Abstract:
Nonparametric control charts can provide a robust alternative in practice to the data analyst when there is
a lack of knowledge about the underlying distribution. A nonparametric exponentially weighted moving average
(NPEWMA) control chart combines the advantages of a nonparametric control chart with the better shift detection
properties of a traditional EWMA chart. A NPEWMA chart for the median of a symmetric continuous distribution
was introduced by Amin and Searcy (1991) using the Wilcoxon signed-rank statistic (see Gibbons and
Chakraborti, 2003). This is called the nonparametric exponentially weighted moving average Signed-Rank
(NPEWMA-SR) chart. However, important questions remained unanswered regarding the practical
implementation as well as the performance of this chart. In this paper we address these issues with a more indepth
study of the two-sided NPEWMA-SR chart. A Markov chain approach is used to compute the run-length
distribution and the associated performance characteristics. Detailed guidelines and recommendations for
selecting the chart’s design parameters for practical implementation are provided along with illustrative examples.
An extensive simulation study is done on the performance of the chart including a detailed comparison with a
number of existing control charts, including the traditional EWMA chart for subgroup averages and some
nonparametric charts i.e. runs-rules enhanced Shewhart-type SR charts and the NPEWMA chart based on signs.
Results show that the NPEWMA-SR chart performs just as well as and in some cases better than the competitors.
A summary and some concluding remarks are given.
