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.