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

Bakir, Saad T.; Reynolds, Marion R.

doi:10.1080/00401706.1979.10489747

Cited by 105 publications

(25 citation statements)

References 7 publications

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“…and 10 (for a detailed discussion on the choice of n see Bakir and Reynolds (1979) wherein they concluded that the best subgroup size is somewhere between 5 and 10 depending on the desired ARL 0 and the size of the shift ( ) to be detected). Using a search algorithm with five values of λ (i.e.…”

Section: Choice Of Design Parametersmentioning

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: Choice Of Design Parametersmentioning

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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“…Bakir and Reynolds [7] probably is the first paper to discuss nonparametric procedures for process control for within-group samples. From early 2000s onward, there is a surge of nonparametric control charting techniques for various process characteristics.…”

Section: Nonparametric Control Chartsmentioning

confidence: 99%

Control Phase

Muralidharan

2015

Six Sigma for Organizational Excellence

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• Document a new or improved process and measurement • Use statistical process control (SPC) for validating collection systems • Use SPC to ascertain the repeatability and reproducibility of metrics in an operational environment • Define the control plan and its supporting plans such as communications plan of the improvements and operational changes to the customers and stakeholders, prepare implementation and risk management plan, consolidate cost-benefit, and change management plan • Establish tracking procedures in an operational environment: monitor implementation, validate and stabilize performance gains, and jointly audit the results and confirm the financials • Setup control plans for tolerances, controls, measures, and standard operating procedures • Validate in-control process and benefits for process capability, MSA and Gage R&R, and documentation • Document and the follow-up steps • Exit review Control PlansSo far, our attempt has been to identify the most important contributing variables of the process. Through the completed five phases, we have been trying to establish the best process model free of all kinds of variations. The method so far enabled us to identify a viable model and helped us to quantify the nature of the relationship between the important variables of the process output. The statistical process control technique can now be employed with considerable effectiveness for monitoring and surveillance of the process. Techniques such as control charts and capability assessment can be used to monitor the process output and detect when changes in the inputs are required to bring the process back to an in-control state.

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“…Graham et al (2012) presented a two-sided nonparametric Phase II exponentially weighted moving average (EWMA) control chart, based on the exceedance statistics (EWMA-EX) in detecting a shift in the location parameter of a continuous distribution. Bakir and Reynolds (1979) considered a cumulative sum chart based on the Wilcoxon signed rank statistics. Nonparametric multivariate CUSUM control charts for location and scale changes were proposed by Li et al (2013).…”

Section: Literature Reviewmentioning

confidence: 99%

A simulation study on the performance of the sign test, Mann-Whitney test, Hodges-Lehmann estimator and control charts for Normal and Weibull data

Jayathavaj¹,

Pongpullponsak²

2014

10.5267/j.ijiec

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The new method to chart the Hodges-Lehmann estimator control chart is proposed in this study. The evaluation of the three nonparametric control charts -the Sign test (ST), Mann-Whitney (MW), and the Hodges-Lehmann estimator (HL), for the known process distribution using normal and Weibull data represent the symmetric and asymmetric shapes of the process based on the original method through the 10000 run lengths simulation. The result illustrates that the average run length performance of the ST and MW correspond to their respective test statistics but for HL's performance, the result indicates that the average run length is much greater than that derived from Wilcoxon signed rank statistics. The Hodges-Lehmann estimator control chart by the new approach for the known process distribution will be the alternative method for the process that needs to robust outliers' properties from this statistics. In addition, the simulation demonstrates that the performances of the Sign test (ST) from mean and median processes are varied in the skewed distribution, and moreover, the Sign test (ST) from the median process represents more accurate performance. Meanwhile, for the control groups, MW generated within control limits or without restriction shows slightly different performance. The performance of dual scheme for the above-mentioned variable parameters control charts also produce the weighted average values that effect from the tight control scheme to the regular control scheme.

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

Cited by 105 publications

References 7 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

Control Phase

A simulation study on the performance of the sign test, Mann-Whitney test, Hodges-Lehmann estimator and control charts for Normal and Weibull data

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