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.

This paper conducts a simulation study of the effects of violating the ANOVA normality assumption in the presence of Weibull data. Twelve specific Weibull distributions, characterizing the life data of a variety of real-world products and systems, are investigated. Confidence intervals on test significance and power are generated and compared against intervals from normally distributed data. The ANOVA procedure is found to be robust in the majority of cases. Furthermore, a designed experiment is conducted to isolate the effects of the Weibull shape and scale parameters within the preceding study. The shape parameter is found to have a significant effect on significance and power, whereas the scale parameter does not have a significant effect at the target α = 0.05 test significance level.