Gráficos de controle adaptativos para monitoramento de perfis

• Autor(a) principal: Fernandes, Viviany Leão
• Data de Publicação: 2014
• Tipo de documento: Tese
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações da UERJ
• Texto Completo: http://www.bdtd.uerj.br/handle/1/13677
• topic: Statistical Process Control; Adaptive control charts; Linear profiles; Nonlinear profiles; Markov chain; Controle de qualidade - Métodos estatísticos; Controle de processo - Métodos estatísticos; Markov, Processos de; Análise de regressão; Gráficos de controle adaptativos; Perfis lineares; Perfis não-lineares; CNPQ::CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::PROBABILIDADE E ESTATISTICA APLICADAS

Production processes need to be continually evaluated so that they are able to produce in the most effective and efficient way. Statistical process control (SPC) consists of a set of tools used for this purpose. The monitoring can be periodically performed through the SPC tools. The most important tool of SPC is the control chart. In this thesis, we focus on the monitoring of a response variable through the parameters or coefficients of a linear regression model. It is proposed adaptive χ2 control charts for monitoring the coefficients of linear regression models. More specifically, seven adaptive χ2 control charts are proposed for monitoring a simple linear regression model, being distinguished by the following properties: variable sample size; variable sampling interval; variable warning and control limits; variable sample size and sampling interval; variable sample size and limits; variable sampling interval and limits and finally, all design parameters varying. Performance measures of these charts were obtained through properties of Markov chain, for both the zero-state and the steady-state situation. It was found that the average time until a signal in the case of small to moderate shifts in the coefficients of the regression model decreased. The proposed charts were applied to an example of semiconductors manufacturing process. Moreover, a sensitivity analysis of the proposed charts is performed for different shifts magnitudes in the process parameters, namely the intercept and the slope, comparing the performance between the developed charts and also with the fixed parameter χ2 chart. The proposed charts in this thesis are suitable for several applications. In this work, it was also considered quality characteristics represented by nonlinear regression models. To the considered nonlinear regression model, the proposal is to use a method that divides the nonlinear profile in linear parts. More specifically, an algorithm for this purpose, proposed in the literature, was utilized. It approximates nonlinear profile by a set of linear profiles. It was possible to validate this technique, showing that it is robust in the sense that it allows different types of nonlinear profiles to be considered. In this way, techniques such as control charts developed here can be used to monitor each linear part. Furthermore, we present the methodology to decompose a nonlinear profile in linear parts in a detailed and complete way, allowing its widespread use.