Nonparametric Control Charts: An Overview and Some Results

Chakraborti, S.; Laan, van der P Paul; Bakir, ST

doi:10.1080/00224065.2001.11980081

Cited by 311 publications

(181 citation statements)

References 29 publications

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“…These charts are attractive because their run-length distribution is the same for all continuous distributions so that they can be applied without any knowledge of the form of the underlying distribution. For comprehensive overviews of the literature on nonparametric control charts see Chakraborti et al (2001Chakraborti et al ( ), (2007Chakraborti et al ( ) and (2010. A control chart that combines the shift detection properties of the EWMA with the robustness of a NP chart is thus clearly desirable.…”

Section: Introductionmentioning

confidence: 99%

A nonparametric exponentially weighted moving average signed-rank chart for monitoring location

Graham

Chakraborti

Human

2011

Computational Statistics & Data Analysis

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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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Section: Introductionmentioning

confidence: 99%

A nonparametric exponentially weighted moving average signed-rank chart for monitoring location

Graham

Chakraborti

Human

2011

Computational Statistics & Data Analysis

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“…In this context, one key problem is the lack of IC robustness of some of the well-known parametric charts (see, e.g. Chakraborti et al (2001Chakraborti et al ( , 2004). This, for example, means that there could be too many false alarms than what is nominally expected and obviously, this could mean considerable loss of time and resources.…”

Section: Introductionmentioning

confidence: 99%

A phase II nonparametric control chart based on precedence statistics with runs-type signaling rules

Chakraborti

Eryılmaz

Human

2009

Computational Statistics & Data Analysis

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a b s t r a c tNonparametric control charts do not require knowledge about the shape of the underlying distribution and can thus be attractive in certain situations. Two new Shewharttype nonparametric control charts are proposed for monitoring the unknown location parameter of a continuous population in Phase II (prospective) applications. The charts are based on control limits given by two specified order statistics from a reference sample, obtained from a Phase I (retrospective) analysis, and using some runs-type signaling rules. The plotting statistic can be any order statistic in a Phase II sample; the median is used here for simplicity and robustness. Exact run length distributions of the proposed charts are derived using conditioning and some results from the theory of runs. Tables are provided for practical implementation of the charts for a given in-control average run length (ARL 0 ) between 300 and 500. Comparisons of the average run length ARL, the standard deviation of run length (SDRL) and some run length percentiles show that the charts have robust in-control performance and are more efficient when the underlying distribution is t (symmetric with heavier tails than the normal) or gamma (1, 1) (right-skewed). Even for the normal distribution, the new charts are quite competitive. An illustrative numerical example is given. An added advantage of these charts is that they can be applied before all the data are collected which might lead to savings in time and resources in certain applications.

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“…To remedy this, a number of distribution-free (or nonparametric) schemes that maintain the same chart properties over a class of distributions have been proposed in the literature. For an overview of nonparametric control charts, see Chakraborti et al [1,2].…”

Section: Introductionmentioning

confidence: 99%

A Nonparametric Shewhart-Type Quality Control Chart for Monitoring Broad Changes in a Process Distribution

Bakir

2012

International Journal of Quality, Statistics, and Reliability

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This paper develops a distribution-free (or nonparametric) Shewhart-type statistical quality control chart for detecting a broad change in the probability distribution of a process. The proposed chart is designed for grouped observations, and it requires the availability of a reference (or training) sample of observations taken when the process was operating in-control. The charting statistic is a modified version of the two-sample Kolmogorov-Smirnov test statistic that allows the exact calculation of the conditional average run length using the binomial distribution. Unlike the traditional distribution-based control charts (such as the Shewhart X-Bar), the proposed chart maintains the same control limits and the in-control average run length over the class of all (symmetric or asymmetric) continuous probability distributions. The proposed chart aims at monitoring a broad, rather than a one-parameter, change in a process distribution. Simulation studies show that the chart is more robust against increased skewness and/or outliers in the process output. Further, the proposed chart is shown to be more efficient than the Shewhart X-Bar chart when the underlying process distribution has tails heavier than those of the normal distribution.

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Nonparametric Control Charts: An Overview and Some Results

Cited by 311 publications

References 29 publications

A nonparametric exponentially weighted moving average signed-rank chart for monitoring location

A nonparametric exponentially weighted moving average signed-rank chart for monitoring location

A phase II nonparametric control chart based on precedence statistics with runs-type signaling rules

A Nonparametric Shewhart-Type Quality Control Chart for Monitoring Broad Changes in a Process Distribution

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