The total median statistic to monitor contaminated normal data. Issue 1 (2nd January 2016) - Figueiredo, Fernanda; Gomes, M. Ivette
Abstract: Despite the advantages of the use of the normal distribution in Statistical Quality Control, the normality assumption is too restrictive for modelling real data sets, which usually exhibit asymmetry or tails heavier than the normal tails. But even in potential normal situations, there is often a small to moderate percentage of contamination in the data. In this paper, we analyze the efficiency and robustness of the total median statistic in comparison with the sample mean and the sample median to estimate the mean value of symmetric contaminated normal distributions, close to the normal, but with heavier-than-normal tails. We also compare the performance of the total median and the sample mean charts to monitor the mean value of such processes. The simulation results lead us to suggest the use of the total median statistic due to its efficiency and degree of robustness.