Chapter 1 gives a brief introduction to statistical quality control (SQC) and provides background information regarding the research conducted in this thesis. We begin Chapter 2 with the design of Shewhart-type Phase I S2, S and R control charts for the situation when the mean and the variance are both unknown and are estimated on the basis of m independent rational subgroups each of size n available from a normally distributed process. The derivations recognize that in Phase I (with unknown parameters) the signaling events are dependent and that more than one comparison is made against the same estimated limits simultaneously; this leads to working with the joint distribution of a set of dependent random variables. Using intensive computer simulations, tables are provided with the charting constants for each chart for a given false alarm probability. Second an overview of the literature on Phase I parametric control charts for univariate variables data is given assuming that the form of the underlying continuous distribution is known. The overview presents the current state of the art and what challenges still remain. It is pointed out that, because the Phase I signaling events are dependent and multiple signaling events are to be dealt with simultaneously (in making an in-control or not-in-control decision), the joint distribution of the charting statistics needs to be used and the recommendation is to control the probability of at least one false alarm while setting up the charts. In Chapter 3 we derive and evaluate expressions for the run-length distributions of the Phase II Shewhart-type p-chart and the Phase II Shewhart-type c-chart when the parameters are estimated. We then examine the effect of estimating and on the performance of the p-chart and the c-chart via their run-length distributions and associated characteristics such as the average run-length, the false alarm rate and the probability of a “no-signal”. An exact approach based on the binomial and the Poisson distributions is used to derive expressions for the Phase II run-length distributions and the related Phase II characteristics using expectation by conditioning (see e.g. Chakraborti, (2000)). We first obtain the characteristics of the run-length distributions conditioned on point estimates from Phase I and then find the unconditional characteristics by averaging over the distributions of the point estimators. The in-control and the out-of-control properties of the charts are looked at. The results are used to discuss the appropriateness of the widely followed empirical rules for choosing the size of the Phase I sample used to estimate the unknown parameters; this includes the number of reference samples m and the sample size n. Chapter 4 focuses on distribution-free control charts and considers a new class of nonparametric charts with runs-type signaling rules (i.e. runs of the charting statistics above and below the control limits) for both the scenarios where the percentile of interest of the distribution is known and unknown. In the former situation (or Case K) the charts are based on the sign test statistic and enhance the sign chart proposed by Amin et al. (1995); in the latter scenario (or Case U) the charts are based on the two-sample median test statistic and improve the precedence charts by Chakraborti et al. (2004). A Markov chain approach (see e.g. Fu and Lou, (2003)) is used to derive the run-length distributions, the average run-lengths, the standard deviation of the run-lengths etc. for our runs rule enhanced charts. In some cases, we also draw on the results of the geometric distribution of order k (see e.g. Chapter 2 of Balakrishnan and Koutras, (2002)) to obtain closed form and explicit expressions for the run-length distributions and/or their associated performance characteristics. Tables are provided for implementation of the charts and examples are given to illustrate the application and usefulness of the charts. The in-control and the out-of-control performance of the charts are studied and compared to the existing nonparametric charts using criteria such as the average run-length, the standard deviation of the run-length, the false alarm rate and some percentiles of the run-length, including the median run-length. It is shown that the proposed “runs rules enhanced” sign charts offer more practically desirable in-control average run-lengths and false alarm rates and perform better for some distributions. Chapter 5 wraps up this thesis with a summary of the research carried out and offers concluding remarks concerning unanswered questions and/or future research opportunities. / Thesis (PhD)--University of Pretoria, 2009. / Mathematics and Applied Mathematics / unrestricted

This research deals with some Statistical Quality Control (SQC) methods, which are used in quality testing. It investigates the problem encountered with statistical process control (SPC) tools when small sample sizes are used. Small sample size testing is a new area of concern especially when using expensive (or large) products, which are produced in small batches (low volume production). Critical literature review and analysis of current technologies and methods in SPC with small samples testing failed to show a conformance with conventional SPC techniques, as the confidence limits for averages and standard deviation are too wide. Therefore, using such sizes will provide unsecured results with a lack in accuracy. The current research demonstrates such problems in manufacturing by using examples, in order to show the lack and the difficulties faced with conventional SPC tools (control charts). Weibull distribution has always shown a clear and acceptable prediction of failure and life behaviour with small sample size batches. Using such distribution enables the accuracy needed with small sample size to be obtained. With small sample control charts generate inaccurate confidence limits, which are low. On the contrary, Weibull theory suggests that using small samples enable achievement of accurate confidence limits. This research highlights these two aspects and explains their features in more depth. An outline of the overall problem and solution point out success of Weibull analysis when Weibull distribution is modified to overcome the problems encountered when small sample sizes are used. This work shows the viability of Weibull distribution to be used as a quality tool and construct new control charts, which will provide accurate result and detect nonconformance and variability with the use of small sample sizes. Therefore, the new proposed Weibull deduction control charts shows a successful replacement of the conventional control chart, and these new charts will compensate the errors in quality testing when using small size samples.

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Statistical quality control (SQC) is one technique companies are using in the development of a Total Quality Management (TQM) culture. Shewhart control charts, a widely used SQC tool, rely on an underlying normal distribution of the data. Often data are skewed. The inverse Gaussian distribution is a probability distribution that is wellsuited to handling skewed data. This analysis develops models and a set of tools usable by practitioners for the constrained economic statistical design of control charts for inverse Gaussian distribution process centrality and process dispersion. The use of this methodology is illustrated by the design of an x-bar chart and a V chart for an inverse Gaussian distributed process.

Analysis of several acceptance sampling procedures is performed and improvement of the procedures is sug- gested in this thesis. The issue of an efficient calculation of exact (P1, P2) single sampling plans for sampling by variables and exact LTPD and AOQL single sampling plans for sampling by variables when the rejected lots are inspected is addressed. The calculation of the plans is done using exact formula for operating characteristic of acceptance sampling plan and the new plans have better characteristics compared to the plans computed in a usual way using just approximately valid formula for operating characteristic. The tables of plans calculated according to procedures suggested in this thesis are provided for a couple of input parameters combinations. Tools designed for working with acceptance sampling plans, tools for analysis and calculation of acceptance sampling plans is one of the outputs of this thesis. R language and environment for statistical computations was chosen for implementation. The tools are satisfactorily efficient and may be easily used even for acceptance sampling plans tables computation. Newly defined functions in R are supplied including their source code and basic documentation so that acceptance sampling plans can be computed as demanded in case that the particular input parameters set is out of the scope covered in the tables of plans provided here.

As obras de infraestrutura rodoviária representam investimentos públicos que influenciam de maneira determinante no desenvolvimento social e econômico de uma região. Pavimentos mal construídos, com controle de qualidade inadequado ou que não atendam às exigências de projeto em termos de características e espessuras dos materiais selecionados representam prejuízos sociais e econômicos na medida em que a deterioração precoce do pavimento implica em aumentos crescentes nos custos diretos e indiretos relacionados à conservação e operação rodoviária. Desta maneira, torna-se imprescindível que sejam adotadas medidas de garantia da qualidade da construção de modo que o investimento apresente melhores condições de atingir o retorno esperado, tal como planejado. Neste contexto, o presente trabalho tem por objetivo realizar revisão bibliográfica e propor ferramentas auxiliares de análise voltados ao controle deflectométrico do sistema de fundação dos pavimentos. Os estudos realizados baseiam-se em critérios estatísticos de análise e em critérios de ruptura adotados nos métodos de dimensionamento em uso corrente no Brasil e no exterior. Simulações e estudos de casos são utilizados na validação e apresentação dos modelos propostos. / The infrastructure road projects represent investments, often public, that influence in a decisive way on social and economic development of a region. Poorly constructed pavements with inadequate quality control or that do not meet design requirements in terms of selected materials characteristics and thickness represent social and economic losses since the early deterioration of the pavement results in incremental increases in direct and indirect costs related the road maintenance and operation. Thus, it is essential that actions be taken to guarantee the construction quality so that investments are more likely to achieve the expected return as planned. In this context, this research aims to conduct a literature review and propose auxiliary analysis tools related with nondestructive deflection tests in the pavements foundation systems. The studies will be based in statistical analysis criteria and failure criteria adopted in design methods currently in use in Brazil and abroad. Simulations and study cases are used in the validation and presentation of the proposed models.

This thesis was carried out at the Special Cables group in the Nexans IKO Sweden AB in Grimsås, The company is a worldwide leader in the cable industry, offers an extensive range of cables and cabling systems.The aim with this thesis is to increase mean average of the electrical resistance in cables and accordingly saving the copper as the raw material. In order to achieve such significance the project offers an approach to find and eliminate causes of variation in a manufacturing process.In the beginning, some germane literature for the area was studied to get a deeper understanding of the problem. Some of the literature is summarized in the theory chapter of the thesis. The process was then defined and mapped out. Sources of variation were also chosen, in this case facts inside different machines.Some statistical analysis was accomplished later in the process by applying the theoretical background in the light of the reality of company. Gage R&R was also performed to examine the measurement system in Nexans IKO Sweden.The study concludes with recommendations for Nexans on five areas for implementation; Tracking and recording data, Optimization of the bunching process, Reach to the state of statistical control, More focus on suppliers, Prevention of over adjustment and main activities within these areas are defined. Finally management commitment is introduced as the most important factor for future success.

The research aims at modeling and analyzing the interactions among functional process variables (FPVs) for process control in semiconductor manufacturing. Interaction is a universal phenomenon and different interaction patterns among system components might characterize the system conditions. To monitor and control the system, process variables are normally collected for observation which could vary with time and present in a functional form. These FPVs interact with each other and contain rich information regarding the process conditions. As an example in one of the semiconductor manufacturing processes, changes of interactions among FPVs like temperature and coefficient of friction (COF) might characterize different process conditions. This dissertation systematically developed a methodology to study interaction among FPVs through statistical and physical modeling. Three main topics are discussed in this dissertation: (1) Interaction patterns of FPVs under varying process conditions are studied both through experiments and statistical approaches. A method based on functional canonical correlation analysis (FCCA) is employed to extract the interaction patterns between FPVs and experiments of wafer polishing processes are conducted to verify the patterns of FPVs under varying process conditions. (2) Interaction among FPVs is further studied based on physics for process condition diagnosis. A mathematical model based on nonlinear dynamics is developed to study the strength of interaction and their directionalities, and advanced statistical control charts followed by this nonlinear dynamics model are established for process monitoring. (3) Complex interaction structures among multiple FPVs are analyzed based on nonlinear dynamics for a better understanding of process mechanism. An approach with extended nonlinear dynamics model is proposed to characterize process conditions, and combined engineering knowledge, complex interaction structure patterns are concluded accordingly for interpretation of process mechanism. The main contribution of this dissertation is to propose a novel methodology based on nonlinear dynamics, which could investigate interactions between components of systems and provide physical understanding of process mechanism for process monitoring and diagnosis. Through studies on interaction among FPVs in semiconductor manufacturing, this research provides guidance for improvement of manufacturing processes. Not limited to manufacturing, the developed methodology can be applied to other areas such as healthcare delivery.

Made available in DSpace on 2014-06-11T19:26:18Z (GMT). No. of bitstreams: 0 Previous issue date: 2011-06-15Bitstream added on 2014-06-13T20:15:05Z : No. of bitstreams: 1 leoni_rc_me_guara.pdf: 1800797 bytes, checksum: 8d64168d2cc2cc40045086a8c4677b9f (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / No planejamento dos gráficos de controle destinados ao monitoramento da média do processo, assume-se que esta permanece fixa em seu valor alvo até a ocorrência de uma causa especial, que a desloca. Em muitos processos, contudo, é mais razoável supor que a média oscila mesmo na ausência de causas especiais. Para descrever este comportamento oscilatório, tem-se utilizado o modelo autoregressivo de 1ª ordem, AR (1). Quando esta oscilação é grande, o melhor desempenho do gráfico de X é obtido com amostras unitárias. O mesmo não se observa com a carta de EWMA (exceto quando o parâmetro de ponderação  é próximo de um); os melhores desempenhos são obtidos com a adoção de amostras de tamanho n>1 e  pequeno, mesmo quando o objetivo é a detecção rápida de grandes deslocamentos da média. Neste estudo, utiliza-se como medida de desempenho o TES – tempo médio entre a ocorrência de uma mudança na posição em torno da qual a média oscila e sua sinalização pelo gráfico de controle. Quando a média do processo oscila, o TES passa a ser uma função do número esperado de visitas aos estados transientes de uma cadeia de Markov / The design of the control charts for the process mean, assumes that this parameter remains fixed on its target value until the occurrence of a special cause that shifts it. In many cases, however, it is more reasonable to assume that the mean wanders even in the absence of special causes. To describe this wandering behavior, has used the AR(1) model. When the wandering behavior is responsible for significant proportion of the data variability, the best performance of the X chart is obtained with samples of size one (n=1). The same is not true with the EWMA control chart (except when the smoothing parameter  is very close to one), its best performance is achieved with the adoption of n>1 and small , even to detect large changes in the process mean position. In this study, the average time between the occurrence of a change in the process mean position and the signal (TES) - is used to assess the chart’s performance. With the process mean wandering, this measure of performance becomes function of the expected number of visits to the transient states of a Markov chain