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

Perceptions of isiZulu-speaking pre-service teachers’ classroom English proficiency

Despite less than 10% of South Africans claiming English as their home language, it has become the de facto language of instruction. Yet we cannot assume that teachers have sufficient command of this language when using it for instructional purposes. As a sub-study, in this article we report on the oral proficiency of isiZulu-speaking pre-service teachers who use English when expounding content in rural schools. The conceptual framework draws primarily on research relating to instructional communication and Classroom English. For this mixed methods case study, using questionnaire data from 52 pre-service teachers and 18 tutors, we sought to establish the perceptions that respondents had of students’ oral proficiency while teaching in situ. Responses were statistically analysed using computing software. Unedited audio recordings of lessons presented in rural KwaZulu-Natal schools during pre-service teachers’ work-integrated learning stint provided oral data from which to gauge proficiency using a self-designed rubric. Findings correspond with those of previous studies, pointing to pre-service teachers’ oral proficiency being less than ideal for effectively facilitating learning. However, what is considered adequate proficiency and what is ideal is yet to be agreed upon. We recommend that interventions which address the development of oral proficiency required for classroom use be considered. Our pilot rubric may serve as a useful data-gathering tool in future research

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

Effective communication of learning intentions and success criteria in the mathematics classroom : MERLO pedagogy for Senior Phase South African schools

A well-designed assessment construct is critical for improving all aspects of quality education and validating the achievement of educational reform. The global prevalence of how teachers communicate learning intentions (LIs) and success criteria (SC) has been of great concern, particularly in the South African context. This study investigates how Meaning Equivalence Reusable Learning Objects (MERLO) pedagogy effectively transforms Senior Phase mathematics teachers’ daily practice in the classroom. The study adopted qualitative participatory action research to frame the evolution of teachers’ praxeologies such as teachers’ meta-didactical and didactical praxeologies, to improve teachers’ beliefs and practices to integrate MERLO pedagogy as assessment activities. Twelve Senior Phase teachers were purposively selected in Gauteng, South Africa. The methods used for data generation were interviews, classroom observation, document analysis, field notes and training sessions. Thematic analysis was used to obtain insight into teachers’ beliefs and practice of effectively communicating LIs and SC in the classroom. At the initial stage, teachers were examined with regard to their beliefs and practices of assessment practices in the classroom, which informed MERLO intervention. In the second stage, teachers were asked to learn about MERLO items by reading the MERLO handout provided to them, participating in the workshop and sharing their opinions and views with others. In the third stage, teachers had to design MERLO assessment items on their own to assess learners’ level of understanding of the mathematical concepts in Senior Phase. The findings revealed that the participating teachers acquired adequate knowledge and skills on MERLO techniques that allowed them to structure and integrate the lesson plan of assessment activities into their mathematics classrooms. This study contributes to the body of knowledge by introducing MERLO pedagogy to Senior Phase South African mathematical teachers as an assessment strategy. COVID-19 caused some teachers to drop out of the study after the pre-MERLO participation phase and, accordingly, future research suggests that more teachers be included in similar studies.National Research Foundation (NRF).http://www.pythagoras.org.za/index.php/pythagorasdm2022Science, Mathematics and Technology Educatio

Synthetic and runs-rules charts combined with an X chart : theoretical discussion

A synthetic and a runs-rules X charts that are combined with a basic X chart are called a Synthetic-X and an improved runs-rules X charts, respectively. This paper gives the zero-state and steady-state theoretical results of the Synthetic-X and improved runs-rules X monitoring schemes. The Synthetic-X and improved runs-rules schemes can each be classified into four different categories, that is, (i) non-side-sensitive, (ii) standard side-sensitive, (iii) revised side-sensitive, and (iv) modified side-sensitive. In this paper, we first give the operation and, secondly, the general form of the transition probability matrices for each of the categories. Thirdly, in steady-state, we show that for each of the categories, the three methods that are widely used in the literature to compute the initial probability vectors result in different probability expressions (or values). Fourthly, we derive the closed-form expressions of the average run-length (ARL) vectors for each of the categories, so that, by multiplying each of these ARL vectors with the zero-state and steady-state initial probability vectors, yield the zero-state and steady-state ARL expressions. Finally, we formulate the closed-form expressions of the extra quadratic loss function for each of the categories.Part of this work was supported by the South African Researchers Chair Initiative (SARChI) Chair at the University of Pretoria. Sandile Shongwe’s research was supported in part by the National Research Foundation and Department of Science and Technology’s Innovation Doctoral scholarship (SFH14081591713, Grant number: 95208) as well as Department of Statistics’ STATOMET, and Marien Graham’s research was supported in part by the National Research Foundation (Thuthuka program: TTK14061168807, Grant number: 94102).http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1099-16382018-02-26hb2016Statistic

A letter to the editor about : “Machado, M.A.G. and Costa A.F.B. (2014). Some comments regarding the synthetic chart. Communications in Statistics - Theory and Methods, 43 (14), 2897-2906”

No abstract available.This research was funded by National Research Foundation (NRF), Department of Science and Technology, STATOMET and South African Researcher’s Chair Initiative.http://www.tandfonline.com/loi/lsta202017-10-31hb2016Statistic

On the performance of Shewhart-type synthetic and runs-rules charts combined with an X chart

Please read abstract in the article.Part of this work was supported by the SARCHI Chair at the University of Pretoria. Sandile Shongwe’s research was supported by National Research Foundation (NRF) and Department of Science and Technology’s Innovation Doctoral Scholarship (SFH14081591713) and Marien Graham’s research was supported in part by the NRF’s (Thuthuka program: TTK14061168807; grant number: 94102).http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1099-16382017-06-30hb2016Statistic

Some theoretical comments regarding the run-length properties of the synthetic and runs-rules monitoring schemes – Part 1: zero-state

Please read abstract in the article.The SARChI Chair at the University of Pretoria, the National Research Foundation (NRF) and Department of Science and Technology’s Innovation Doctoral scholarship, and the Department of Statistics’ STATOMET.hj2020Science, Mathematics and Technology EducationStatistic

Comparing the use of educational technology in mathematics education between South African and German schools

This mixed-method study investigated how primary school mathematics teachers in South Africa and Germany utilise educational technology. The perceptions of the principals and teachers regarding the use of educational technology and the obstacles to its integration were contrasted. In addition, the Trends in International Mathematics and Science Study (TIMSS) 2019 data from these countries were used to evaluate the relationship between educational technology and learner accomplishment. The results showed that teachers from both nations employed educational technology as a presentation-, reinforcement-, supplement-, and problem-solving tool, and also used it to stimulate the learning environment, as shown through semi-structured interviews and classroom observations. In addition, obstacles such as a lack of tablets/computers, technical support, and a lack of relevant continuous professional development impeded the incorporation of educational technology in mathematics by these teachers. Additionally, multi-level models revealed that access to a computer and internet connectivity at home correlated positively with German learners’ mathematics performances, while no statistically significant relationship was observed in South Africa. The results of this study have policy implications and are discussed at the end of this paper.DATA AVAILABILITY STATEMENT : The qualitative data, especially the interviews, are not being made available due to privacy and confidentiality reasons. However, the quantitative data is freely available at https://timss2019.org/international-database/ (accessed on 19 January 2023).The National Research Foundation, Deutscher Akademischer Austauschdienst and the Human Sciences Research Council of South Africa.http://www.mdpi.com/journal/sustainabilityhj2023Science, Mathematics and Technology Educatio

A modified side-sensitive synthetic chart to monitor the process mean

Please read abstract in the article.Part of this work was supported by the SARCHI Chair at the University of Pretoria. Sandile Shongwe‟s research was supported in part by the National Research Foundation and Department of Science and Technology‟s Innovation Doctoral scholarship (SFH14081591713) and Marien Graham‟s research was supported in part by the National Research Foundation (Thuthuka programme: TTK20100724000013247, Grant number: 76219).2018-01-31hb2016Statistic