THE APPLICATION OF BOX-BEHNKEN METHOD TO OPTIMIZE THE DESIGN OF EWMA CHART FOR AUTOCORRELATED PROCESSES

Karin Kandananond

Abstract: This research aims to evaluate the performance of the exponentially weighted moving average (EWMA) control chart under the situation that the observations are autocorrelated. Three autoregressive integrated moving average (ARIMA) models, AR (1), ARMA (1, 1) and IMA (1, 1), and a step func tion were utilized to characterize the process model. The auto correlated observations were monitored by the exponentially weighted moving average (EWMA) chart and the average run length (ARL) was used as the performance index. A response surface method, Box- Behnken design, was utilized to carry out the optimal design of the EWMA parameters, λ and L, while the robustness of the control chart was still maintained when there was no shift in the process. The empirical results show that the auto correlation has asignificant effect on the value of the ARL, i.e., the ability to detect a special cause and the occurrence frequency of a false alarm. Another important finding is that, under the autocorrelated situation (both stationary and non-stationary), the control limits of the EWMA chart should be narrowed down to L = 2 for the best performance. On the other hand, the value of λ does not seem to have a significant effect on the ARL except only when the observation follows ARMA (1, 1). Moreover, the results also reveal that the size of a shift will impact the detection sensitivity of the EWMA to a shift only when the process is stationary. According to the study, if the EWMA chart utilized under the autocorrelated environment is appropriately designed, the practitioners on the shop floor will have a state of the art guidelines for achieving the highest possible performance when deploying the EWMA chart.

Keywords: autocorrelation, autoregressive integrated moving average (ARIMA), average run length (ARL), box-behnken design, exponentially weighted moving average (EWMA) chart

DOI:

Recieved: 25 February 2013  Accepted: 10 May 2013  UDC: 638.1248

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