Study On Nonparametric Quality Control Methods For Attribute Data

Attribute data are very common in practice,ranging from manufacturing industries,service processes,to public health.Also,attribute data may be a univariate variable,a multivariate variable or a response variable of profiles.Some parametric models,such as the binomial distribution,the multivariate Poisson distribution and generalized linear models,are usually used to describe the attribute data.Many control charts based on these parametric models have been proposed to monitor attribute data.However,the performance of the parametric control charts almost completely depends on the underlying parametric models.In other words,existing research on monitoing attribute data is very limited.This study aims to fill the gap by discussing different nonparametric methods to solve the monitoing problem as follows:First,this study adoptes two novel nonparametric control charts to monitor univariate attribute data,based on Pearson Chi-squared test and likelihood ratio test,respectively.To be more specific,the consequence to use a parametric control chart is investigated in cases when the underlying parametric distribution model is invalid.Furthermore,the in-control and out-of-control performance of the two nonparametric control charts are compared with some classic parametric control charts.Based on the simulation results,nonparametric control charts are suggested when engineers are uncertain that the attribute data can be described by a parametric distribution model.Second,based on Log-Linear model and Pearson Chi-squared test,this study proposes a nonparametric control chart to monitor multivariate attribute data.Specifically,the consequence of using a parametric control chart is showed in cases when the underlying parametric distribution is invalid.Then,the performance of some parametric and nonparametric control charts in monitoring multiple attribute data are thoroughly investigated by simulations.The numerical results show that nonparametric methods can provide a more reliable and effective process monitoring in such cases.A real-data example is used for illustrating the implementation of the related nonparametric control charts.Third,this study proposes a novel Phase I nonparametric scheme to detect the change point in the reference profile dataset with attribute data as response variables.The proposed method integrates change-point model with the generalized likelihood ratio test based on nonparametric regression,which could handle the generalized linear profiles and nonlinear profiles.Numerical simulations are conducted to demonstrate the detection effectiveness and the diagnostic accuracy of the proposed scheme.A real example is used to illustrate the implementation of the proposed change-point detection scheme.Finally,a unified framework of control schemes based on nonparametric regression is proposed,including three kinds of Phase II nonparametric control charts,to monitor profiles with attribute data on-line.These methods could tackle generalized linear profiles or nonlinear profiles with a wide class of response variables.The performance of the proposed methods is studied under the binomial and Poisson profiles by numerical simulations.Furthermore,a real-data example about the automobile warranty claims is used for illustrating the implementation of the three proposed control charts.This study is of significant importance for enriching the research on statistical process control and broadening the scope of nonparametric monitoring.The study results could also provide methodology and practical guidelines for manufacturing and service industries to monitor attribute data.