Economic-statistical design of variable parameters non-central chi-square control chart
Projeto econômico-estatístico de gráficos de controle qui-quadrado não-central com parâmetros variáveis
Magalhães, Maysa Sacramento de; Moura Neto, Francisco Duarte
http://dx.doi.org/10.1590/S0103-65132011005000031
Prod, vol.21, n2, p.259-270, 2011
Abstract
Production processes are monitored by control charts since their inception by Shewhart (1924). This surveillance is useful in improving the production process due to increased stabilization of the process, and consequently standardization of the output. Control charts keep track of a few key quality characteristics of the outcome of the production process. This is done by means of univariate or multivariate charts. Small improvements in control chart methodology can have significant economic impact in the production process. In this investigation, we propose the monitoring of a single variable by means of a variable parameter non-central chi-square control chart. The design of the chart is accomplished by means of optimizing a cost function. We use here a simulated annealing optimization tool, due to the difficulty of classical gradient based optimization techniques to handle the optimization of the cost function. The results show some of the drawbacks of using this model.
Keywords
Statistical process control. Economic design. Chi-square control chart. Variable parameters. Simulated annealing.
Resumo
Processos de produção são monitorados por gráficos de controle desde a sua introdução por Shewhart (1924). Este monitoramento é útil na melhoria do processo de produção devido à crescente estabilização do processo, e consequentemente, padronização do produto. Gráficos de controle mantêm vigilância de características de qualidade de um processo de produção. Isto é feito por intermédio de gráficos univariados ou multivariados. Melhorias na metodologia de gráficos de controle podem levar a um impacto econômico significativo no processo de produção. Neste artigo, propomos um gráfico de controle de parâmetros variáveis baseado na estatística qui-quadrado nãocentral para monitorar uma característica de qualidade de interesse. O projeto do gráfico é realizado através da otimização de uma função custo. O algoritmo simulated annealing é usado devido à dificuldade dos métodos clássicos de otimização baseados no gradiente, de lidarem com a otimização da função custo. Os resultados mostram algumas das dificuldades de se usar este modelo.
Palavras-chave
Controle estatístico de processos. Projeto econômico. Gráfico de controle qui-quadrado. Parâmetros variáveis. Simulated annealing
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