A Phase II nonparametric adaptive exponentially weighted moving average control chart

摘要

Purpose:To investigate in-control average run-length robustness for an adaptive exponentially weighted moving average control chart using a simulation study.Summary:EWMA and CUSUM charts are more efficient compared to Shewhart control charts in detecting small changes. These charts use the information from the samples until the point new sample information is incorporated into the chart. There are some practical difficulties in implementation of EWMA charts since they do not signal the direction of shift. To take care of such situations, Capizzi and Masarotto (Ref. 1) consider an adaptive EWMA chart (AEWMA) where the weighting parameter is calculated adaptively as the data point arrives. This approach enables AEWMA charts to be efficient in detecting even small shifts. Mahmoud and Zahran (Ref. 2) proposed a multivariate AEWMA chart (MAEWMA) that can detect the direction of shift. This chart was proposed for normality and with known parameters. The effects of estimators of process parameters on the performance of the AEWMA chart were also studied. By and large, all studies acknowledge the effectiveness of AEWMA over other charts. However, the in-control average run length (ICARL) robustness depends on the assumption of normality, and ICARL robustness is important in practical use of the chart. This article studies the normality violations and their impact on ICARL for the AEWMA chart. The study examines robustness of ICARL for normal, Laplace, t and uniform distributions. The study is extended to six distributions: normal like, symmetric heavy-tailed, symmetric light-tailed, slightly right- skewed, slightly right-skewed and heavy-tailed and highly left-skewed distributions. The results show that AEWMA charts are sensitive to nonnormality and precaution must be used in application of these charts when the underlying distribution is non-normal. To overcome this problem, the authors propose a non parametric chart called NPAEWMA that is distribution-free and have many useful additional properties compared to AEWMA charts.Results:The AEWMA chart proposed by Capizzi and Masarotto (Ref. 1) adapt the weights given to the past observations in a EWMA chart.