A nonparametric CUSUM chart for process dispersion

We propose a distribution-free cumulative sum (CUSUM) chart for joint monitoring of location and scale based on a Lepage-type statistic that combines the Wilcoxon rank sum and the Mood statistics. Monte Carlo simulations were used to obtain control limits and examine the in-control and out-of-control performance of the new chart. A direct comparison of the new chart was made with the original CUSUM Lepage based on Wilcoxon rank sum and Ansari-Bradley statistics. The result is a more powerful chart in most of the considered scenarios and thus a more useful CUSUM chart. An example using real data illustrates how the proposed control chart can be implemented.

Section: Discussionmentioning

confidence: 99%

A distribution‐free CUSUM chart for joint monitoring of location and scale based on the combination of Wilcoxon and Mood statistics

Tercero-Gómez

Aguilar-Lleyda

Cordero-Franco

et al. 2020

“…The first existing method considered is the T‐CUSUM chart suggested by Lucas, 3 which is constructed and designed based on the assumption that the process under monitoring has a regular Poisson distribution. We also consider the nonparametric CUSUM chart suggested by Shirke and Barale 23 for monitoring process dispersion based on a sign test, which is denoted as S‐CUSUM. The control limit of T‐CUSUM is determined based on the Poisson distribution assumption.…”

Section: Simulation Studiesmentioning

confidence: 99%

“…See Qiu 19 for an overview on nonparametric SPC. Some nonparametric or distribution-free control charts have been proposed to monitor changes in data dispersion, including those based on the squared rank test, 20,21 the sign statistic, [22][23][24] the Ansari-Bradley statistic, 25 and the statistic with a binomial distribution. 26,27 There are also nonparametric control charts that can jointly monitor process mean and dispersion, such as the ones based on the Lepage statistic [28][29][30][31][32] and the Cucconi statistic, [33][34][35] among others.…”

Section: Introductionmentioning

confidence: 99%

Novel nonparametric control charts for monitoring dispersion of count data

Wang,

Wu,

Qiu

2023

Count data are common in practice. Statistical process control for count data thus has attracted much attention in recent years. Most existing methods on this topic focus on the detection of mean shifts of count data based on parametric modeling. However, their assumed parametric models (e.g., the Poisson probability model) are often invalid in practice due mainly to the potential impact of some latent confounding risk factors, which would lead to unreliable performance of the related control charts. In addition, it is highly desirable and important to monitor the dispersion of count data when the Poisson probability model is invalid. To this end, new nonparametric cumulative sum control charts and their corresponding self‐starting versions are suggested in this paper for monitoring the dispersion of count data based on data categorization and categorical data analysis. Numerical results show that the proposed method can provide more effective and robust monitoring of count data in comparison with some representative existing methods. A real‐data example is used to demonstrate its implementation and application.

“…There are only a few nonparametric control charts available in the SPC literature for monitoring process dispersion based on the sign statistic. Amin et al 14 proposed Shewhart sign chart for process dispersion based on in-control quartiles (see also, Bradley 30 ), Shirke and Barale 31 proposed CUSUM sign chart for process dispersion based on in-control deciles. Motivated by the works of Shirke and Barale, 31 Riaz and Abbasi, 18 and Alevizakos et al, 19 in this paper, we propose the EWMA, double EWMA (DEWMA), and triple EWMA (TEWMA) sign charts for process dispersion based on in-control deciles.…”

Section: Introductionmentioning

confidence: 99%

“…Amin et al 14 proposed Shewhart sign chart for process dispersion based on in-control quartiles (see also, Bradley 30 ), Shirke and Barale 31 proposed CUSUM sign chart for process dispersion based on in-control deciles. Motivated by the works of Shirke and Barale, 31 Riaz and Abbasi, 18 and Alevizakos et al, 19 in this paper, we propose the EWMA, double EWMA (DEWMA), and triple EWMA (TEWMA) sign charts for process dispersion based on in-control deciles. For a review on nonparametric EWMA-type control charts, see Triantafyllou and Ram.…”

Section: Introductionmentioning

confidence: 99%

Deciles‐based EWMA‐type sign charts for process dispersion

Godase

Rakitzis

Mahadik

et al. 2022

In this paper, we propose and study nonparametric exponentially weighted moving average (EWMA) control charts based on the sign statistic, which are suitable for detecting changes in process dispersion. The sign statistic is defined by using appropriate deciles of the in‐control process distribution. The statistical performances of the proposed charts are determined through Monte Carlo simulation. Practical guidelines are provided for the statistical designs of these charts. We evaluate the statistical performances of the proposed charts by comparing them with that of the deciles‐based CUSUM sign chart and the EWMA lnS2 chart. The comparisons show that the proposed charts are viable nonparametric methods for monitoring the process dispersion. Finally, we provide an illustrative example to demonstrate the implementation of the proposed charts in practice.