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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.

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Distribution-free (nonparametric) control charts provide a robust alternative to a data analyst when there is lack of knowledge about the underlying distribution. A two-sided nonparametric Phase II exponentially weighted moving average (EWMA) control chart, based on the exceedance statistics (EWMA-EX), is proposed for detecting a shift in the location parameter of a continuous distribution. The nonparametric EWMA chart combines the advantages of a nonparametric control chart (known and robust in-control performance) with the better shift detection properties of an EWMA chart. Guidance and recommendations are provided for practical implementation of the chart along with illustrative examples. A performance comparison is made with the traditional (normal theory) EWMA chart for subgroup averages and a recently proposed nonparametric EWMA chart based on the Wilcoxon-MannWhitney statistics. A summary and some concluding remarks are given.Keywords: Binomial, Nonparametric, Markov chain, Quality control, Robust, Run-length, Search algorithm, Simulation IntroductionThe exponentially weighted moving average (EWMA) control charts have enjoyed widespread popularity in practice with data analysts. These charts are similar to the cumulative sum (CUSUM) charts in the sense that they both use accumulated data up until the most recent time point in order to detect process shifts. These sequential charts are particularly effective in d e t e c t i n g r e l a t i v e l y s m a l l a n d p e r s i s t e n t c h a n g e s ( s t e p s h i f t s ) i n t h e p r o c e s s ( s e e e . g .Montgomery, 2009 pages 400 and 419). However, the EWMA charts are preferred by some in the industry. They are easier to implement and as Steiner and Jones (2010) put it, "The main advantage of an EWMA is that it provides an ongoing local estimate of the average score…Another minor advantage is the inherent two-sided nature of an EWMA." Traditional EWMA charts for subgroup averages were introduced by Roberts (1959) and since then there has been a tremendous amount of work on EWMA charts (see e.g. the overview by Ruggeri et al. (2007) and the references therein). Some newer references include Huwang et al. (2010), Maravelakis and Castagliola (2009) and Su et al. (2011). In typical applications of the Page | 2 traditional EWMA charts for subgroup averages it is usually assumed that the underlying process distribution is normal, or, at least, approximately so. However, in certain situations in practice, the normality assumption may not be tenable or justifiable for lack of information or data. Human et al. (2011) recently showed that the traditional EWMA chart can lack in-control (IC) robustness for some non-normal distributions such as the symmetric bi-modal and the contaminated normal distribution. Their observations call into question routine applications of the traditional EWMA chart in practice. It should be noted that although Montgomery (2001) page 433 stated "It (the EWMA) is almost a perfectly nonparametric (distribution-free)proc...

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.

Nonparametric control charts provide a robust alternative in practice when the form of the underlying distribution is unknown. Nonparametric CUSUM (NPCUSUM) charts blend the advantages of a CUSUM with that of a nonparametric chart in detecting small to moderate shifts. In this paper, we examine efficient design and implementation of Phase II NPCUSUM charts based on exceedance (EX) statistics, called the NPCUSUM-EX chart. We investigate the choice of the order statistic from the reference (Phase I) sample that defines the exceedance statistic. We see that choices other than the median, such as the 75 th percentile, can yield improved performance of the chart in certain situations. Furthermore, observing certain shortcomings of the average run-length (ARL), we use the median run-length (MRL) as the performance metric. The NPCUSUM-EX chart is compared with the NPCUSUM-Rank chart proposed by Li et al. (2010) based on the popular Wilcoxon rank-sum statistic. We also study the choice of the reference value, k, of the CUSUM charts. An illustration with real data is provided.

In this paper, we propose a modified side-sensitive (MSS) synthetic ̅ chart which signals only if all the consecutive plotting statistics that lead to an out-of-control event fall on one side of the center line; unlike the non-side-sensitive, standard and revised side-sensitive synthetic ̅ charts that also signal even when some of the plotting statistics fall on opposite sides of the center line. Moreover, we use the Markov chain imbedding technique to study and compare the zero-state and steady-state average run-length (ARL), extra quadratic loss, average ratio of the ARLs and performance comparison index of the proposed MSS chart with other Shewhart-type synthetic and runs-rules charts. The synthetic ̅ chart with this MSS feature has a better overall zero-state and steady-state performance than the existing synthetic ̅ charts and hence makes it a strong contender in many applications where existing synthetic ̅ charts are currently used.