The impact of Weibull data and autocorrelation on the performance of the Shewhart and exponentially weighted moving average control charts

Abstract

Many real-world processes generate autocorrelated and/or Weibull data. In such cases, the independence and/or normality assumptions underlying the Shewhart and EWMA control charts are invalid. Although data transformations exist, such tools would not normally be understood or employed by naive practitioners. Thus, the question arises, "What are the effects on robustness whenever these charts are used in such applications?" Consequently, this paper examines and compares the performance of these two control charts when the problem (the model) is subjected to autocorrelated and/or Weibull data. A variety of conditions are investigated related to the magnitudes of various parameters related to the process shift, the autocorrelation coefficient and the Weibull shape parameter. Results indicate that the EWMA chart outperforms the Shewhart in 62% of the cases, particularly those cases with low to moderate autocorrelation effects. The Shewhart chart outperforms the EWMA chart in 35% of the cases, particularly those cases with high autocorrelation and zero or high process shift effects.

Application of multistage process control methodology for software quality management

“…Table 3 shows that the residuals of all the three models are normally distributed (p-value ≥ 0.05). Hence the residuals can be monitored using a control chart (Jayathavaj & Pongpullponsak, 2014;Black et al, 2011).…”

A new distribution-free generally weighted moving average monitoring scheme for detecting unknown shifts in the process location

“…Thereafter, a number of researchers investigated the performance of parametric GWMA schemes, to count a few, Sheu and Yang (2006), Sheu and Hsieh (2009), Tai and Lin (2009), Teh et al (2012), Aslam et al (2017), Chakraborty et al (2017), etc. SPM schemes have been applied to a variety of fields, including engineering, production, manufacturing, finance, food industry, chemistry and biochemistry, see Simoglou et al (1997), Black et al (2011), Bag et al (2012), Lim et al (2017), etc. In practice, the underlying process distribution is generally unknown.…”

A wavelet‐based nonparametric CUSUM control chart for autocorrelated processes with applications to network surveillance

“…It has been shown that, for conventional control charts including Shewhart charts, cumulative sum (CUSUM) charts, and exponentially weighted moving average (EWMA) charts, and deviations from either the distributional assumption and/or the uncorrelated assumption may result in either more frequent false alarms or reduced anomaly detection power. See, for example, Johnson and Bagshaw 3 and Black et al 4 There has been work in developing SPC methods for correlated observations under a normality assumption. Most methods are "residual-based" methods, where a model is assumed to describe the correlation structure within the data, and the approximately uncorrelated residuals are extracted for use in a control chart.…”

“…It has been shown that, for conventional control charts including Shewhart charts, cumulative sum (CUSUM) charts, and exponentially weighted moving average (EWMA) charts, and deviations from either the distributional assumption and/or the uncorrelated assumption may result in either more frequent false alarms or reduced anomaly detection power. See, for example, Johnson and Bagshaw and Black et al…”