Methodology for the Application of Nonparametric Control Charts into Practice

Classical parametric statistical methods are based on several basic assumptions about data (normality, independence, constant mean and variance). Unfortunately, these assumptions are not always fulfilled in practice, whether due to problems arising during manufacturing or because these properties are not typical for some processes. Either way, when we apply parametric methods to such data, whether Shewhart’s or other types of parametric control charts, it is not guaranteed that they will provide the right results. For these cases, reliable nonparametric statistical methods were developed, which are not affected by breaking assumptions about the data. Nonparametric methods try to provide suitable procedures to replace commonly used parametric statistical methods. The aim of this paper is to introduce the reader to an alternative way of evaluating the statistical stability of the process, in cases where the basic assumptions about the data are not met. First, possible deviations from the data assumptions that must be met in order to use classical Shewhart control charts were defined. Subsequently, simulations were performed to determine which nonparametric control chart was better suited for which type of data assumption violation. First, simulations were performed for the in-control process. Then simulations for an out-of-control process were performed. This is for situations with an isolated and persistent deviation. Based on the performed simulations, flow charts were created. These flow charts give the reader an overview of the possibilities of using nonparametric control charts in various situations. Based on the performed simulations and subsequent verification of the methodology on real data, it was found that nonparametric control charts are a suitable alternative to the standard Shewhart control charts in cases where the basic assumptions about the data are not met

A Nonparametric HEWMA-p Control Chart for Variance in Monitoring Processes

Control charts are considered as powerful tools in detecting any shift in a process. Usually, the Shewhart control chart is used when data follows the symmetrical property of a normal distribution. In practice, the data from the industry may follow a non-symmetrical distribution or an unknown distribution. The average run length (ARL) is a significant measure to assess the performance of the control chart. The ARL may mislead when the statistic is computed from an asymmetric distribution. To handle this issue, in this paper, an ARL-unbiased hybrid exponentially weighted moving average proportion (HEWMA-p) chart is proposed for monitoring the process variance for a non-normal distribution or an unknown distribution. The efficiency of the proposed chart is compared with the existing chart in terms of ARLs. The proposed chart is more efficient than the existing chart in terms of ARLs. A real example is given for the illustration of the proposed chart in the industry.11Ysciescopu

A generally weighted moving average signed-rank control chart

The idea of process monitoring emerged so as to preserve and improve the quality of a manufacturing process. In this regard, control charts are widely accepted tools in the manufacturing sector for monitoring the quality of a process. However, a specific distributional assumption for any process is restrictive and often criticised. Distribution-free control charts are efficient alternatives when information on the process distribution is partially or completely unavailable. In this article, we propose a distribution-free generally weighted moving average (GWMA) control chart based on the Wilcoxon signed-rank (SR) statistic. Extensive simulation is done to study the performance of the proposed chart. The performance of the proposed chart is then compared to a number of existing control charts including the parametric GWMA chart for subgroup averages, a recently proposed GWMA chart based on the sign statistic and an exponentially weighted moving average (EWMA) chart based on the signed-rank statistic. The simulation results reveal that the proposed chart performs just as well and in many cases better than the existing charts, and therefore can serve as a useful alternative in practice.Research of the first author was supported in part by STATOMET at the University of Pretoria, South Africa and National Research Foundation through the SARChI Chair at the University of Pretoria, South Africa.http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1099-16382017-12-31hb2017Statistic

Analysis and application of selected control charts suitable for smart manufacturing processes

Nonparametric control charts (NPCC) have shown great potential for monitoring processes in conditions of smart manufacturing with complex structures, various monitored characteristics and the need to process big data. Practical applications of NPCCs are very rare. The main reasons for this situation are a deficiency in software support and a lack of simple but complete instructions for their application. The introduction of such manual, which is based on the authors' own simulations of performance of wide spectrum of NPCCs in conditions of different violations of data prerequisites, leading to recommendations for the selection of the most effective NPCC in various practical situations, is the main goal of this paper. Compared to other similar studies, this approach covers a wider range of control charts, and it was applied to a wider spectrum of data assumption violations. As an integral part of these analyses, an examination of various control chart performance indicators such as ARL, MRL, x(5) and x(95) was performed using simulations to select the best of them. The designed methodology was verified using real data.Web of Science1211art. no. 541

A generally weighted moving average chart for time between events

Shewhart-type attribute charts are known to be inefficient for small changes in monitoring nonconformities. An alternative way is to use a time-weighted chart to monitor the time between events (TBE). We propose a one-sided Generally Weighted Moving Average control chart to monitor the time between events (TBE); regarded as the GWMA-TBE chart. To aid the implementation of the chart, the necessary design parameters are provided. An extensive performance analysis shows that the GWMA-TBE chart is better than the well-known EWMA and Shewhart charts at detecting very small to moderate changes. Finally, a summary and some conclusions are provided.STATOMET (Grant number: SMB2015A), University of Pretoria, South Africa.http://www.tandfonline.com/loi/lssp202018-05-09hj2018Statistic

Nonparametric (distribution-free) control charts : an updated overview and some results

Control charts that are based on assumption(s) of a specific form for the underlying process distribution are referred to as parametric control charts. There are many applications where there is insufficient information to justify such assumption(s) and, consequently, control charting techniques with a minimal set of distributional assumption requirements are in high demand. To this end, nonparametric or distribution-free control charts have been proposed in recent years. The charts have stable in-control properties, are robust against outliers and can be surprisingly efficient in comparison with their parametric counterparts. Chakraborti and some of his colleagues provided review papers on nonparametric control charts in 2001, 2007 and 2011, respectively. These papers have been received with considerable interest and attention by the community. However, the literature on nonparametric statistical process/quality control/monitoring has grown exponentially and because of this rapid growth, an update is deemed necessary. In this article, we bring these reviews forward to 2017, discussing some of the latest developments in the area. Moreover, unlike the past reviews, which did not include the multivariate charts, here we review both univariate and multivariate nonparametric control charts. We end with some concluding remarks.https://www.tandfonline.com/loi/lqen20hj2020Science, Mathematics and Technology Educatio