Effects of imprecise measurement on the two dependent processes control for the autocorrelated observations

The observations from the process output are always assumed to be independent when using a control chart to monitor a process. However, for many processes the observations are autocorrelated and including the measurement error due to the measurement instrument. This autocorrelation and measurement error can have a significant effect on the performance of the process control. This paper considers the problem of monitoring the mean of a quality characteristic X on the first process, and the mean of a quality characteristic Y on the second process, in which the observations X can be modeled as an ARMA model and observations Y can be modeled as an transfer function of X since the state of the second process is dependent on the state of the first process. To distinguish and maintain the state of the two dependent processes with measurement errors, the Shewhart control chart of residuals and the cause-selecting control chart, based on residuals, are proposed. The performance of the proposed control charts is evaluated by the rate of true or false alarms. By numerical analysis, it shows that the performance of the proposed control charts is significantly influenced by the variation of measurement errors. The application of the proposed control charts is illustrated by a numerical example .

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