Abstract:
Nonparametric control charts are useful when there is limited
or complete lack of knowledge about the form of the underlying distribution.
Though traditional statistical process control (SPC) applications of
control charts involve subgrouped data, recent advances have led to more
and more instances where individual measurements (data) are collected
over time. A two-sided nonparametric exponentially weighted moving average
(EWMA) control chart for i.i.d. individual data is proposed based on the
sign (SN) statistic. A Markov chain approach is used to determine the
run-length distribution of the chart and some associated performance characteristics.
An important advantage of the nonparametric EWMA-SN chart is
its inherent in-control robustness. In fact, the in-control run-length distribution
and hence all of its associated characteristics (e.g., false alarm rate,
average, standard deviation, median, etc.) of the chart remain the same
for all unknown continuous distributions. In order to aid practical
implementation, tables are provided for the chart’s design parameters. An
extensive simulation study shows that on the basis of minimal required
assumptions, robustness of the in-control run-length distribution and out-ofcontrol
performance, the proposed nonparametric EWMA-SN chart can be a
strong contender in many applications where traditional parametric charts
are currently used.
