This diploma thesis deals with a Six Sigma method, about especially analysis defects of forms for tire production company Barum Continental. In the first, theoretic part, there is the Six Sigma method, improvement method and implementation into practice defined, and at last I attended to the tools of Six Sigma method, e. g. Control Charts, Regression analysis, Pareto analysis. In the second, practical part, there is the industrial process analyzed. Then I was introduced Barum Continental spol. s.r.o. concern, which data extended. Up to data processing I was used tools of Six Sigma method and also histogram.

The diploma thesis deals with usage of statistical methods to assure capability of production process. The theoretical part includes the definition of quality management, basic statistical concepts and statistical process control. The practical part presents basic information about the company P & L, spol. s r. o. and analyzes the production process of selected parts. The tools of statistical process control are applied and measures to assure capability of production process are proposed.

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.

[ES] En la actualidad resulta de gran importancia el análisis de los fenómenos como el crecimiento poblacional y la reducción de la mortalidad por la repercusión económica y social que dichos procesos tienen en el desarrollo de los países. En este sentido las tablas de vida constituyen una herramienta para comprender, a través de las probabilidades de muerte, la esperanza de vida y otros indicadores, la dinámica poblacional. Lee y Carter (1992), plantearon un modelo, cuyo ajuste permite a los analistas obtener una visión dinámica del comportamiento de la mortalidad durante un periodo de análisis. Esta tesis doctoral busca contribuir en la comprensión de los cambios que ha experimentado la población colombiana en cuanto a mortalidad. Para lograrlo se plantearon cuatro objetivos. El primero, construir modelos estocásticos de mortalidad como Lee-Carter para datos de Colombia y hacer un estudio comparativo de dichos modelos para evaluar su coherencia a partir de la calidad de los resultados obtenidos. El segundo, calcular y analizar algunos indicadores relacionados con la mortalidad tales como la mortalidad infantil, la esperanza de vida al nacer, la esperanza de vida a los 65 años, el índice de Gini al nacer y el índice de Gini a los 65 años. El tercero, aplicar gráficos de control para identificar los momentos en el tiempo y los intervalos de edad en los que la probabilidad de muerte observada es sustancialmente diferente de la pauta de mortalidad en el período estudiado. Para esto, los residuos de los modelos seleccionados se vigilaron mediante el gráfico de control multivariado T2 de Hotelling para detectar cambios sustanciales en la mortalidad que no fueron identificados por los modelos. El cuarto, analizar el comportamiento de la mortalidad para los departamentos de Colombia mediante técnicas de análisis multivariado como el análisis de componentes principales, el clúster jerárquico y el fuzzy clúster, para posteriormente identificar grupos de departamentos con comportamientos similares y caracterizarlos mediante los indicadores de mortalidad estudiados. La metodología descrita relacionada con los tres primeros objetivos se aplicó a datos de las tablas de vida abreviadas por sexo para Colombia para el período 1973-2005, utilizando la información disponible en The Latin America Human Mortality Database. Para el análisis de la mortalidad por departamentos se construyeron nuevas tablas de vida abreviadas por sexo con la información de los departamentos para el período 1985-2014, ajustándonos a la información disponible para los departamentos de Colombia en cuanto a defunciones y población. La metodología fue implementada a través del software estadístico libre R, lo que permite la replicabilidad y reproducibilidad de los resultados. / [CA] En l'actualitat resulta de gran importància l'anàlisi dels fenòmens com el creixement poblacional i la reducció de la mortalitat per la repercussió econòmica i social que aquests processos tenen en el desenvolupament dels països. En aquest sentit les taules de vida constitueixen una eina per a comprendre, a través de les probabilitats de mort, l'esperança de vida i altres indicadors, la dinàmica poblacional. Lee i Carter (1992), van plantejar un model, l'ajust del qual permet als analistes obtenir una visió dinàmica del comportament de la mortalitat durant un període d'anàlisi. Aquesta tesi doctoral cerca contribuir en la comprensió dels canvis que ha experimentat la població colombiana quant a mortalitat. Per a aconseguir-ho es van plantejar quatre objectius. El primer, construir models estocàstics de mortalitat com Lee-Carter per a dades de Colòmbia i fer un estudi comparatiu d'aquests models per a avaluar la seua coherència a partir de la qualitat dels resultats obtinguts. El segon, calcular i analitzar alguns indicadors relacionats amb la mortalitat tals com la mortalitat infantil, l'esperança de vida en nàixer, l'esperança de vida als 65 anys, l'índex de Gini en nàixer i l'índex de Gini als 65 anys. El tercer, aplicar gràfics de control per a identificar els moments en el temps i els intervals d'edat en els quals la probabilitat de mort observada és substancialment diferent de la pauta de mortalitat en el període estudiat. Per a això, els residus dels models seleccionats es van vigilar mitjançant el gràfic de control multivariat T2 de Hotelling per a detectar canvis substancials en la mortalitat que no van ser identificats pels models. El quart, analitzar el comportament de la mortalitat per als departaments de Colòmbia mitjançant tècniques d'anàlisi multivariada com l'anàlisi de components principals, el clúster jeràrquic i el fuzzy clúster, per a posteriorment identificar grups de departaments amb comportaments similars i caracteritzar-los mitjançant els indicadors de mortalitat estudiats. La metodologia descrita relacionada amb els tres primers objectius es va aplicar a dades de les taules de vida abreujades per sexe per a Colòmbia per al període 1973-2005, utilitzant la informació disponible en The Latin America Human Mortality Database. Per a l'anàlisi de la mortalitat per departaments es van construir noves taules de vida abreujades per sexe amb la informació dels departaments per al període 1985-2014, ajustant-nos a la informació disponible per als departaments de Colòmbia quant a defuncions i població. La metodologia va ser implementada a través del programari estadístic lliure R, la qual cosa permet la replicabilidad i reproducibilidad dels resultats. / [EN] The analysis of phenomena such as population growth and mortality reduction is currently of great importance because of the economic and social impact that these processes have on the development of countries. In this sense, life tables are a tool for understanding population dynamics through death probabilities, life expectancy and other indicators. Lee and Carter (1992) proposed a model whose adjustment allows analysts to obtain a dynamic view of the behavior of mortality during a period of analysis. This doctoral thesis seeks to contribute to the understanding of the changes experienced by the Colombian population in terms of mortality. To achieve this, four objectives were proposed. The first, to construct stochastic mortality models such as Lee-Carter for Colombian data and to make a comparative study of these models to evaluate their coherence based on the quality of the results obtained. The second is to calculate and analyze some mortality-related indicators such as infant mortality, life expectancy at birth, life expectancy at age 65, the Gini index at birth and the Gini index at age 65. The third is to apply control charts to identify moments in time and age intervals in which the observed probability of death is substantially different from the mortality pattern in the period studied. For this, the residuals of the selected models were monitored using Hotelling's T2 multivariate control chart to detect substantial changes in mortality that were not identified by the models. Fourth, to analyze the behavior of mortality for the departments of Colombia using multivariate analysis techniques such as principal component analysis, hierarchical clustering and fuzzy clustering, in order to subsequently identify groups of departments with similar behavior and characterize them by means of the mortality indicators studied. The methodology described in relation to the first three objectives was applied to data from the abbreviated life tables by sex for Colombia for the period 1973-2005, using the information available in The Latin America Human Mortality Database. For the analysis of mortality by department, new abbreviated life tables by sex were constructed with information from the departments for the period 1985-2014, adjusting to the information available for the departments of Colombia in terms of deaths and population. The methodology was implemented through the free statistical software R, which allows the replicability and reproducibility of the results. / Díaz Rojo, G. (2021). Ajuste y predicción de la mortalidad. Aplicación a Colombia [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/179995 / TESIS

[pt] Em um mundo globalizado, em contínua transformação, são cada vez mais freqüentes mudanças no perfil da demanda. Se não detectadas rapidamente, elas podem gerar impactos negativos no progresso de um negócio devido à baixa qualidade nas previsões de venda, que começam a gerar valores sistematicamente acima ou abaixo da demanda real indicando a presença de viés. Para evitar esse cenário, técnicas formais para detecção de viés podem ser incorporadas ao processo de previsão de demanda. Diante desse quadro, a presente dissertação compara os desempenhos, via simulação, das principais técnicas formais de detecção de viés em previsão de demanda presentes na literatura. Nesse sentido, seis técnicas são identificadas e analisadas. Quatro são baseadas em estatísticas Tracking Signal e duas são adaptadas de técnicas de Controle Estatístico de Processos. Os modelos de previsão de demanda monitorados pelas técnicas em questão são os de séries temporais estruturadas, associados ao método de amortecimento exponencial simples e ao método de Holt, respectivamente, para séries com nível médio constante e séries com tendência. Três tipos de alterações no perfil da demanda – que acarretam em viés na previsão – são examinados. O primeiro consiste em mudanças no nível médio em séries temporais de nível médio constante. O segundo tipo também considera séries temporais de nível médio constante, porém com o foco em surgimentos de tendências. O terceiro viés consiste em mudanças na tendência em series temporais com tendência pré-incorporada. Entre os resultados obtidos, destaca-se a conclusão de que, para a maioria das situações estudadas, as técnicas baseadas nas estatísticas Tracking Signal possuem desempenho superior às demais técnicas com relação à eficiência na detecção de viés. / [en] In a globalized world, in continuous transformation, changes in the demand pattern are increasingly frequent. If not rapidly detected, they can have a negative and persistent impact in the wellbeing of a business due to continuously poor quality sales forecasts, which begin to generate values systematically above or below the actual demand indicating the presence of bias. To avoid this happening, statistical techniques can be incorporated in a prediction process with the objective known as bias detection in demand forecasting. Considering this situation, the present dissertation compares, through simulation, the efficiency performance of the main existing formal techniques of monitoring demand forecasting models, with the view of bias detection. Six of such techniques are identified and analyzed in this work. Four are based on Tracking Signal Statistics and two are adapted from the Statistical Process Control approach. The demand forecasting models monitored by the techniques in question can be classified as structured time series, for a constant level or trend pattern, and using both the simple exponential smoothing and the Holt s methods. Three types of changes in the demand pattern - which result in biased prediction - are examined. The first one focus on simulated changes on the average level of various constant times series. The second type also considered various constant times series, but now simulating the appearance of different trends. And the third refers to simulate changes in trends in various times series with pre-established trends. Among the results attained, one stands out: the techniques based on Tracking Signal Statistics - when compares to other methods - showed superior performance insofar as efficient bias detection in demand forecasting.

Statistical quality control is the application of statistical methods to problems for which it is of interest to evaluate, establish, or verify the quality of a product. The two basic areas of statistical quality control that have received both the greatest attention in the literature and the widest acceptance in industry are acceptance sampling and statistical process control. In the majority of such techniques, a single characteristic of an item is used to describe its quality. In such cases, one of two basic types of product quality measures is typically used: attributes product quality measures and variables product quality measures. Variables product quality measures evaluate an item’s quality by measuring its quality characteristic on a continuous scale. Attributes product quality measures assign a 0 to an item if its characteristic is conforming to some specification, and 1 if its characteristic is nonconforming. Although attributes and variables product quality measures have many appropriate applications, there are many situations m which product quality is best described by classifying a single characteristic of the item using three or more discrete levels. A multilevel discrete product quality measure is a function that assigns a numerical value to such an item corresponding to the level in which it is classified. Several acceptance sampling plans and control charts that incorporate the use of multilevel discrete product quality measures are defined here. In addition to the multilevel discrete product quality measure, each of the defined methods utilizes a quality value function. A quality value function assigns a numerical value to an item based on the classification it receives from the multilevel discrete product quality measure. Each of the defined multilevel acceptance sampling plans and multilevel control charts is evaluated with respect to its probabilistic behavior. In addition, the problem of parameter selection and quality value function specification is addressed for each of the defined techniques. The cases considered are the 3-level case, the 4-level case, and the general j-level case. / Ph. D.

[pt] Os gráficos de controle de S(2) são ferramentas fundamentais amplamente utilizados para monitoramento da dispersão do processo em aplicações de CEP. O desempenho na Fase II de diferentes tipos de gráficos de controle, incluindo o gráfico de S(2), com parâmetros desconhecidos pode ser significativamente diferente do desempenho nominal por causa do efeito da estimação de parâmetros. Nos anos mais recentes, este efeito tem sido abordado predominantemente sob a perspectiva condicional, que considera a variabilidade das estimativas de parâmetros obtidas a partir de diferentes amostras de referência da Fase I em vez das típicas medidas de desempenho baseadas na distribuição marginal (incondicional) do número de amostras até o sinal (Run Length-RL), como sua média. À luz dessa nova perspectiva condicional, a análise do desempenho da Fase II e do projeto de gráficos de controle é frequentemente realizada usando o Exceedance Probability Criterion para a média da distribuição condicional do RL (CARL 0), isto é, o critério que garante uma alta probabilidade de que CARL 0 seja pelo menos um valor mínimo tolerado e especificado. Intervalos de tolerância para variâncias amostrais são úteis quando o maior interesse está focado na precisão dos valores de uma característica de qualidade, e podem ser usados na tomada de decisões sobre a aceitação de lotes por amostragem. Motivado pelo fato de que estes intervalos, especificamente no caso dos intervalos bilaterais, não foram abordados na literatura, limites bilaterais de tolerância exatos e aproximados de variâncias amostrais são derivados e apresentados neste trabalho. A relação matemática-estatística entre o intervalo de tolerância para a variância amostral e o Exceedance Probability (função de sobrevivência) da CARL 0 do gráfico de S(2) com parâmetro estimado é reconhecida, destacada e usada neste trabalho de tal forma que o estudo do desempenho na Fase II e o projeto desse gráfico pode ser baseado no intervalo de tolerância para a variância amostral, e vice-versa. Os trabalhos sobre o desempenho e projeto do gráfico de S(2) com parâmetro estimado focaram-se em apenas uma perspectiva (incondicional ou condicional) e consideraram somente um tipo de gráfico (unilateral superior ou bilateral). A existência de duas perspectivas e dois tipos de gráficos poderia ser confusa para os usuários. Por esse motivo, o desempenho e o projeto do gráfico de S(2) de acordo com essas duas perspectivas são comparados, considerando cada tipo de gráfico. Da mesma forma, esses dois tipos de gráficos também são comparados para cada perspectiva. Alguns resultados importantes relacionados ao projeto do gráfico de S(2), que ainda não estão disponíveis na literatura, foram necessários e obtidos neste trabalho para fornecer um estudo comparativo completo que permita aos usuários estarem cientes das diferenças significativas entre as duas perspectivas e os dois tipos de gráficos para tomar decisões informadas sobre a escolha do projeto do gráfico de S(2). Além disso, dado que a distribuição condicional do RL é em geral fortemente enviesada à direita, a mediana e alguns quantis extremos desta distribuição são propostos como medidas de desempenho complementares à sua tradicional média (CARL 0). Finalmente, algumas recomendações práticas são oferecidas. / [en] The S(2) control charts are fundamental tools widely used to monitor the process dispersion in applications of Statistical Process Monitoring and Control. Phase II performance of different types of control charts, including the S(2) chart, with unknown process parameters may be significantly different from the nominal performance due to the effect of parameter estimation. In the last few years, this effect has been addressed predominantly under the conditional perspective, which considers the variability of parameter estimates obtained from different Phase I reference samples instead of the traditional unconditional performance measures based on the marginal (unconditional) run length (RL) distribution, such as the unconditional average run length. In light of this new conditional perspective, the analysis of the Phase II performance and design of control charts is frequently undertaken using the Exceedance Probability Criterion for the conditional (given the parameter estimates) in-control average run length (CARL 0), that is, the criterion that ensures a high probability that the CARL 0 is at least a specified minimum tolerated value. Tolerance intervals for sample variances are useful when the main concern is the precision of the values of the quality characteristic and then they can be used in decision-making on lot acceptance sampling. Motivated by the fact that these tolerance intervals, specifically in the case of the two-sided intervals, have not been addressed in the literature so far, exact and approximate two-sided tolerance limits for the population of sample variances are derived and presented in this work. The mathematical-statistical relationship between tolerance interval for the sample variance and the exceedance probability (survival probability) of the CARL 0 for the S(2) control chart with estimated parameter is recognized, highlighted and used in this work in such a way that the study of the Phase II performance and design of this chart can be based on tolerance interval for the sample variance, and vice versa. Works on performance and design of S(2) chart with estimated parameter generally focused on only one perspective (either unconditional or conditional) and considered only one type of chart (either upper one-sided chart or two-sided chart). The existence of both perspectives and two types of charts may be confusing for practitioners. For that reason, the performance and design of S(2) control chart according to these two perspectives are compared, considering each type of chart. Similarly, these two types of charts are also compared for each perspective. Some important results related to the S(2) chart design, which are not yet available in the literature, were required and obtained in this work to provide a comprehensive comparative study that enables practitioners to be aware of the significant differences between these two perspectives and the two types of charts so that proper informed decisions about the chart design to choose can be made. Furthermore, because the conditional RL distribution is usually highly rightskewed, the median and some extreme quantiles of the conditional RL distribution are proposed as complementary performance measures to the customary mean (CARL 0). Finally, some practical recommendations are offered.

由近期的研究中發現變動所有參數的管制圖在偵測小幅度偏移時的速度比起傳統的舒華特管制圖來的快，許多文獻也討論到利用調適性管制技術同時監控製程的平均數和變異數。而在這份研究中，為了改善現有管制圖的偵測效率，依序提出了U-V管制圖以及Max-M管制圖來偵測單一製程與兩相依製程的平均數和變異數。採用AATS及ANOS來衡量管制圖的偵測績效，並利用馬可夫鏈推導計算得之。透過兩階段的範例來介紹所提出的管制圖的應用方法並將VP U-V管制圖、VP Max-M管制圖與FP Z(X-bar)-Z(Sx^2)管制圖加以比較。從所研究的數值分析中發現VP Max-M管制圖比另兩種管制圖的表現來的好，再加上只需要單一管制圖在使用上對工程師來說也較為簡便，因此建議Max-M管制圖値得在實務上被使用。 / Recent studies have shown that the variable parameters (VP) charts detect small process shifts faster than the traditional Shewhart charts. There have been many papers discussed adaptive control schemes to monitor process mean and variance simultaneously. In the study, to improve the efficiency and performance of the existing control charts, the U-V control charts and Max-M control charts are respectively proposed to monitor the process mean and variance for a single process and two dependent process steps. The performance of the proposed control charts is measured by using adjusted average time to signal (AATS) and average number of observations to signal (ANOS). The calculation of AATS and ANOS is derived by Markov chain approach. The application of the proposed control charts is illustrated by a numerical example for two dependent process steps, and the performance of VP U-V control charts, VP Max-M control charts and FP Z(X-bar)-Z(Sx^2) control charts is compared. From the results of data analyses, it shows that the VP Max-M control charts have better performance than VP U-V control charts and FP Z(X-bar)-Z(Sx^2) control charts. Furthermore, using a single chart to monitor a process is easier than using two charts for engineers. Hence, Max-M control charts are recommended in real industrial process.

最小成本下，規格及X-bar-S管制圖之設計 / The design of economic statistical control charts and specification are both crucial research areas in industry. Furthermore, the determination of consumer and producer specifications is important to producer. In this study, we consider eight cost models including the consumer loss function and/or the producer loss function with the economic statistical X-bar and S charts or Shewhart-type economic X-bar and S charts. To determine the design parameters of the X-bar and S charts and consumer tolerance and/or producer tolerance, we using the Genetic Algorithm to minimizing expected cost per unit time. In the comparison of examples and sensitivity analyses, we found that the optimal design parameters of the Shewhart-type economic X-bar and S charts are similar to those of economic statistical X-bar and S control charts, and the expected cost per unit time may lower than the actual cost per unit time when the cost model only considering consumer loss or producer loss. When considering both consumer and producer tolerances in the cost model, the design parameters of the economic X-bar and S charts are not sensitive to the cost models. If the producer tolerance is smaller than the consumer tolerance, and the producer loss is smaller than the consumer loss, the optimal producer tolerance should be small.

近年來有許多研究發現，適應性管制圖在偵測製程或產品幅度偏移時的速度比傳統的舒華特管制圖來的快，許多文獻也討論到利用適應性管制技術同時監控製程的平均數和變異數。隨著科技的發達，許多產品在製造上更加精密，現今普遍使用的固定參數管制圖並無法有效率的偵測出製程失控，導致巨大的成本損失。為了改善現有管制圖的偵測效率與有效控制製程失控下的損失，我們提出了三種適應性加權損失管制圖，包括變動抽樣間隔(VSI)、變動樣本數與抽樣間隔(VSI)、變動管制參數(VP)來偵測單一製程與兩相依製程的平均數和變異數。採用製程發生變動後到管制圖偵測出異常訊息所需的平均時間(AATS)與所需的總觀測數(ANOS)來衡量管制圖的偵測績效，並利用馬可夫鏈推導計算得之。從數值分析中發現，適應性加權損失管制圖在「偵測小偏移幅度時的偵測效率」與「成本的控制」明顯比傳統管制圖表現的更好，再加上每一個製程僅需採用單一管制圖，對使用者也較為簡便並且容易理解，因此適應性加權損失管制圖在實務上是值得被推薦使用的。 / Recent research has shown that control charts with adaptive features detect process shifts faster than traditional Shewhart charts. In this article, we propose three kinds of adaptive weighted loss (WL) control charts, variable sampling intervals (VSI) WL control charts , variable sample sizes and sampling intervals (VSSI) WL control charts and variable parameters (VP) WL control charts, to monitor the target and variance on a single process step and two dependent process steps simultaneously. These adaptive WL control charts may effectively distinguish which process step is out-of-control. We use the Markov chain approach to calculate the adjusted average time to signal (AATS) and average number of observations to signal (ANOS) in order to measure the performance of the proposed control charts. From the numerical examples and data analyses, we find the adaptive WL control charts have better detection abilities and performance than fixed parameters (FP) WL control charts and FP Z(X-bar)-Z(Sx^2) and Z(e-bar)-Z(Se^2) control charts. We also proposed the optimal adaptive WL control charts using an optimization technique to minimize AATS when users cannot specify the values of the variable parameters. In addition, we discuss the impact of misusing weighted loss of outgoing quality control chart. In conclusion, using a single chart to monitor a process is inherently easier than using two charts. The WL control charts are easy to understand for the users, and have better performance and detection abilities than the other charts, thus, we recommend the use of WL control charts in the real industrial process.