A general class of nonparametric control charts

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

“…However, in many applications, the location parameter is unknown and in such cases, different nonparametric statistics are used (see Refs. [32][33][34][35][36][37][38][39] ). An extensive analysis of nonparametric control charts is presented by Chakraborti and Graham 10 and Koutras and Triantafyllou, 40 while an overview up to 2019 is given in Chakraborti and Graham.…”

Section: Introductionmentioning

confidence: 99%

Nonparametric triple exponentially weighted moving average signed‐rank control chart for monitoring shifts in the process location

Alevizakos

Chatterjee

Koukouvinos

2021

Nonparametric (or distribution-free) control charts are used for monitoring processes where there is a lack of knowledge about the underlying distribution. In this article, a triple exponentially weighted moving average control chart based on the signed-rank statistic (referred as TEWMA-SR chart) is proposed for monitoring shifts in the location parameter of an unknown, but continuous and symmetric, distribution. The run-length characteristics of the proposed chart are evaluated performing Monte Carlo simulations. A comparison study with other existing nonparametric control charts based on the signed-rank statistic, the TEWMA sign chart, and the parametric TEWMAchart indicates that the proposed chart is more effective in detecting small shifts, while it is comparable with the other charts for moderate and large shifts. Finally, two illustrative examples are provided to demonstrate the application of the proposed chart.

“…Haq 14 suggested a synthetic non‐parametric EWMA chart under the sign test. Koutras 15 proposed a general class of Shewhart type non‐parametric control charts. Castagliola et al 16 .…”

Section: Introductionmentioning

confidence: 99%

A non‐parametric double homogeneously weighted moving average control chart under sign statistic

Riaz

Abid

Shabbir

et al. 2020

In practical situations, the underlying process distribution sometimes deviates from normality and their distribution is partially or completely unknown. In that instance, rather than staying with/depending on the conventional parametric control charts, we consider non‐parametric control charts due to their exceptional performance. In this paper, a new non‐parametric double homogeneously weighted moving average sign control chart is proposed with the least assumptions. This chart is based on a sign test statistic for catching the smaller deviations in the process location. Run‐length (RL) properties of the proposed chart are studied with the help of Monte Carlo simulations. Both in‐control and out‐of‐control RL properties show that the proposed chart is a better contender as compared to some existing charts from the literature. A real‐life application for practical consideration of the proposed chart is also provided.