Monitoring feedback-controlled processes using adaptiveT²schemes

Abstract

The integration of engineering process control (EPC) and statistical process control (SPC) has drawn wide attention because of its capability to minimize long-term process variation and improve product quality. However, dynamic shift patterns are usually observed when feedback-control loops exist, which consequently lead to poor charting performance. In this paper, the dynamic patterns in mean shifts of proportional integral (PI) controlled and minimum mean square error (MMSE) controlled processes are formulated and analysed.In conjunction with a model-free forecasting algorithm, an adaptive T 2 charting procedure is applied to improve detection power. This adaptive procedure is constructed upon the uniformly most powerful (UMP) unbiased test with the consideration of time-varying patterns. Monte Carlo simulations have shown that the proposed strategy possesses significantly improved detection sensitivity over intended shift ranges.

Adaptive Charting Techniques: Literature Review and Extensions

“…However, at any step, the adaptive chart is still a one-sided chart. If true process mean shifts are difficult to be estimated via EWMA, such as the feedbackcontrolled process discussed by Wang and Tsung (2007b), the resulting performance may be seriously deteriorated.…”

“…Apley and Tsung (2002), Tsung and Apley (2002), Wang and Tsung (2007a) and Wang and Tsung (2007b) studied the detection of dynamic shifts in multivariate processes. Since the performance of some multivariate charts is dominated by not only shift magnitudes but also shift directions, we will investigate this issue extensively in following sections and propose a new double-sided directionally variant chart for multivariate process monitoring.…”

“…To tackle strong oscillations found in feedback-controlled processes, Wang and Tsung (2007b) proposed an oscillated EWMA for shift forecasting. Similar to the EWMA forecasting with uses exponentially decaying weights, the oscillated EWMA uses decaying weights with alternative signs.…”

“…Dynamic shifts could be generated due to process autocorrelation, inertia properties or the existence of feedback controller (Tucker et al (1993), Wang and Tsung (2007b)). Compared to sustained shifts, shifts that change over time are more difficult to capture.…”

“…Table 2 summarizes the adaptive charts that have variable design parameters. Adaptive EWMA (Capizzi and Masarotto (2003)) Adaptive CUSUM (Sparks (2000)) GLRT (Apley and Shi (1999) T (Wang and Tsung (2007a), Wang and Tsung (2007b)) One fundamental assumption behind the above study is that the process is undergoing a sustained mean shift. Therefore, directionally variant charts show good performance in designated areas and the adaptive 2 T chart with EWMA forecasting exhibit satisfactory results in detecting small shifts.…”