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

Theory and applications of univariate distribution-free Shewhart, CUSUM and EWMA control charts

Statistical quality control charts originated in the late 1920’s by Shewhart (1926, 1931 and 1939). Their applications in various disciplines have been ever-increasing. Although most control charts are distribution-based, recent literature witnessed the development of a considerable number of distribution-free or nonparametric control charts. The purpose of this thesis is to present the concepts and introduce the researcher to the essentials of univariate nonparametric control charts. Various properties of nonparametric control charts are comprehensively discussed and concepts are clearly explained. Proofs and detailed calculations have been given to help the reader to study and understand the subject more thoroughly. This text contains a wide variety of illustrative examples to give an overall picture of how nonparametric control charts are used. Both simulated and real data examples have been integrated throughout the text. Since most practical problems are too large to be solved using hand calculations, some type of statistical software package is required to solve these problems. There are several excellent statistical packages available and in this thesis we make use of Microsoft Excel, SAS, Minitab, Mathcad and Mathematica to construct (almost all) the tables in this thesis. We point out that a number of Mathematica programs are provided by Chakraborti and Van de Wiel (2003) by means of the website www.win.tue.nl/~markvdw. The aim throughout is to convey the concepts of univariate nonparametric control charts in a way that readers will find attractive and interesting. Since the majority of nonparametric procedures, to be distribution-free, require a continuous population, only variables control charts are covered. We only consider control charts for monitoring the location of a process, since very few nonparametric charts are available for monitoring the spread. In this thesis we consider the three main classes of control charts: the Shewhart, CUSUM and EWMA control charts and their refinements. The text is divided into several chapters. An introduction to nonparametric control charts is presented in Chapter 1. A discussion of some of the advantages of nonparametric control charts is included while pointing out some of the disadvantages. In Chapter 2 we describe the Shewhart-, CUSUMand EWMA-type sign control charts with (and without) warning limits. In Chapter 3 we describe the Shewhart-, CUSUM- and EWMA-type signed-rank control charts with (and without) runs-type signalling rules. The Shewhart-type sign-like control chart with (and without) signalling rules is considered in Chapter 4. In Chapter 5 we consider the Shewharttype signed-rank-like control chart. Finally, in Chapter 6 we consider the Shewhart- and CUSUM-type Mann-Whitney-Wilcoxon control charts. We considered decision problems under both Phase I and Phase II (see Section 1.5 for a distinction between the two phases). In all the sections of this thesis we considered Phase II process monitoring, except in Section 6.2 where a CUSUM-type control chart for the preliminary Phase I analysis of individual observations based on the Mann-Whitney two-sample test is proposed. In the last chapter we have some concluding remarks along with some ideas for future research.Dissertation (MSc)--University of Pretoria, 2011.Statisticsunrestricte

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

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 simple approach for monitoring business service time variation.

Control charts are effective tools for signal detection in both manufacturing processes and service processes. Much of the data in service industries comes from processes having nonnormal or unknown distributions. The commonly used Shewhart variable control charts, which depend heavily on the normality assumption, are not appropriately used here. In this paper, we propose a new asymmetric EWMA variance chart (EWMA-AV chart) and an asymmetric EWMA mean chart (EWMA-AM chart) based on two simple statistics to monitor process variance and mean shifts simultaneously. Further, we explore the sampling properties of the new monitoring statistics and calculate the average run lengths when using both the EWMA-AV chart and the EWMA-AM chart. The performance of the EWMA-AV and EWMA-AM charts and that of some existing variance and mean charts are compared. A numerical example involving nonnormal service times from the service system of a bank branch in Taiwan is used to illustrate the applications of the EWMA-AV and EWMA-AM charts and to compare them with the existing variance (or standard deviation) and mean charts. The proposed EWMA-AV chart and EWMA-AM charts show superior detection performance compared to the existing variance and mean charts. The EWMA-AV chart and EWMA-AM chart are thus recommended

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

On Phase II Monitoring of the Probability Distributions of Univariate Continuous Processes

Statistical process control (SPC) charts are widely used in industry for monitoring the stability of certain sequential processes like manufacturing, health care systems etc. Most SPC charts assume that the parametric form of the “in-control” process distribution F1 is available. However, it has been demonstrated in the literature that their performances are unreliable when the pre-specified process distribution is incorrect. Moreover, most SPC charts are designed to detect any shift in mean and/or variance. In real world problems, shifts in higher moments can happen without much change in mean or variance. If we fail to detect those and let the process run, it can eventually become worse and a shift in mean or variance can creep in. Moreover, the special cause that initiated the shift can inflict further damage to the system, and it may become a financial challenge to fix it. This paper provides an efficient and easy-to-use control chart for Phase II monitoring of univariate continuous processes when the parametric form of the “in-control” process distribution is unknown, but Phase I observations that are believed to be i.i.d. realizations from unknown F1 are available. Data-driven practical guidelines are also provided to choose the tuning parameter and the corresponding control limit of the proposed SPC chart. Numerical simulations and a real-life data analysis show that it can be used in many practical applications