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https://prod.org.br/article/doi/10.1590/S0103-65132007000300009
Production
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Otimização conjunta de gráficos de X-barra – S ou X-barra – R: um procedimento de fácil implementação

Joint optimization of X-bar – S or X-bar – R charts: an easily implemented procedure

Epprecht, Eugenio Kahn; Leiras, Adriana

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Resumo

Este trabalho desenvolve um modelo para escolha ótima dos parâmetros de operação de gráficos de X-barra e R (ou de X-barra e S) que minimiza a razão entre o custo de amostragem e a rapidez de detecção de desvios na média ou aumentos na dispersão do processo. Admitem-se três formas alternativas para o problema: minimizar os tempos médios de sinalização sob uma restrição ao custo de amostragem; minimizar esse custo sob uma restrição aos tempos de sinalização; e o problema multiobjetivo de minimizar o custo e os tempos de sinalização. Restrições adicionais são permitidas, para tratar de variantes do problema encontráveis na prática. O procedimento evita a complexidade dos modelos de projeto econômico usuais. São detalhados métodos para determinação dos poucos parâmetros de especificação e entrada exigidos pelo modelo. Um exemplo mostra que o procedimento é de fácil aplicação. Tudo isto aumenta sua aplicabilidade para um grande espectro de situações práticas típicas.

Palavras-chave

Controle estatístico de processos, gráficos de controle, projeto semi-econômico, otimização, multiobjetivo

Abstract

A model is developed for optimum choice of the operation parameters for X-bar - R (or X-bar - S) charts, which minimizes the ratio of sampling costs to detection speed of shifts in the process mean or increases in the process dispersion. Three alternative problem formulations are allowed: minimization of the average time to signal subject to a sampling cost constraint; minimization of the sampling cost subject to a constraint on the average times to signal; and multi-objective optimization of both the average time to signal and the sampling cost. Through optional additional constraints, several practical variants of the problem are admitted. The procedure avoids the complexity of usual economic design models, and methods for determining the values for the few input and specification parameters required are given in detail. An example shows that the procedure is easy to apply. All these features increase its applicability for a wide range of typical practical situations.

Keywords

Statistical process control, control charts, semi-economic design, optimization, multi-objective

References



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