Optimization design of the CUSUM and EWMA charts for autocorrelated processes

Abstract

The traditional control charts produce frequent false alarm signals in the presence of autocorrelation. The implementation of the modified chart scheme is a way of handling the problem of autocorrelation in control charts. In modified charts, the standard control limits of the traditional charts are adjusted to offset the influence because of the autocorrelation. The exponentially weighted moving average– and cumulative sum–modified charts are 2 widely used charts for monitoring autocorrelated data. These charts have design parameters in their formulation, and the choice of these parameters play significant roles in the detection of out‐of‐control situations. In reality, the magnitude of the mean shift is uncertain, and this leads to a difficulty in the choice of design parameters by the practitioner. The use of optimal parameters can enhance process performance in such situations. In this paper, we determine optimal design parameters for the charts using an exhaustive search procedure. In the optimization process, we determine the parameters that produce the smallest extra quadratic loss (EQL) value for each autocorrelation coefficient. This criterion measures the anticipated loss attributed to poor quality in the process. The loss in quality is lowered by minimizing the EQL and the combination of parameters in the chart that yields the smallest EQL has a better detection ability over the entire shift range. For the purpose of this work, we concentrate on autocorrelation that can be specifically modelled with autoregressive models. This article provides the practitioner with optimal parameters that can be used to enhance the overall effectiveness of the charts over an entire shift range.

On autoregressive model selection for the exponentially weighted moving average control chart of residuals in monitoring the mean of autocorrelated processes

“…The second method is to revise the upper and lower control limits of control charts to achieve an expected performance. [9][10][11][12][13][14][15][16][17][18] The third approach is to use residual control charts. [19][20][21][22][23][24][25][26] In this case, the residuals are obtained by subtracting predicted values from observed values.…”

“…Also, because only every 10th data is used, the discovery of process shifts may be delayed. The second method is to revise the upper and lower control limits of control charts to achieve an expected performance 9–18 . The third approach is to use residual control charts 19–26 .…”

Model based Level Shift Detection in Autocorrelated Data Streams using a moving window

“…They propose a formula for adjusting the expected ARL of an in-control AR(1) process. As this method is not suitable for more general ARMA-processes, Osei-Aning et al (2017) propose an optimization scheme, that chooses the optimal parameter settings of either CUSUM or Exponentially Weighted Moving Average (EWMA) charts, given an ARMA model and a specified range of interest for the size of a level shift. Zhang (1998) proposes the method EWMAST, which uses the autocorrelation function up to M steps to estimate the variation of the EWMA test statistic, and thus correcting the critical value.…”

Parameter Estimation Effect of the Homogeneously Weighted Moving Average Chart to Monitor the Mean of Autocorrelated Observations With Measurement Errors

“…min , max ], ∆ is the number of increments from min to max . To preserve writing space, increments of 0.1 in the summations in(23) are used, with min =0 and max =2.…”