Control chart for complex systems with trended mean and non-constant variance

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2012-05

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Abstract

This research focuses on the monitoring of complex systems. Specifically, the main objective is to define a technique to monitor a quadratic behavior when the standard deviation is linearly trended. A three-paper format is chosen for this Dissertation. The first paper shows the mathematical model that the data follows and presents the first approach for a control chart where time series analysis (with an autoregressive approach to identify the parameters of the quadratic behavior) is used to model the central line and the control limits are established considering traditional control charting theory. A correction factor was identified as necessary to provide adequate results and the control chart is able to detect almost all signals; a numerical example is provided. The second paper uses the same principles as the first one but uses the likelihood function to identify the parameters of the quadratic behavior and, as a result, the central line is again estimated. Results show the control limits are smoother in comparison with the first approach; the control chart seems to provide even better results. The third paper performs extensive Monte Carlo simulation to determine the performance of the proposed approaches and to compare them with an equivalent method: the regression control chart (RCC). Results show both LSE and MLE perform well for larger shifts by detecting most signals and controlling the Type-I error.

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Keywords

Engineering systems, Engineering systems modelling and control series, Series mathematical modelling in physics, Engineering, Cognitive science

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