Dissertations / Theses on the topic 'Shewhart's control charts'

O presente trabalho propõe um framework que inclui a organização de procedimentos e técnicas estatísticas para a verificação da premissa e suposições dos gráficos de controle. Ao final do framework o usuário tem a indicação de qual gráfico é mais propício a condição dos dados em relação as suposições verificadas. O método é dividido em 4 fases que engloba a verificação da premissa de estacionariedade e das suposições de normalidade, independência e homocedasticidade. Procedimentos com o objetivo de adequar os dados as suposições são apresentados. Esta dissertação apresenta sugestões para solução dos problemas relacionados a violação da suposição de homocedasticidade. Descreve os principais modelos de obtenção de resíduos independentes e normal e identicamente distribuídos como solução para a violação de independência. São efetuados dois estudos de simulação Monte Carlo onde, como principais resultados, obteve-se: (i) um procedimento eficiente para verificação da premissa de que o processo encontra-se sob controle antes da implantação dos gráficos de controle e; (ii) o efeito da não normalidade na probabilidade de erros do tipo I nos gráficos X e S de Shewhart. Além disso, apresenta a relação entre tamanho de amostra e não normalidade como aspecto importante na construção de gráficos de controle do tipo X e S de Shewhart em relação ao erro do tipo I.
This paper proposes a framework that includes the organization of procedures and statistical techniques for the verification of the control chart's premise and assumptions. At the end of the framework is an indication of which chart has more favorable data condition on assumptions noted. The method is divided into 4 phases which includes verification of the stationarity premise and assumptions of normality, independence and homoscedasticity. Procedures with the goal of matching the data were been presented. This Master's work presents suggestions for solving problems related to violation of the homoscedasticity assumption. Describes the main types of models to intend get normal independent and identically distributed residuals as a solution to the violation of assumptions in the original data. Two studies are performed in Monte Carlo simulation and the main results obtained is: (i) an efficient procedure for verifying the premise that the process is under control before the implantation of control charts, (ii) the effect of non-normality in the probability of Type I error in and S Shewhart's control charts. In addition, shows the relationship between sample size and non-normality as important factor in building and S Shewhart's control charts on the error of Type I.

Quality, as well as stability of processes check is nowadays gaining on its significance. The main driving force of its increasing importance is the rapid expansion of series production. Large-scale manufacturing processes are concerned, in terms of the number of operators, direct and indirect influence on rejects, but also on process stability. There are several quality characteristics, defined by utility properties, that can be easily measurable (linear dimensions, solidity, elongation, humidity, concentration) or directly immeasurable, mostly subjective (fragrance, taste, color, comfort while using, appearance). Statistical Process Control-SPC features the preventive tool of quality control, because based on the early detection of significant divergences of the process from the predetermined level, it is possible to execute interventions in the process with the aim of maintaining the acceptable and stable level and improving the process. This manufacturing process check will be the topic of my thesis. At first, Shewhart's control charts analysis will be done to determine strong process instability. Consequently, analysis will be carried out in test chi-square, used to determine the influence of each factor on the process of stability (operators, type of shift, type of product, type of defect on the product). All the practical part will be processed in statistical software MINITAB15. The thesis will be complemented by the findings from the examination of the features of interval estimates of parameter p for binomial distribution - numeric stability in the various statistical software (specifically Minitab 15, Statistica, Matlab 7.8.0). Master's thesis was supported by project from MSMT of the Czech Republic no. 1M06047 Center for Quality and Reliability of Production.

Industrial processes are subject to changes that can adversely affect product quality. A change in the process that increases the variability of the output of the process causes the output to be less uniform and increases the probability that individual items will not meet specifications. Statistical control charts for monitoring process variance can be used to detect an increase in the variability of the output of a process so that the situation can be repaired and product uniformity restored. Control charts that increase the sampling rate when there is evidence the variance has changed gather information more quickly and detect changes in the variance more quickly (on average) than fixed sampling rate procedures. Several variable sampling rate procedures for detecting increases in the process variance will be developed and compared with fixed sampling rate methods. A control chart for the variance is usually used with a separate control chart for the mean so that changes in the average level of the process and the variability of the process can both be detected. A simple method for applying variable sampling rate techniques to dual monitoring of mean and variance will be developed. This control chart procedure increases the sampling rate when there is evidence the mean or variance has changed so that changes in either parameter that will negatively impact product quality will be detected quickly.
Ph. D.

A control chart that simultaneously tracks the mean and variance of a normally distributed variable with no compensation effect is defined in this work. This joint control chart is compared to five other charts: an Χ chart, an s² chart, a Reynolds and Ghosh chart, a Repko process capability plot, and a t-statistic chart. The criterion for comparison is the probability of a Type II sampling error. Several out-of-control cases are examined. In the case of Repko, an equation is defined to compute the Type II error probability. The results indicate that the Reynolds and Ghosh statistic is powerful for cases when the variance shifts out of control. The Χ chart is powerful when the mean shifts with moderate changes in the variance. The joint chart is powerful for moderate changes in the mean and variance.
Master of Science

In this study, neural networks are developed under conditions of nonnormality as alternatives to standard control charts, and their performance is compared with those of standard ‾x and CUSUM control charts.

A common problem encountered in practice is determining when it is appropriate to change the sampling interval for control charts. This thesis examines this problem for Shewhart X̅ charts. Duncan's economic model (1956) is used to develop a relationship between the most appropriate sampling interval and the present rate of"disturbances,” where a disturbance is a shift to an out of control state. A procedure is proposed which switches the interval to convenient values whenever a shift in the rate of disturbances is detected. An example using simulation demonstrates the procedure.
M.S.

This study develops a heuristic procedure for specifying parameters for a neural network configuration (learning rate, momentum, and the number of neurons in a single hidden layer) in Shewhart X-bar control chart applications. Also, this study examines the replicability of the neural network solution when the neural network is retrained several times with different initial weights.

The generalized likelihood ratio (GLR) control charts are studied for monitoring a process proportion of defective or nonconforming items. The type of process change considered is an abrupt sustained increase in the process proportion, which implies deterioration of the process quality. The objective is to effectively detect a wide range of shift sizes. For the first part of this research, we assume samples are collected using rational subgrouping with sample size n>1, and the binomial GLR statistic is constructed based on a moving window of past sample statistics that follow a binomial distribution. Steady state performance is evaluated for the binomial GLR chart and the other widely used binomial charts. We find that in terms of the overall performance, the binomial GLR chart is at least as good as the other charts. In addition, since it has only two charting parameters that both can be easily obtained based on the approach we propose, less effort is required to design the binomial GLR chart for practical applications. The second part of this research develops a Bernoulli GLR chart to monitor processes based on the continuous inspection, in which case samples of size n=1 are observed. A constant upper bound is imposed on the estimate of the process shift, preventing the corresponding Bernoulli GLR statistic from being undefined. Performance comparisons between the Bernoulli GLR chart and the other charts show that the Bernoulli GLR chart has better overall performance than its competitors, especially for detecting small shifts.
Ph. D.

Distribution-free (nonparametric) control charts can be useful to the quality practitioner when the underlying distribution is not known. The term nonparametric is not intended to imply that there are no parameters involved, in fact, quite the contrary. While the term distribution-free seems to be a better description of what we expect from these charts, that is, they remain valid for a large class of distributions, nonparametric is perhaps the term more often used. In the statistics literature there is now a rather vast collection of nonparametric tests and confidence intervals and these methods have been shown to perform well compared to their normal theory counterparts. Remarkably, even when the underlying distribution is normal, the efficiency of some nonparametric tests relative to the corresponding (optimal) normal theory methods can be as high as 0.955 (see e.g. Gibbons and Chakraborti (2010) page 218). For some other heavy-tailed and skewed distributions, the efficiency can be 1.0 or even higher. It may be argued that nonparametric methods will be ‘less efficient’ than their parametric counterparts when one has a complete knowledge of the process distribution for which that parametric method was specifically designed. However, the reality is that such information is seldom, if ever, available in practice. Thus it seems natural to develop and use nonparametric methods in statistical process control (SPC) and the quality practitioners will be well advised to have these techniques in their toolkits. In this thesis we only propose univariate nonparametric control charts designed to track the location of a continuous process since very few charts are available for monitoring the scale and simultaneously monitoring the location and scale of a process. Chapter 1 gives a brief introduction to SPC and provides background information regarding the research conducted in this thesis. This will aid in familiarizing the reader with concepts and terminology that are helpful to the following chapters. Details are given regarding the three main classes of control charts, namely the Shewhart chart, the cumulative sum (CUSUM) chart and the exponentially weighted moving average (EWMA) chart. We begin Chapter 2 with a literature overview of Shewhart-type Phase I control charts followed by the design and implementation of these charts. A nonparametric Shewhart-type Phase I control chart for monitoring the location of a continuous variable is proposed. The chart is based on the pooled median of the available Phase I samples and the charting statistics are the counts (number of observations) in each sample that are less than the pooled median. The derivations recognize that in Phase I the signalling events are dependent and that more than one comparison is © University of Pretoria v made against the same estimated limits simultaneously; this leads to working with the joint distribution of a set of dependant random variables. An exact expression for the false alarm probability is given in terms of the multivariate hypergeometric distribution and this is used to provide tables for the control limits. Some approximations are discussed in terms of the univariate hypergeometric and the normal distributions. In Chapter 3 Phase II control charts are introduced and considered for the case when the underlying parameters of the process distribution are known or specified. This is referred to as the ‘standard(s) known’ case and is denoted Case K. Two nonparametric Phase II control charts are considered in this chapter, with the first one being a nonparametric exponentially weighted moving average (NPEWMA)-type control chart based on the sign (SN) statistic. A Markov chain approach (see e.g. Fu and Lou (2003)) is used to determine the run-length distribution of the chart and some associated performance characteristics (such as the average, standard deviation, median and other percentiles). In order to aid practical implementation, tables are provided for the chart’s design parameters. An extensive simulation study shows that on the basis of minimal required assumptions, robustness of the in-control run-length distribution and out-of-control performance, the proposed NPEWMA-SN chart can be a strong contender in many applications where traditional parametric charts are currently used. Secondly, we consider the NPEWMA chart that was introduced by Amin and Searcy (1991) using the Wilcoxon signed-rank statistic (see e.g. Gibbons and Chakraborti (2010) page 195). This is called the nonparametric exponentially weighted moving average signed-rank (NPEWMA-SR) chart. In their article important questions remained unanswered regarding the practical implementation as well as the performance of this chart. In this thesis we address these issues with a more in-depth study of the 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. Results show that the NPEWMA-SR chart performs just as well as and in some cases better than the competitors. In Chapter 4 Phase II control charts are introduced and considered for the case when the underlying parameters of the process distribution are unknown and need to be estimated. This is referred to as the ‘standard(s) unknown’ case and is denoted Case U. Two nonparametric Phase II control charts are proposed in this chapter. They are a Phase II NPEWMA-type control chart and a nonparametric cumulative sum (NPCUSUM)-type control chart, based on the exceedance statistics, © University of Pretoria vi respectively, for detecting a shift in the location parameter of a continuous distribution. The exceedance statistics can be more efficient than rank-based methods when the underlying distribution is heavy-tailed and / or right-skewed, which may be the case in some applications, particularly with certain lifetime data. Moreover, exceedance statistics can save testing time and resources as they can be applied as soon as a certain order statistic of the reference sample is available. We also investigate the choice of the order statistics (percentile), from the reference (Phase I) sample that defines the exceedance statistic. It is observed that other choices, such as the third quartile, can play an important role in improving the performance of these exceedance charts. It is seen that these exceedance charts perform as well as and, in many cases, better than its competitors and thus can be a useful alternative chart in practice. 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. © University
Thesis (PhD)--University of Pretoria, 2013.
gm2013
Statistics
restricted

This dissertation investigates the effects of autocorrelation on the performances of various sampling plans for control charts in detecting special causes that may produce sustained or transient shifts in the process mean and/or variance. Observations from the process are modeled as a first-order autoregressive process plus a random error. Combinations of two Shewhart control charts and combinations of two exponentially weighted moving average (EWMA) control charts based on both the original observations and on the process residuals are considered. Three types of sampling plans are investigated: samples of n = 1, samples of n > 1 observations taken together at one sampling point, or samples of n > 1 observations taken at different times. In comparing these sampling plans it is assumed that the sampling rate in terms of the number of observations per unit time is fixed, so taking samples of n = 1 allows more frequent plotting. The best overall performance of sampling plans for control charts in detecting both sustained and transient shifts in the process is obtained by taking samples of n = 1 and using an EWMA chart combination with a observations chart for mean and a residuals chart for variance. The Shewhart chart combination with the best overall performance, though inferior to the EWMA chart combination, is based on samples of n > 1 taken at different times and with a observations chart for mean and a residuals chart for variance.
Ph. D.

This study uses simulation to examine differences between fixed sampling interval (FSI) and variable sampling interval (VSI) Shewhart X-bar control charts for processes that produce positively autocorrelated data. The influence of sample size (1 and 5), autocorrelation parameter, shift in process mean, and length of time between samples is investigated by comparing average time (ATS) and average number of samples (ANSS) to produce an out of control signal for FSI and VSI Shewhart X-bar charts. These comparisons are conducted in two ways: control chart limits pre-set at ±3σ_x / √n and limits computed from the sampling process. Proper interpretation of the Shewhart X-bar chart requires the assumption that observations are statistically independent; however, process data are often autocorrelated over time. Results of this study indicate that increasing the time between samples decreases the effect of positive autocorrelation between samples. Thus, with sufficient time between samples the assumption of independence is essentially not violated. Samples of size 5 produce a faster signal than samples of size 1 with both the FSI and VSI Shewhart X-bar chart when positive autocorrelation is present. However, samples of size 5 require the same time when the data are independent, indicating that this effect is a result of autocorrelation. This research determined that the VSI Shewhart X-bar chart signals increasingly faster than the corresponding FSI chart as the shift in the process mean increases. If the process is likely to exhibit a large shift in the mean, then the VSI technique is recommended. But the faster signaling time of the VSI chart is undesirable when the process is operating on target. However, if the control limits are estimated from process samples, results show that when the process is in control the ARL for the FSI and the ANSS for the VSI are approximately the same, and exceed the expected value when the limits are fixed.

This diploma thesis deals with the evaluation of the capability of a specific production process. The theoretical part of the work contains a description of statistical process control, types of control charts and evaluation of process capability. The practical part is focused on evaluating the capability of a specific process. The method of dataset collection is described at first, then this data are analyzed and the capability of this process is evaluated.

CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel Superior
A utilizaÃÃo dos GrÃficos de Shewhart como ferramenta de monitoramento de processos, cujos produtos advÃm de vÃrios fluxos de produÃÃo (processos paralelos), deve ser vista com cautela, pois as amostras podem estar sendo construÃdas com itens de diferentes populaÃÃes. Na construÃÃo desses grÃficos, nÃo se deve misturar diferentes fontes de variaÃÃo do processo, pois tal atitude pode levar a conclusÃes equivocadas e, assim, reduzir o poder do grÃfico na detecÃÃo de causas assinalÃveis. Uma soluÃÃo para esse problema à o uso de um grÃfico de controle para cada fluxo, o GrÃfico Tradicional de Shewhart (GCS), contudo torna o controle difÃcil e burocrÃtico. Uma outra alternativa à a adoÃÃo do chamado GrÃfico de Controle por Grupos (GG), que permite o controle de mÃltiplos fluxos atravÃs de um Ãnico grÃfico. A presenÃa de uma estrutura de correlaÃÃo no processo produtivo, inserida em ambos os tipos de cartas, pode comprometer a anÃlise violando a restriÃÃo de independÃncia das amostras. A literatura especializada à carente em estudos dessa natureza. Diante deste cenÃrio, o objetivo geral deste trabalho à desenvolver um estudo, por meio de simulaÃÃo com software R (R Development Core Team, 2011), do GrÃfico de Controle por Grupos em termos de seu desempenho e eficiÃncia, como uma alternativa ao modelo de Shewhart em processos paralelos com fluxos correlacionados. O estudo consiste em uma anÃlise acerca da alteraÃÃo na mÃdia e na variÃncia do processo individual e conjuntamente. Este trabalho, entÃo, contextualiza a importÃncia do Controle EstatÃstico de Processo (CEP) dentro da logÃstica de produÃÃo e sua contribuiÃÃo teÃrica e prÃtica para o CEP dentro do objetivo proposto. Resultados indicam que a eficiÃncia do GG em relaÃÃo ao tradicional aumenta à medida que a correlaÃÃo cresce. AlÃm disso, para pequenas perturbaÃÃes e com 3 fluxos, o grÃfico por grupos chega a ser 55% mais lento quanto à detecÃÃo de um deslocamento conjunto na mÃdia e na variÃncia do processo em relaÃÃo ao tradicional de Shewhart. Destaca-se ainda que, para 10 fluxos, o GG apresenta um desempenho superior ao GCS na ordem de 36% para correlaÃÃo 0,5, dando evidÃncias de que, para uma grande quantidade de fluxos (k maior ou igual a 10), o GG à melhor do que o GCS na presenÃa de correlaÃÃo entre os fluxos.
The use of Shewhart charts as a tool for process monitoring, whose products come from various production flows (parallel processes), should be viewed with caution because the samples could be determined based on items from different populations. In the construction of these charts, is not recommended mix different sources of process variation, because such an attitude can lead to wrong conclusions and thus reduce the power of the chart in detecting assignable causes. One solution to this problem is the use of a control chart for each stream, which makes control difficult and bureaucratic. Another alternative is to adopt the Groups Charts, which allows control of multiple streams from a single graph. The presence of a correlation structure in the production process, inserted in both types of charts, can compromise the analysis violating the restriction of independence of samples. The literature is lacking in studies of this nature. Given this scenario, the objective of this work is to develop a study through simulation using the Software R, Group Charts in terms of its performance and efficiency, as an alternative to Model Shewhart in parallel processes with correlated streams. The study is an analysis of the change in the mean and the variance of the process individually and jointly. This work then contextualizes the importance of Statistical Control in the Process (SPC) logistics and its contribution to the theory and practice SPC within the proposed objective. Results indicate that the efficiency of GG compared to traditional increases as the correlation grows. Furthermore, for small disturbances, with 3 flows, the GG becomes 55% slower as to detect a displacement set average and the variance of the process compared to the traditional of Shewhart. Note also that, for 10 streams, the GG has outperformed GCS in the order of 36% correlation to 0:5, giving evidence that, for a large number of flows (k >= 10), the GG is better than the GCS in the presence of correlation between the streams.

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Water use, both to supply the population, as for food production, in increasing numbers, forces countries like Brazil to adopt strict regulations regarding the use of water, which soon will be in effect throughout the Brazilian territory. The drip irrigation systems have increased employment in the face of the above. This thesis aimed to adapt the methodology of statistical process control, widely used in the industry since 1924, to the evaluation process of irrigation and drip fertirrigation, marketed as "drip irrigation kit for household farming". The research was developed at the Experimental Center of Agricultural Engineering - NEEA, State University of West of Paraná - UNIOESTE, in Cascavel, Paraná State, Brazil. Two different systems were settled: an irrigation one and a fertirrigation other, each system was subjected to four treatments (T) according to the variation of hydraulic head (H) applied by gravity, for which we used plastic stents with the capacity of to 200 L, reused from the property. The treatments and their heads identification were as follows: for the irrigation system treatment 1 (T1), H = 12 kPa; treatment 2 (T2), H = 14 kPa; treatment 3 (T3), 16 kPa; treatment 4 ( T4), H = 18kPa; for fertirrigation H = 12 kPa T5, T6 H = 14 kPa, 16 kPa H = T7, T8 = 18kPa. In each treatment were carried out 25 tests on irrigation and 27 ones on fertirrigation, each test was composed of three repetitions, in each repetition the collected volumes of water or fertilizer solution of 40 emitters, 10 seconds on each side line according of the Keller & Karmella Deniculi's methodologies and over a period of four minutes. It was also measured the pressure in the second input (Pinício) and in the fifth lateral line (Pfinal). With these data, flow rates were computed, as well as the Distribution Uniformity (DU), total coefficients of variation (CVt), mean pressure; analyses of descriptive statistics were performed, charts to evaluate the hydraulic performance were elaborated, as well as control charts or Shewhart control charts for DU and CVt. It were applied the ratio of process capability (Cp) and the centrality of process (Cpk) for assessment of uniformity. The statistical analysis, hydraulics, uniformity and statistical process control checked and confirmed that all irrigation tested meets the specifications provided by the manufacturer. The methodology is the beginning of further research for other types of emitters, material manufacturing, culture, and diversity of relief.
A pauta mundial, desde 1990, é a seguridade alimentar, podendo ser afetada em grande maneira pelas mudanças climáticas devido às políticas de desenvolvimento sem os cuidados necessários para evitar efeitos nocivos ao meio ambiente. O uso da água, tanto para abastecimento populacional como para a produção de alimentos, em quantidade cada vez maior, obriga países como o Brasil a adotar regulamentações rígidas quanto ao uso da água, que em breve estarão em vigor em todo o território brasileiro. Os sistemas de irrigação por gotejamento têm emprego crescente, diante das situações acima mencionadas. Esta tese teve por objetivo adaptar a metodologia do controle estatístico de processos, muito utilizado na indústria desde 1924, ao processo de avaliação dos sistemas de irrigação e de fertirrigação por gotejamento, comercializado como ―Kit de irrigação por gotejamento para agricultura familiar‖. A pesquisa desenvolveu-se nas dependências do Núcleo Experimental de Engenharia Agrícola NEEA, da Universidade Estadual do Oeste do Paraná UNIOESTE, no Município de Cascavel, Paraná, Brasil. Instalaram-se 2 sistemas um de irrigação e outro de fertirrigação, cada sistema submeteu-se a 4 tratamentos (T) em função da variação da carga hidráulica (H) aplicada por gravidade, para o qual utilizaram-se contenedores de plástico com capacidade de 200 L, reaproveitados da propriedade. Os tratamentos e respectivas cargas identificaram-se da seguinte forma: para o sistema de irrigação, tratamento 1 (T1), H = 12 kPa; tratamento 2 (T2), H = 14 kPa; tratamento 3 (T3), H = 16 kPa; e tratamento 4 (T4) = 18kPa; para o de fertirrigação, tratamento 5 (T5), H = 12 kPa; tratamento 6 (T6), H = 14 kPa; tratamento 7 (T7), H = 16 kPa; e tratamento 8 (T8), H = 18kPa. Em cada tratamento realizaram-se 25 ensaios na irrigação e 27 na fertirrigação, cada ensaio compôs-se de 3 repetições. Em cada repetição coletaram os volumes de água ou de solução do fertilizante de 40 emissores, 10 em cada linha lateral segundo as metodologias de Keller & Karmelli e Deniculi, num período de 4 minutos. Mensuraram-se também as pressões de entrada na segunda (Pinício) e na penúltima linha lateral (Pfinal). Com estes dados calcularam-se as vazões, os Coeficientes de Uniformidade (CUD), Coeficientes de Variação Total (CVt), pressões médias; realizaram-se análises de estatística descritiva; confeccionaram-se gráficos para avaliação do desempenho hidráulico, gráficos de controle ou cartas de Shewhart para CUD e CVt. Empregou-se a razão de capacidade de processo (Cp) e o de centralidade de processo (Cpk) para avaliação das uniformidades. As análises estatística, hidráulica, de uniformidade e de controle estatístico de processo verificaram e confirmaram que o conjunto de irrigação ensaiado atende às especificações fornecidas pelo fabricante. A metodologia desenvolvida é o início do desenvolvimento de novas pesquisas para outros tipos de emissores, de materiais de fabricação, de culturas e diversidade de relevo.

This diploma thesis deals with use of Shewhart Control Charts in quality control. The thesis describes the currently used process of quality control in the enterprise. Afterwards practical guidance for implementation of the statistical process control of the selected component and evaluation of capability is provided. An application for creating control charts and monitoring the quality of the product is included.

碩士
淡江大學
統計學系碩士班
96
The thesis extends the three-level Shewhart control chart proposed by Cassady and Nachlas [8] to exponentially weighted moving average and Shewhart-EWMA control charts for monitoring the quality of three-level (conforming, marginal, nonconforming) products. The control limits of the proposed control chart are established based on the zero-state average run lengths using Markov chain approximation. Basically, the proposed control charts improve the performance of the three-level Shewhart control chart signi‾cantly and are able to detect small shifts in a process more quickly.

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.
Statistics
unrestricted

碩士
國立屏東科技大學
工業管理系所
102
Based on literature review, when the process has a large offsets, Shewhart control chart's detect effects will better than the others. But for today's high-quality products requirement, the detect ability for large offsets has been insufficient to meet the demand. Therefore, when the process has a small offsets, EWMA control chart or CUSUM control chart should be used to monitor the process. When the process is in-control, the average run length is hoped the bigger the better. On the contrary, when the process is out-control, the average run length is hoped the smaller the better. In this paper, we will explore and compare the detecting performance among the Shewhart, CUSUM and EWMA control charts under a variant of quality characteristics. Finally, seven conclusions are drawn for future studies and practical applications.

碩士
淡江大學
統計學系碩士班
96
In many manufacturing processes, the overall process variation can be decomposed into relevant components of variation. If the associated special causes of respective variance components can be identified, it is more effective and appropriate to monitor these components with separate control chart instead of monitoring the overall variance with single control chart. This thesis develops Shewhart control charts for monitoring the variance components under the random effects model with single- factor design based on a numerical method. A numerical study is conducted for the comparison of performances based on the proposed method with the other existing methods in the literature. The numerical results indicate that the proposed method is more sensitive to detect the changes of variance components in process. Moreover, the proposed method is illustrated with real manufacturing data.

碩士
國立雲林科技大學
工業工程與管理系
104
In the industrial products often do life test, life test usually care about the average change in manufacturing process, consider the time and cost, often using censored data. Control chart is a good tool monitor the process. But Steiner & Mackay (2000,2001) proposed using traditional control charts monitor censored data, the occurrence of adverse characteristics such as large-alarm rate and low power, therefore right-censored data assumes a life is Normal distribution and Weibull distribution proposed methods to monitor the average change in the process, there are good monitoring capability. Due mostly to the right-censored data the follow-up study as censored data, less discussion of multiply-censored data, it often happens in experiment. Therefore, this study used Steiner & Mackay (2000,2001) proposed the Conditional Expected Value (CEV) X-bar control charts and Weibull CEV、Maximum Likelihood Estimation (MLE) 、Exponential CEV　control chart ,multiply-censored data life are Normal distribution and Weibull distribution, establish new control procedures for one-sided control charts to monitor the process of decreasing the average, and discuss using simulated the various parameters in the control chart performance , average run length (ARL) as control charts to detect performance indicators , the results showed that Conditional Expected Value (CEV) X-bar control charts can effectively monitor Normal distribution of multiply-censored data, Other three control charts can effectively monitor the Weibull distribution of multiply-censored data, Can provide in multiply-censored data of life monitoring to avoid the larger Type II error risk.

Routine pipette calibration is an essential part of any quality assurance and quality control program in the forensic sciences and beyond. Pipette calibration standards in a forensic laboratory are typically set to the limits outlined by the document ISO8655, published by the International Organization for Standardization for the general scientific community. Alternative methods exist that may be capable of monitoring pipette stability across time in a forensic setting. Statistical process control charts, or Shewhart charts, are one such form of process control, which is being investigated for its potential application to pipette calibration monitoring for forensic DNA laboratories. Indeed, the application of process control lines for monitoring the calibration of volumetric equipment is not without precedent.1 To investigate the applicability of process control charts for monitoring pipette stability, a series of X ̅ and S charts, a type of Shewhart chart, have been produced from eight years of collected calibration data. A total of 71 pipettes of the following sizes were examined: 1-10 µL, 1-10 µL multi-channel, 10-100 µL, 100-1000 µL, 1-3 µL, 30-300 µL, 5-50 µL, 5-50 µL multi-channel, and 500-5000 µL pipettes. The ISO8655 calibration recommended volume limits of these pipettes have been added to the charts for the purposes of comparison. With these charts, it is possible to assess pipette performance over time in comparison to the ISO8655 calibration standards and to the control limits imposed by the Shewhart charts. The completed charts suggest that the methodology proposed by Shewhart shows promise as a supplement to ISO8655 recommendations for monitoring pipette stability across time. To corroborate the value of using Shewhart charts to monitor pipette performance, a serial dilution study in conjunction with a series of simulations with dynamic modeling software was performed. This dilution study investigated whether the systematic biases shown by the Shewhart charts could be measured in a laboratory setting. The simulations investigated multiple hypothetical pipetting scenarios concerning various levels of systematic bias. The simulations consistently corroborated the value of Shewhart charts to enforce better compliance between a pipette’s nominal and actual volume delivery, while the serial dilution study offered partial evidence of systematic pipetting bias.

碩士
輔仁大學
應用統計學研究所
99
Technology is growing dramatically. The latest technology has been applied on electric products extensively. It also leads the rapid development of semi-conductor industry. Therefore, quality and technology are getting important. However, single-variable control chart has not been able to met the need for process monitor. Hence, process monitor with multi-variable method is getting popular and significant. How to implement it effectively has consequently become an important issue. Photolithography is one of critical processes in DRAM industry and critical dimension at lithography is a considerable control item. Therefore, the study is going to compare single-variable control chart and Hotelling control chart with the case of three variables which are related to critical dimension. The result of analysis shows Hotelling control chart provides a great help to process engineers to discover problems before the process gets out of control.

碩士
元智大學
工業工程與管理學系
107
Structural Health Monitoring is one of the most important things that must be considered in establishing a building, one of them is the construction of a bridge. Bridge Health Monitoring (BHM) is a condition that must be met in the construction of a bridge to monitor the real condition of the bridge. Suramadu Bridge is a long-Span bridge located in Indonesia that connects the city of Surabaya and the city of Madura. In order to achieve one of the requirements of BHM, a GPS sensor is one of the sensors is used in Suramadu bridge to provide the condition of the bridge in real-time and three coordinates of the object, Latitude, Longitude, and Height coordinates are generated by GPS sensor are believed to represent the real condition of the Suramadu bridge. But the generated data from this GPS sensor must be processed statistically to provide an accurate warning. This study provides a study of Statistical Process Control (SPC) tools comparison, in order to know the behavior of the SPC tools, which are CUSUM and EWMA in detecting the deformation of the bridge. ARL and the lengths of the error are 2 parameters which will be tested for each chart in assessing the speed of the chart in detecting any kind of magnitude of shift and seeing errors generated from the chart respectively. Simulated auxiliary shifts and the occurrence of the chart towards the following occurrences. Some of the results can be found from this study such as CUSUM and EWMA charts have proven as an improvement chart from Shewhart's basic chart in terms of detecting the smaller shift. The results of the comparison between CUSUM and EWMA for this case are CUSUM chart outperforms the EWMA chart in terms of error lengths, it is found that from the error length of EWMA is the lower for all occurrences. In the end, this chart provides the result of the performance of the chart in detecting the simulated additional shift.

碩士
國立臺灣科技大學
工業管理系
93
The data are usually supposed to be a random sample from normal distribution in the discussion of control chart. But in actual production process, the machine could create the correlative products because of the attrition. If we still use the traditional control chart to analyze them, it will lead to the wrong conclusion. We assume that the correlative data come from the time series model, MA(1), to discuss the monitoring abilities of EWMA control chart and Shewhart control chart. Since it is not true that the white noise is always from the normal distribution in MA(1) model, we also consider other distributions for the white noise in our paper. In theory, it is hard to calculate the ARL values for Shewhart and EWMA control charts, so we compute them by simulation. Finally, the simulation shows that the monitoring ability of EWMA control chart is better than Shewhart control chart for the correlative data.

碩士
輔仁大學
應用統計學研究所
99
With the technology and process progressing, the Critical Dimension of DRAM is getting smaller and smaller. According to this reason, the precision of detect ability is requested higher and higher relatively. To the Semi-conductor industry, the Statistic Process Control chart was conducted for years, especially was the Photolithography which used the Shewhart control chart to monitor the Critical Dimension of litho process. The difficulty of Photolithography process is the light-sensitive deviation between the inter-batches of photo-resist which caused the shift of Critical Dimension. Meantime, the insufficient sensitivity of Shewhart control chart was revealed. This paper will appraise the deviation sensitivity of the EWMA, CUSUM and Shewhart control charts by the actual data from the semiconductor company. The result was shown in the article clearly that EWMA and CUSUM control charts could monitor the smaller shifts and more efficient detective ability than Shewhart control chart. The deviation in inter-batches photo-resist detective capacity will be enhanced efficiently, if alternative control chart could be adopted in Photolithography process.