Cumulative Sum Chart Modeled under the Presence of Outliers

Abstract

Cumulative sum control charts that are based on the estimated control limits are extensively used in practice. Such control limits are often characterized by a Phase I estimation error. The presence of these errors can cause a change in the location and/or width of control limits resulting in a deprived performance of the control chart. In this study, we introduce a non-parametric Tukey's outlier detection model in the design structure of a two-sided cumulative sum (CUSUM) chart with estimated parameters for process monitoring. Using Monte Carlo simulations, we studied the estimation effect on the performance of the CUSUM chart in terms of the average run length and the standard deviation of the run length. We found the new design structure is more stable in the presence of outliers and requires fewer amounts of Phase I observations to stabilize the run-length performance. Finally, a numerical example and practical application of the proposed scheme are demonstrated using a dataset from healthcare surveillance where received signal strength of individuals' movement is the variable of interest. The implementation of classical CUSUM shows that a shift detection in Phase II that received signal strength data is indeed masked/delayed if there are outliers in Phase I data. On the contrary, the proposed chart omits the Phase I outliers and gives a timely signal in Phase II. of estimation error may occur when there exist some extreme values or outliers in the Phase I observations [4]. Outliers may occur by chance in the process data or could be due to some incorrect specifications of instruments or as a result of human reporting error. The presence of outliers in a process data can adversely affect parametric computations. Of course, dropping the outliers from the sampled observations is the simplest remedy often used to avoid such a problem. However, this may not be appropriate for small sample data. Thus, outlier detection is key to adequate monitoring of process parameters. Recently, some non-parametric and robust outlier detection procedures have been suggested to enhance the performance of control charts in the presence of outliers. For example, see Schoonhoven, Nazir [5], Nazir, Riaz [6], Amdouni, Castagliola [7], Abid, Nazir [8], Zhang, Li [9] and Mahmood, Nazir [10], and the references therein. Hawkins [11], Beckman and Cook [12] and Barnett and Lewis [13] have studied several outlier detectors. The common parametric outlier detectors are the Student-type and Grubbs-type detectors mostly used in the regression residuals and when the data is normally distributed (cf. Grubbs [14] and Tietjen and Moore [15]). For non-normal data, the Tukey's outlier detection model is more robust since its independence of the sample mean and standard deviation [16]. Teoh, Khoo [17] suggested the local outlier factor, a non-parametric outlier detector for detecting the outliers in the multivariate setup. Knorr, Ng [18] designed a detector based on classification methodology while a detector based on order statistics was studied by T...

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