Robustness of the EWMA median control chart to non-normality

Abstract

Abstract:The control charts with exponentially weighted moving average (EWMA) had been shown to be effective for detecting small shifts in the mean of the process characteristic. When the data depart from normality or have the presence of outliers, the sample median might be used to provide a fairer representation of centrality of the data. In the present paper, the performances of the EWMA median control charts are evaluated under several distributions. The average run length (ARL) is applied to evaluate the performance of control charts, and the method for calculating ARL of the EWMA median chart is developed using the integral equation approach. Based on our study, the EWMA median chart with a small value of smoothing constant has a low false alarm rate. But as the shift of process mean is large, to maintain the detection ability of the chart, the value of smoothing constant should be increased. In addition, if the data follow a heavy-tailed distribution, it can be shown that the EWMA median chart is always more efficient than the EWMA average chart in detecting the shift of process mean.

The modified control charts for monitoring the error detection of process control under different estimators 

“…But what can organizations do if the normality assumption fails in practical life. There are very few studies available in the literature that highlighted this issue, including , Noorossana et al (2016), Zhang et al (2017), Lin et al (2017), Erto et al (2018), Li et al (2018), and Liang et al (2019). As many production processes do not necessarily follow the normality assumption, the study aims to introduce the memory-based control charts, i.e., HEWMA and EEWMA control charts assume that the underlying process distribution follows an RPFD.…”

Control theory for skewed distribution under operation side of the telecommunication industry and hard-bake process in the semiconductor manufacturing process

“…23 Although the skewed distribution occurs more often in different real-life scenarios but very less work has been discussed for such situations when the process distribution does not follow the normality but a skewed distribution. Interested readers may read Noorossana et al, 24 Lin et al, 25 Erto et al, 26 Liang et al 27 and Khan et al 28 Also, the control monitoring for the shape parameter of Power function distribution, weighted power function distribution was done by Zaka et al, 29 Zaka et al 30 The KL2PFD introduced by Zaka et al 29 is more flexible to use for the positively skewed data than Kumaraswamy distribution and Power function distribution. By considering this advantage of Kumaraswamy distribution, we will discuss the importance of the shape parameter distribution and its application in reliability engineering problems.…”

Control Charts for the Shape Parameter of Power Function Distribution under Different Classical Estimators

“…In a real life scenario, this is not always possible to fulfil the normality assumption for the distributions of error during the process. A very few work in literature is about this situation including [12][13][14][15][16][17][18].…”