Cartas de controle para o monitoramento da média em processos ajustados pela distribuição Weibull

Abstract

In a production process, it is important to keep the control of the process average in order to verify if the production system is predictable. The X ̅ Control Chart developed in the 1920s by Walter A. Shewhart, is still widely used for this purpose in the industrial environment, not only because it is simple, but because it quickly detects medium or large shifts relative to the population mean. However, for small shifts from the mean, its performance may be insufficient. Another problem is that the distribution of the quality variable of interest may not have a Normal distribution, being more suitable, for example, the Weibull distribution. In this work we discuss and evaluate proposals for the mean control chart in which the quality characteristic the quality feature best fits the weibull distribution. We present two alternatives in which in one the control limits are obtained by Monte Carlo simulation and in the other alternative the control limits are obtained numerically using the Gamma distribution. Additionally, to decrease the value of ARL (Average Run Length) in order to detect small changes in the mean considering the Weibull distribution, we incorporate the supplementary rules of Klein and Khoo in the graph of proposed control with limits obtained based on the Gamma distribution. Numerical examples are presented and discussed.