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

A Binary Control Chart to Detect Small Jumps

The classic N p chart gives a signal if the number of successes in a sequence of inde- pendent binary variables exceeds a control limit. Motivated by engineering applications in industrial image processing and, to some extent, financial statistics, we study a simple modification of this chart, which uses only the most recent observations. Our aim is to construct a control chart for detecting a shift of an unknown size, allowing for an unknown distribution of the error terms. Simulation studies indicate that the proposed chart is su- perior in terms of out-of-control average run length, when one is interest in the detection of very small shifts. We provide a (functional) central limit theorem under a change-point model with local alternatives which explains that unexpected and interesting behavior. Since real observations are often not independent, the question arises whether these re- sults still hold true for the dependent case. Indeed, our asymptotic results work under the fairly general condition that the observations form a martingale difference array. This enlarges the applicability of our results considerably, firstly, to a large class time series models, and, secondly, to locally dependent image data, as we demonstrate by an example

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

On Data Depth and the Application of Nonparametric Multivariate Statistical Process Control Charts

The purpose of this article is to summarize recent research results for constructing nonparametric multivariate control charts with main focus on data depth based control charts. Data depth provides data reduction to large-variable problems in a completely nonparametric way. Several depth measures including Tukey depth are shown to be particularly effective for purposes of statistical process control in case that the data deviates normality assumption. For detecting slow or moderate shifts in the process target mean, the multivariate version of the EWMA is generally robust to non-normal data, so that nonparametric alternatives may be less often required

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

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 Cumulative Summation Nonparametric Multiple Stream Process Control Chart Based on the Extended Median Test

In statistical process control applications, situations may arise in which several presumably identical processes or “streams” are desired to be simultaneously monitored. Such a monitoring scenario is commonly referred to as a “Multiple Stream Process (MSP).” Charts which have been designed to monitor an MSP typically monitor the means of the streams through collecting samples from each stream and calculating some function of the sample means. The resulting statistic is then iteratively compared to control limits to determine if a single stream or subset of streams may have shifted away from a specified target value. Traditional MSP charting techniques rely on the assumption of normality, which may or may not be met in practice. Thus, a cumulative summation nonparametric MSP control charting technique, based on a modification of the classical extended median test was developed and is referred to as the “Nonparametric Extended Median Test – Cumulative Summation (NEMT-CUSUM) chart.” The development of control limits and estimation of statistical power are given. Through simulation, the NEMT-CUSUM is shown to perform consistently in the presence of normal and non-normal data. Moreover, it is shown to perform more optimally than parametric alternatives in certain circumstances. Results suggest the NEMT-CUSUM may be an attractive alternative to existing parametric MSP monitoring techniques in the case when distributional assumptions about the underlying monitored process cannot reasonably be made