams follow complex processes and their exact distributions are often untraceable.In view of this,a host of researchers have advocated in favor of the nonparametric or robust control charts.A d-dimensional continuous distribution function is expressible in terms of the d univariate marginal distribution functions and a copula by Sklar's theorem.The univariate marginal distributions determine the behaviour of individual variables,and the copula function demonstrates the dependence structure between variables.Motivated by this,we develop a simple method for simultaneous monitoring of the location and shape parameters of a bivariate process in Chapter 6.We recommend monitoring two marginal distributions and empirical copula simultaneously using appropriate distribution-free test statistics.We introduce two robust Shewhart-type monitoring schemes for bivariate processes,referred to as the Lepage-Copula and Cucconi-Copula schemes.At each stage of Phase-II monitoring,we adopt the permutation method for computing the individual p-values and derive the plotting statistics of our proposed schemes combining suitable transforms of the three p-values of the component testing using the Tippett's combining function.We study the robustness concerning distributional assumptions employing Monte-Carlo simulation.We compare the performance of the proposed schemes with the Mathur scheme.The comparison results show that the proposed plans perform more efficiently than the Mathur scheme in many cases.Apart from quickly detecting an OOC state,our proposed technique indigenously helps in identifying the source of the signal which is not easy with the traditional bivariate process monitoring schemes.Also,we investigate the percentage of correct diagnosis of a signal via the proposed schemes.In most cases,the Lepage-Copula and Cucconi-Copula schemes correctly diagnose the real source of a signal with a high degree of accuracy.Although we confine attention to the bivariate problem for simplicity,it is straightforward to extend our approaches to the more general multivariate problem.