A Distribution-Free Shewhart Quality Control Chart Based on Signed-Ranks

Bakir, Saad T.

doi:10.1081/qen-120038022

Cited by 137 publications

(96 citation statements)

References 20 publications

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“…For the three EWMA charts we choose the design parameters (λ, L) so that ≈ 370 and 500 for Examples 1 and 2, respectively. It should be noted that the industry standard ARL 0 values of 370 and 500 are far from being attainable when using the 1-of-1 Shewhart-type SR chart, because the highest ARL 0 that it can attain for subgroups of size 5 is 16 (see Bakir (2004), page 616). In addition, the 2-of-2 SR charts under the DR and KL schemes also can't attain the industry standard ARL 0 values; see Chakraborti and Eryilmaz (2007) …”

Section: Examplesmentioning

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: Examplesmentioning

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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“…The control limits are computed by using Lugannani-Rice-saddle point, Edgeworth, and Monte Carlo approximation for estimation (Chakraborti & Van de Wiel, 2008). The control chart based on median (Graham et al, 2010) and Signed-rank (Bakir, 2004) (Ghute & Shirke, 2012). Chakraborti and Eryilmaz (2007) developed the effective Shewhart-type chart based on the Wilcoxon signed rank statistics by incorporating some "runs" type signaling rules.…”

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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“…The normality assumption, however, may not be valid for some manufacturing data; citations are given in Bakir [5], Chakraborti and Graham [6], and Chakraborti et al [7].…”

Section: Introductionmentioning

confidence: 99%

A Nonparametric Scheme for Monitoring a Process Output with a Block Effect

Bakir

2012

International Journal of Quality, Statistics, and Reliability

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This paper proposes a distribution-free (or nonparametric) control scheme to monitor a process output that contains two special causes of variation called "block or batch" effects and "treatment or position" effects. The scheme properties (control limits, false alarm rate, and in-control average run length) stay the same under any assumed continuous probability distribution. For moderate sample sizes, these properties can be computed exactly from available tables without the need to estimate the mean or variance of the process. The proposed monitoring scheme requires ranking the observations within blocks and using the method of analysis of means by ranks. The paper includes an illustrative example concerning the grinding process of silicon wafers used in integrated circuits production.

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A Distribution-Free Shewhart Quality Control Chart Based on Signed-Ranks

Cited by 137 publications

References 20 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 simulation study on the performance of the sign test, Mann-Whitney test, Hodges-Lehmann estimator and control charts for Normal and Weibull data

A Nonparametric Scheme for Monitoring a Process Output with a Block Effect

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