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.

Early identification and detection of abnormal time series patterns is vital for a number of manufacturing. Slide shifts and alterations of time series patterns might be indicative of some anomaly in the production process, such as machinery malfunction. Usually due to the continuous flow of data monitoring of manufacturing processes requires automated Control Chart Pattern Recognition(CCPR) algorithms. The majority of CCPR literature consists of supervised classification algorithms. Less studies consider unsupervised versions of the problem. Despite the profound advantage of unsupervised methodology for less manual data labeling their use is limited due to the fact that their performance is not robust enough for practical purposes. In this study we propose the use of a consensus clustering framework. Computational results show robust behavior compared to individual clustering algorithms.

Profile monitoring is a relatively new approach in quality control best used where the process data follow a profile (or curve) at each time period. The essential idea for profile monitoring is to model the profile via some parametric, nonparametric, and semiparametric methods and then monitor the fitted profiles or the estimated random effects over time to determine if there have been changes in the profiles. The majority of previous studies in profile monitoring focused on the parametric modeling of either linear or nonlinear profiles, with both fixed and random effects, under the assumption of correct model specification. Our work considers those cases where the parametric model for the family of profiles is unknown or at least uncertain. Consequently, we consider monitoring profiles via two techniques, a nonparametric technique and a semiparametric procedure that combines both parametric and nonparametric profile fits, a procedure we refer to as model robust profile monitoring (MRPM). Also, we incorporate a mixed model approach to both the parametric and nonparametric model fits. For the mixed effects models, the MMRPM method is an extension of the MRPM method which incorporates a mixed model approach to both parametric and nonparametric model fits to account for the correlation within profiles and to deal with the collection of profiles as a random sample from a common population. For each case, we formulated two Hotelling's T 2 statistics, one based on the estimated random effects and one based on the fitted values, and obtained the corresponding control limits. In addition,we used two different formulas for the estimated variancecovariance matrix: one based on the pooled sample variance-covariance matrix estimator and a second one based on the estimated variance-covariance matrix based on successive differences. A Monte Carlo study was performed to compare the integrated mean square errors (IMSE) and the probability of signal of the parametric, nonparametric, and semiparametric approaches. Both correlated and uncorrelated errors structure scenarios were evaluated for varying amounts of model misspecification, number of profiles, number of observations per profile, shift location, and in- and out-of-control situations. The semiparametric (MMRPM) method for uncorrelated and correlated scenarios was competitive and, often, clearly superior with the parametric and nonparametric over all levels of misspecification. For a correctly specified model, the IMSE and the simulated probability of signal for the parametric and theMMRPM methods were identical (or nearly so). For the severe modelmisspecification case, the nonparametric andMMRPM methods were identical (or nearly so). For the mild model misspecification case, the MMRPM method was superior to the parametric and nonparametric methods. Therefore, this simulation supports the claim that the MMRPM method is robust to model misspecification. In addition, the MMRPM method performed better for data sets with correlated error structure. Also, the performances of the nonparametric and MMRPM methods improved as the number of observations per profile increases since more observations over the same range of X generally enables more knots to be used by the penalized spline method, resulting in greater flexibility and improved fits in the nonparametric curves and consequently, the semiparametric curves. The parametric, nonparametric and semiparametric approaches were utilized for fitting the relationship between torque produced by an engine and engine speed in the automotive industry. Then, we used a Hotelling's T 2 statistic based on the estimated random effects to conduct Phase I studies to determine the outlying profiles. The parametric, nonparametric and seminonparametric methods showed that the process was stable. Despite the fact that all three methods reach the same conclusion regarding the –in-control– status of each profile, the nonparametric and MMRPM results provide a better description of the actual behavior of each profile. Thus, the nonparametric and MMRPM methods give the user greater ability to properly interpret the true relationship between engine speed and torque for this type of engine and an increased likelihood of detecting unusual engines in future production. Finally, we conclude that the nonparametric and semiparametric approaches performed better than the parametric approach when the user's model is misspecified. The case study demonstrates that, the proposed nonparametric and semiparametric methods are shown to be more efficient, flexible and robust to model misspecification for Phase I profile monitoring in a practical application. Thus, our methods are robust to the common problem of model misspecification. We also found that both the nonparametric and the semiparametric methods result in charts with good abilities to detect changes in Phase I data, and in charts with easily calculated control limits. The proposed methods provide greater flexibility and efficiency than current parametric methods used in profile monitoring for Phase I that rely on correct model specification, an unrealistic situation in many practical problems in industrial applications. / Ph. D.

近年來,許多調適性管制圖都只探討單一製程,然而現今存在許多相依製程的問題.因此本論文提出兩相依製程之調適性管制圖,並以ATS測量管制圖的績效.本論文所提出的變動抽樣間隔時間之調適性管制圖對於偵測製程中幅度及小幅度的偏移有良好的績效.此外,本論文所提出的變動抽樣樣本大小及變動抽樣間隔時間之調適性管制圖對於偵測製程極小幅度的偏移有良好的績效. / In recent years, many research papers about adaptive control charts all consider a single process step. However, there are many multiple process steps in industry process. In this article, we propose adaptive control charts to monitor two dependent process steps, and their average time to signal (ATS) is calculated by Markov chain approach to measure the performance of these proposed control charts. It has been shown that the performance of the adaptive sampling interval (ASI) control charts in detecting small and moderate shifts in process means is better than the fixed sampling interval control charts, especially for small shifts, and the proposed adaptive sample size and sampling interval (ASSI) control charts have better performance in detecting very small shifts in process means than the fixed sample size and sampling interval control charts and the adaptive sample size control charts.

É crescente o número de laboratórios que têm implantado sistemas de gestão da qualidade conforme a norma ABNT NBR ISO/IEC 17025, entretanto, para continuidade no atendimento aos requisitos da norma e às necessidades dos clientes, os laboratórios podem apresentar dificuldades que precisam ser identificadas e analisadas para melhoria continua da qualidade dos resultados. Desta maneira, uma avaliação preliminar das dificuldades operacionais após implantação do sistema de gestão da qualidade ABNT NBR ISO/IEC 17025 aponta como um dos requisitos de maior dificuldade a garantia da qualidade de resultados (requisito 5.9). Este requisito abrange a importância do monitoramento contínuo para validade dos ensaios realizados e acompanhamento de possíveis tendências das análises realizadas pelos laboratórios. Para realização desse monitoramento são aplicadas as cartas de controle que requerem maior atenção na sua aplicabilidade e interpretação em função do método de análise, da amostra de controle e da periodicidade do acompanhamento. As cartas de controle são ferramentas que possibilitam o monitoramento contínuo dos processos analíticos e permitem a avaliação de possíveis otimizações das atividades técnicas como, por exemplo, com a redução de custo analítico decorrente das curvas de calibração em análises cromatográficas. Desta maneira, neste trabalho, após realizar uma pesquisa de mercado e confirmar que o requisito 5.9 está entre os requisitos de maior dificuldades para laboratórios de rotina, foi realizado um estudo prático e orientativo de aplicação dos diferentes tipos de cartas de controle que podem ser utilizados pelos laboratórios de ensaio na manutenção contínua da qualidade dos resultados. Este estudo demonstra que a escolha de uma carta de controle está relacionada com a criticidade do método analítico e que pode gerar controles adequados dentro de uma relação custo/benefício que seja satisfatória. A interpretação de todos estes resultados também gerou a proposta de um guia orientativo para aplicação de cartas de controle aos laboratórios analíticos. / A growing number of laboratories have implemented quality management systems according to ISO / IEC 17025 standard, however, for continuity in meeting the requirements of the standard and the needs of customers, laboratories may present difficulties that need to be identified and analyzed to continuously improvement of the quality results. In this way, a preliminary assessment of operational difficulties following the implementation of ISO / IEC 17025 points as one of the most difficult requirements to guarantee the quality of results (requirement 5.9). This requirement covers the importance of continuous monitoring for validity of testing and monitoring of possible trends of the analyzes performed by laboratories. To conduct this monitoring are applied control charts that need more attention in its applicability and interpretation depending on the method of analysis, the control sample and the monitoring frequency. Control charts are tools that enable continuous monitoring of analytical processes and make assessments of possible optimizations of the technical activities, for example, by reducing analytical costs arising from the calibration curves in chromatographic analysis. Thus, in this study, after conducting market research and confirm that the requirement 5.9 is among the most difficult requirements for routine labs, was developed a practical study of application of different types of control charts that can be used by testing laboratories in the ongoing maintenance of the quality of results. This study demonstrates that the choice of a control chart is related to the criticality of the analytical method and that can generate adequate controls within a cost / benefit that is satisfactory. The interpretation of all these results also led to the proposal of an reference guide to application of control charts to analytical laboratories.

É crescente o número de laboratórios que têm implantado sistemas de gestão da qualidade conforme a norma ABNT NBR ISO/IEC 17025, entretanto, para continuidade no atendimento aos requisitos da norma e às necessidades dos clientes, os laboratórios podem apresentar dificuldades que precisam ser identificadas e analisadas para melhoria continua da qualidade dos resultados. Desta maneira, uma avaliação preliminar das dificuldades operacionais após implantação do sistema de gestão da qualidade ABNT NBR ISO/IEC 17025 aponta como um dos requisitos de maior dificuldade a garantia da qualidade de resultados (requisito 5.9). Este requisito abrange a importância do monitoramento contínuo para validade dos ensaios realizados e acompanhamento de possíveis tendências das análises realizadas pelos laboratórios. Para realização desse monitoramento são aplicadas as cartas de controle que requerem maior atenção na sua aplicabilidade e interpretação em função do método de análise, da amostra de controle e da periodicidade do acompanhamento. As cartas de controle são ferramentas que possibilitam o monitoramento contínuo dos processos analíticos e permitem a avaliação de possíveis otimizações das atividades técnicas como, por exemplo, com a redução de custo analítico decorrente das curvas de calibração em análises cromatográficas. Desta maneira, neste trabalho, após realizar uma pesquisa de mercado e confirmar que o requisito 5.9 está entre os requisitos de maior dificuldades para laboratórios de rotina, foi realizado um estudo prático e orientativo de aplicação dos diferentes tipos de cartas de controle que podem ser utilizados pelos laboratórios de ensaio na manutenção contínua da qualidade dos resultados. Este estudo demonstra que a escolha de uma carta de controle está relacionada com a criticidade do método analítico e que pode gerar controles adequados dentro de uma relação custo/benefício que seja satisfatória. A interpretação de todos estes resultados também gerou a proposta de um guia orientativo para aplicação de cartas de controle aos laboratórios analíticos. / A growing number of laboratories have implemented quality management systems according to ISO / IEC 17025 standard, however, for continuity in meeting the requirements of the standard and the needs of customers, laboratories may present difficulties that need to be identified and analyzed to continuously improvement of the quality results. In this way, a preliminary assessment of operational difficulties following the implementation of ISO / IEC 17025 points as one of the most difficult requirements to guarantee the quality of results (requirement 5.9). This requirement covers the importance of continuous monitoring for validity of testing and monitoring of possible trends of the analyzes performed by laboratories. To conduct this monitoring are applied control charts that need more attention in its applicability and interpretation depending on the method of analysis, the control sample and the monitoring frequency. Control charts are tools that enable continuous monitoring of analytical processes and make assessments of possible optimizations of the technical activities, for example, by reducing analytical costs arising from the calibration curves in chromatographic analysis. Thus, in this study, after conducting market research and confirm that the requirement 5.9 is among the most difficult requirements for routine labs, was developed a practical study of application of different types of control charts that can be used by testing laboratories in the ongoing maintenance of the quality of results. This study demonstrates that the choice of a control chart is related to the criticality of the analytical method and that can generate adequate controls within a cost / benefit that is satisfactory. The interpretation of all these results also led to the proposal of an reference guide to application of control charts to analytical laboratories.

自Duncan在1956年提出管制圖的經濟設計以來,陸續有許多學者提出各種不同型態管制圖的經濟設計,但是在這些文章中,尚無將描點的連串檢定列入考慮者,然而在管制圖中加入描點的連串檢定實有其必要性,加入描點的連串檢定可增加管制圖的偵測能力,但是這種作法頗為麻煩,因此Jaehn(1987)提出了區域管制圖來取代傳統管制圖加上連串檢定的不便,本研究提出X Bar-S Square 區域管制圖的經濟設計以改善一般經濟管制圖未將描點的連串檢定列入考慮的缺點.我們以製程中各項製程和成本資料為因子,對經濟區域管制圖的最佳設計參數值做敏感度分析,以找出製程中的關鍵參數.另外我們應用Saniga(1989)經濟統計管制圖的觀念設計經濟統計區域管制圖.雖然經濟統計區域管制圖所計算出的成本會比經濟區域管制圖稍大,但是在統計表現上卻符合我們的要求.

管制圖之經濟模型首由Duncan(1956)提出，自此之後陸續有學者致力研究經濟管制圖，包括X-bar管制圖、S管制圖等。但R管制圖之經濟設計目前尚無人提出。而在實務上，部份產業可能由於產品過於昂貴，或者產品的製造時間所需甚長，而使得品檢時所抽取的樣本數無法達到25個，這時若採用傳統的管制圖來分析製程，將無法顯示製程真正的狀態。因此本研究首先探討少量連串下X-bar和R管制圖之製作原理，並計算及整理出較完整的少量連串下X-bar和R的管制係數表。接著假設非機遇因素只影響製程運用Banerjee和Rahim(1987)的更新理論方法，建立少量連串情形下的R經濟管制圖。再利用最佳化方法，即可求得最適設計參數值。於是，少量連串情形下的R經濟管制圖得以建立。最後，我們將舉一個例子來說明如何獲得最適設計參數值、決定關鍵參數，以及少量連串情形下R經濟管制圖之建立與應用。

管制圖設計的經濟模式在最近三十年已經被廣泛的研究。本研究利用更新 理論方法(Renewal Theory Approach) 解出兩個非隨機因素下之S 經濟管 制圖。與其它的多重非隨機因素製程模式相比較，我們的模式不僅假設更 合理且以此方法表示平均循環時間(The Expected Cycle Time) 及平均循 環成本(The Expected Cycle Cost)會比擴展Duncan的方法或其它的方法 簡單容易。文中以數值例子說明建立 S 經濟管制圖的過程，並比較 S經 濟管制圖與Shewhart S 管制圖成本的大小及偵錯能力。另外，當製程上 有多重非隨機因素發生時，其成本模式也可容易的以更新理論方法擴展而 得。在實務上，若業者希望以最小成本維持製程之穩定，則可依本文所提 出的方法建立經濟管制圖。

量測誤差是工業製程中影響產品值常見的因素。大的量測誤差會使得產品的量測值偏離實際值，並引導監控者至錯誤的結論。本文提出一種新的捲積管制圖。提出指數分配形式的時間間隔型資料，並加上量測誤差的考量，應用在指數加權移動平均管制圖上。此外，假設量測誤差為常態或是指數分配。研究顯示出，在兩種不同分配的量測誤差之下，管制圖的表現都會顯著的受到影響。 / Measurement error is an important factor in industry that influences the outcome of a process. Large measurement error would cause the observation measure deviate from the true value and consequently lead to a wrong decision. In this project, we propose a convolution control chart. We then design the EWMA ‘time between events’ (TBE) control chart with the measurement error, with the assumption that the observations are exponentially distributed. In addition, we assumed the measurement error follows a normal distribution or an exponential distribution. We showed that, in two cases of the measurement error, the performance of the proposed chart monitoring the process mean is greatly affected.