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

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Sparks, Ross; Chakraborti, Subha


2017-12-28


Journal Article


Journal of Quality Technology


31


577–2595


This paper proposes a simple distribution-free control chart for monitoring shifts in location when the process distribution is unknown. In particular we are concerned with big data applications where there is sufficient in-control (reference) data that can be used as a baseline. These reference data are used to calculate certain quantiles of interest which, in turn, are used to assess whether the new, incoming data to be monitored, are in-control. In fact the size of the reference data is so large in these applications that the estimated quantile values can be assumed to be the true underlying values. The distribution-free chart is shown to lose very little power on the Shewhart charts designed for normally distributed data. However, it is at times much more efficient than the current practice of applying the classical Shewhart chart to the best Box-Cox transformed data to normality. Therefore the proposed charts offer a practical and robust alternative to the classical Shewhart charts which assume normality, or when these charts are applied to transformed data, particularly when the data distributions are skewed. Additionally, a distribution-free EWMA chart is considered for detecting smaller shifts with rational subgroups and individual data. The effect of the size of the reference sample is examined on the assumption that the quantiles are known. The proposed charts are shown to be applicable with minor adjustments when the data are auto-correlated. Conclusions and recommendations are offered.


ASQ


Monitoring, non-parametric, statistical process control


Applied Statistics


https://doi.org/10.1002/qre.2219


EP166273


Journal article - Refereed


English


Sparks, Ross; Chakraborti, Subha. Detecting changes in location using distribution-free control charts with big data. Journal of Quality Technology. 2017; 31:577–2595.https://doi.org/10.1002/qre.2219



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