A Nonparametric Procedure for Process Control Based on Within-Group Ranking

Bakir, Saad T.; Reynolds, Marion R.

doi:10.2307/1268514

Cited by 59 publications

(67 citation statements)

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“…It would be possible to consider multiple sections representing, for example, diþ erent seasons by using the Kruskal± Wallis test (see Conover, 1999) but that is not discussed here. There have been earlier descriptions of other non-parametric cusums based upon the signedrank test in Bakir & Reynolds (1979) and Rank-based EWMA charts, see for example Hackl & Ledolter (1991). A similar technique to the one discussed here, which compares process data against a standard set of reference data, was discussed in Park & Reynolds (1987).…”

Section: The Summed Rank Cusum (Src)mentioning

confidence: 90%

Using the Summed Rank Cusum for monitoring environmental data from industrial processes

Stewardson¹,

Coleman²

2001

Journal of Applied Statistics

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Environmental issues have become a hot topic recently, especially those surrounding industrial outputs. Effluents, emissions, outflows, by-products, waste materials, product de-commissioning, land reclamation and energy consumption are all the subject of monitoring, either under new legislation or through economic necessity. Many types of environmental data are often difficult to understand or measure because of their unusual distribution of values however. Standard methods of monitoring these data types often fail or are unwieldy. The scarcity of events, small volume measurements and the unusual time scales sometimes involved add to the complexity of the task. One recently developed monitoring technique is the Summed Rank Cusum (SRC) that applies non-parametric methods to a standard chart. The SRC can be used diagnostically and this paper describes the application of this new tool to three data sets, each derived from a different problem area. These are measuring industrial effluent, assessing the levels of potentially harmful proteins produced by an industrial process and industrial land reclamation in the face of harmful waste materials. The use of the SRC to spot change points in time retrospectively is described. The paper also shows the use of SRC in the significant-difference testing mode, which is applied via the use of spreadsheets. Links to other similar methods described in the literature are given and formulae describing the statistical nature of the transformation are shown. These practical demonstrations illustrate that the graphical interpretation of the method appears to help considerably in practice when trying to find time-series change points. The charts are an effective graphical retrospective monitoring technique when dealing with non-normal data. The method is easy to apply and may help considerably in dealing with environmental data in the industrial setting when standard methods are not appropriate. Further work is continuing on the more theoretical aspects of the method.

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Section: The Summed Rank Cusum (Src)mentioning

confidence: 90%

Using the Summed Rank Cusum for monitoring environmental data from industrial processes

Stewardson¹,

Coleman²

2001

Journal of Applied Statistics

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“…Early motivation of rank based control charts can be found in Bakir and Reynolds (1979), Park and Reynolds (1987) and Hack and Ledolter (1992). In the last two decades, several researchers studied rank based control charts, see, for example, Qiu and Hawkins (2001), Zou, Wang, and Tsung (2012) among others.…”

Section: Please Scroll Down For Articlementioning

confidence: 99%

Comparisons of Shewhart-type rank based control charts for monitoring location parameters of univariate processes

Mukherjee

Sen

2015

International Journal of Production Research

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The nonparametric (distribution-free) control charts are robust alternatives to the conventional parametric control charts when the form of underlying process distribution is unknown or complicated. In this paper, we consider two new nonparametric control charts based on the Hogg-Fisher-Randle (HFR) statistic and the Savage rank statistic. These are popular statistics for testing location shifts, especially in right-skewed densities. Nevertheless, the control charts based on these statistics are not studied in quality control literature. In the current context, we study phase-II Shewhart-type charts based on the HFR and Savage statistics. We compare these charts with the Wilcoxon rank-sum chart in terms of false alarm rate, out-of-control average run-length and other run length properties. Implementation procedures and some illustrations of these charts are also provided. Numerical results based on Monte Carlo analysis show that the new charts are superior to the Wilcoxon rank-sum chart for a class of non-normal distributions in detecting location shift. New charts also provide better control over false alarm when reference sample size is small.

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“…The articles by Bakir and Reynolds (1979), McGilchrist and Woodyer (1975) and Bhattacharya and Frierson (1981) explore nonparametric summary statistics. The use of nonparametric summary statistics in the CUSUM (a) alleviates the need for assuming normality of the observed data and (b) simplifies the calculation of the ARL of the procedure assuming the distribution of the nonparametric statistic under a shift in the center of the observed data can be found.…”

Section: King and Longneckermentioning

confidence: 99%

Computing the distribution of the wilcoxon statistic with applications to process control

King

Longnecker

1990

Communications in Statistics - Simulation and Computation

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A computer algorithm for computing the alternative distributions of the Wilcoxon signed rank statistic under shift alternatives is discussed. An explicit error bound is derived for the numeric integration approximation to these distributions.A nonparametric process control procedure in which the standard CUSUM procedure is applied to the Wilcoxon signed rank statistic is discussed. In order to implement this procedure, the distribution of the Wilcoxon statistic under shift of the underlying distribution from its point of symmetry needs to be computed. The average run length of the nonparametric and parametric CUSUM are compared.

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A Nonparametric Procedure for Process Control Based on Within-Group Ranking

Cited by 59 publications

References 0 publications

Using the Summed Rank Cusum for monitoring environmental data from industrial processes

Using the Summed Rank Cusum for monitoring environmental data from industrial processes

Comparisons of Shewhart-type rank based control charts for monitoring location parameters of univariate processes

Computing the distribution of the wilcoxon statistic with applications to process control

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