Detecting changes in location using distribution-free control charts with big data

摘要

This paper proposes a simple distribution-free control chart for monitoring shifts in location when the process distribution is continuous but unknown. In particular, we are concerned with big data applications where there are sufficient in-control data that can be used to specify certain quantiles of interest which, in turn, are used to assess whether the new, incoming data to be monitored are in control. The distribution-free chart is shown to lose very little power against the Shewhart charts designed for normally distributed data. The proposed charts offer a practical and robust alternative to the classical Shewhart charts which assume normality, particularly when monitoring quantiles and the data distribution is skewed. The effect of the size of the reference sample is examined on the assumption that the quantiles are known. Conclusions and recommendations are offered.