Nonparametric statistical process control : an overview and some results

An overview of the literature on some nonparametric or distribution-free quality control procedures is presented for univariate data. A nonparametric control chart is defined along with some general motivations and formulations. Various advantages of these charts are highlighted while some disadvantages of the more traditional, distribution-based. control charts are pointed out. Specific observations are made in the course of the review of articles and constructive criticism is offered. so that opportunities for further research can be identified. Connections to some areas of active research are made. such as sequential analysis, that are of relevance to process control. It is hoped that this article would lead to a wider acceptance of distribution-free control charts among the practitioners and would serve as an impetus to future research and development in this area

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

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

Affine invariant signed-rank multivariate exponentially weighted moving average control chart for process location monitoring

Multivariate statistical process control (SPC) charts for detecting possible shifts in mean vectors assume that data observation vectors follow a multivariate normal distribution. This assumption is ideal and seldom met. Nonparametric SPC charts have increasingly become viable alternatives to parametric counterparts in detecting process shifts when the underlying process output distribution is unknown, specifically when the process measurement is multivariate. This study examined a new nonparametric signed-rank multivariate exponentially weighted moving average type (SRMEWMA) control chart for monitoring location parameters. The control chart was based on adapting a multivariate spatial signed-rank test. The test was affine-invariant and the weighted version of this test was used to formulate the charting statistic by incorporating the exponentially weighted moving average (EWMA) scheme. The test\u27s in-control (IC) run length distribution was examined and the IC control limits were established for different multivariate distributions, both elliptically symmetrical and skewed. The average run length (ARL) performance of the scheme was computed using Monte Carlo simulation for select combinations of smoothing parameter, shift, and number of p-variate quality characteristics. The ARL performance was compared to the performance of the multivariate exponentially weighted moving average (MEWMA) and Hotelling T2. The control charts for observation vectors sampled the multivariate normal, multivariate t, and multivariate gamma distributions. The SRMEWMA control chart was applied to a real dataset example from aluminum smelter manufacturing that showed the SRMEWMA performed well. The newly investigated nonparametric multivariate SPC control chart for monitoring location parameters--the Signed-Rank Multivariate Exponentially Weighted Moving Average (SRMEWMA)--is a viable alternative control chart to the parametric MEWMA control chart and is sensitive to small shifts in the process location parameter. The signed-rank multivariate exponentially weighted moving average performance for data from elliptically symmetrical distributions is similar to that of the MEWMA parametric chart; however, SRMEWMA\u27s performance is superior to the performance of the MEWMA and Hotelling\u27s T2 control charts for data from skewed distributions

New extended distribution-free homogenously weighted monitoring schemes for monitoring abrupt shifts in the location parameter

A homogeneously weighted moving average (HWMA) monitoring scheme is a recently proposed memory-type scheme that gained its popularity because of its simplicity and superiority over the exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) schemes in detecting small disturbances in the process. Most of the existing HWMA schemes are designed based on the assumption of normality. It is well-known that the performance of such monitoring schemes degrades significantly when this assumption is violated. Therefore, in this paper, three distribution-free monitoring schemes are developed based on the Wilcoxon rank-sum W statistic. First, the HWMA W scheme is introduced. Secondly, the double HWMA (DHWMA) W scheme is proposed to improve the ability of the HWMA W scheme in detecting very small disturbances in the location parameter and at last, the hybrid HWMA (HHWMA) W scheme is also proposed because of its flexibility and better performance in detecting shifts of different sizes. The zero-state performances of the proposed schemes are investigated using the characteristics of the run-length distribution. The proposed schemes outperform their existing competitors, i.e. EWMA, CUSUM and DEWMA W schemes, in many situations, and particularly the HHWMA W scheme is superior to these competitors regardless of the size of the shift in the location parameter. Real-life data are used to illustrate the implementation and application of the new monitoring schemes.DATA AVAILABILITY STATEMENT : The data used for the illustration example are available from Mukherjee et al. (2019) (10.1016/j.cie.2019.106059).SUPPLEMENTARY MATERIAL : S1 Appendix. Properties of the HWMA W scheme. https://doi.org/10.1371/journal.pone.0261217.s001S2 Appendix. Properties of the DHWMA W scheme. https://doi.org/10.1371/journal.pone.0261217.s002S3 Appendix. Properties of the HHWMA W chart.http://www.plosone.orgdm2022Statistic

Some new nonparametric distribution-free control charts based on rank statistics

Ph.DDOCTOR OF PHILOSOPH

Improved Nonparametric Control Chart Based on Ranked Set Sampling with Application of Chemical Data Modelling

e statistical performance of parametric control charts is questionable when the underlying process does not follow any speci ed probability distribution. Nonparametric control charts are the best substitute for this situation. On the other hand, the ranked set sampling technique is preferred over the simple random sampling technique because it reduces the variability of process parameters and improves the control chart’s performance. is study aims to o er a nonparametric double homogeneously weighted moving average control chart under Wilcoxon signed-rank test considering the ranked set sampling technique (regarded as NPDHWMARSS), to further enhance the process location monitoring. e proposed chart’s run-length performance is compared with competing control charts, such as DEWMA-X, NPDEWMA-SR, NPRDEWMA-SR, DHWMA, and NPHWMARSS control charts. e comparison revealed that the proposed NPDHWMARSS control chart outperformed the other competing control charts, particularly for small to moderate shifts in process location. Finally, a real-life application is also o ered for quality practitioners to show the strength of the proposed control chartScopu

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

A nonparametric exponentially weighted moving average signed-rank chart for monitoring location

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.http://www.elsevier.com/locate/csdanf201

An Explanatory Study on the Non-Parametric Multivariate T2 Control Chart

Most control charts require the assumption of normal distribution for observations. When distribution is not normal, one can use non-parametric control charts such as sign control chart. A deficiency of such control charts could be the loss of information due to replacing an observation with its sign or rank. Furthermore, because the chart statistics of T2 are correlated, the T2 chart is not a desire performance. Non-parametric bootstrap algorithm could help to calculate control chart parameters using the original observations while no assumption regarding the distribution is needed. In this paper, first, a bootstrap multivariate control chart is presented based on Hotelling’s T2 statistic then the performance of the bootstrap multivariate control chart is compared to a Hotelling’s T2 parametric multivariate control chart, a multivariate sign control chart, and a multivariate Wilcoxon control chart using a simulation study. Ultimately, the bootstrap multivariate control chart is used in an empirical example to study the process of sugar production