Control Charts with Robust Probability Limits

Two of the main problems in constructing a control chart for detecting shifts in process variation are to estimate the process variation based on preliminary samples taken from the process and to evaluate its control limits. The unknown process variation is generally estimated from either the sample standard deviations or ranges of the preliminary samples. These classical estimates of process variation are highly sensitive to the presence of contaminated data in the preliminary samples and subsequently reduce the power of control charts in detecting assignable causes. The 3-sigma control limits of the Shewhart control charts are evaluated based on the assumption that the sample statistic being plotted is Gaussian distributed. However, the sampling distributions of the sample standard deviation and range are skewed even if the samples are taken from a Gaussian population. The aims of this paper are (i) to discuss robust estimates of scale parameter from preliminary samples taken from the process under study, and (ii) to construct control charts with probability limits evaluated using robust estimators that are resistance to contaminated preliminary samples.