Wide bandwidth envelope trackers with reduced switching frequency for RF power amplifier

El requerimiento de proveer alta frecuencia de datos en los modernos sistema de comunicación inalámbricos resulta en complejas señales moduladas de radio-frequencia (RF) con un gran ancho de banda y alto ratio pico-promedio (PAPR). Para garantizar la linealidad del comportamiento, los amplificadores lineales de potencia comunes funcionan típicamente entre 4 y 10 dB de back-o_ desde la máxima potencia de salida, ocasionando una baja eficiencia del sistema. La eliminación y restauración de la evolvente (EER) y el seguimiento de la evolvente (ET) son dos prometedoras técnicas para resolver el problema de la eficiencia. Tanto en EER como en ET, es complicado diseñar un amplificador de potencia que sea eficiente para señales de RF de alto ancho de banda y alto PAPR. Una propuesta común para los amplificadores de potencia es incluir un convertidor de potencia de muy alta eficiencia operando a frecuencias más altas que el ancho de banda de la señal RF. En este caso, la potencia perdida del convertidor ocasionado por la alta frecuencia desaconseja su práctica cuando el ancho de banda es muy alto. La solución a este problema es el enfoque de esta disertación que presenta dos arquitecturas de amplificador evolvente: convertidor híbrido-serie con una técnica de evolvente lenta y un convertidor multinivel basado en un convertidor reductor multifase con control de tiempo mínimo. En la primera arquitectura, una topología híbrida está compuesta de una convertidor reductor conmutado y un regulador lineal en serie que trabajan juntos para ajustar la tensión de salida para seguir a la evolvente con precisión. Un algoritmo de generación de una evolvente lenta crea una forma de onda con una pendiente limitada que es menor que la pendiente máxima de la evolvente original. La salida del convertidor reductor sigue esa forma de onda en vez de la evolvente original usando una menor frecuencia de conmutación, porque la forma de onda no sólo tiene una pendiente reducida sino también un menor ancho de banda. De esta forma, el regulador lineal se usa para filtrar la forma de onda tiene una pérdida de potencia adicional. Dependiendo de cuánto se puede reducir la pendiente de la evolvente para producir la forma de onda, existe un trade-off entre la pérdida de potencia del convertidor reductor relacionada con la frecuencia de conmutación y el regulador lineal. El punto óptimo referido a la menor pérdida de potencia total del amplificador de evolvente es capaz de identificarse con la ayuda de modelo preciso de pérdidas que es una combinación de modelos comportamentales y analíticos de pérdidas. Además, se analiza el efecto en la respuesta del filtro de salida del convertidor reductor. Un filtro de dampeo paralelo extra es necesario para eliminar la oscilación resonante del filtro de salida porque el convertidor reductor opera en lazo abierto. La segunda arquitectura es un amplificador de evolvente de seguimiento de tensión multinivel. Al contrario que los convertidores que usan multi-fuentes, un convertidor reductor multifase se emplea para generar la tensión multinivel. En régimen permanente, el convertidor reductor opera en puntos del ciclo de trabajo con cancelación completa del rizado. El número de niveles de tensión es igual al número de fases de acuerdo a las características del entrelazamiento del convertidor reductor. En la transición, un control de tiempo mínimo (MTC) para convertidores multifase es novedosamente propuesto y desarrollado para cambiar la tensión de salida del convertidor reductor entre diferentes niveles. A diferencia de controles convencionales de tiempo mínimo para convertidores multifase con inductancia equivalente, el propuesto MTC considera el rizado de corriente por cada fase basado en un desfase fijo que resulta en diferentes esquemas de control entre las fases. La ventaja de este control es que todas las corrientes vuelven a su fase en régimen permanente después de la transición para que la siguiente transición pueda empezar muy pronto, lo que es muy favorable para la aplicación de seguimiento de tensión multinivel. Además, el control es independiente de la carga y no es afectado por corrientes de fase desbalanceadas. Al igual que en la primera arquitectura, hay una etapa lineal con la misma función, conectada en serie con el convertidor reductor multifase. Dado que tanto el régimen permanente como el estado de transición del convertidor no están fuertemente relacionados con la frecuencia de conmutación, la frecuencia de conmutación puede ser reducida para el alto ancho de banda de la evolvente, la cual es la principal consideración de esta arquitectura. La optimización de la segunda arquitectura para más alto anchos de banda de la evolvente es presentada incluyendo el diseño del filtro de salida, la frecuencia de conmutación y el número de fases. El área de diseño del filtro está restringido por la transición rápida y el mínimo pulso del hardware. La rápida transición necesita un filtro pequeño pero la limitación del pulso mínimo del hardware lleva el diseño en el sentido contrario. La frecuencia de conmutación del convertidor afecta principalmente a la limitación del mínimo pulso y a las pérdidas de potencia. Con una menor frecuencia de conmutación, el ancho de pulso en la transición es más pequeño. El número de fases relativo a la aplicación específica puede ser optimizado en términos de la eficiencia global. Otro aspecto de la optimización es mejorar la estrategia de control. La transición permite seguir algunas partes de la evolvente que son más rápidas de lo que el hardware puede soportar al precio de complejidad. El nuevo método de sincronización de la transición incrementa la frecuencia de la transición, permitiendo que la tensión multinivel esté más cerca de la evolvente. Ambas estrategias permiten que el convertidor pueda seguir una evolvente con un ancho de banda más alto que la limitación de la etapa de potencia. El modelo de pérdidas del amplificador de evolvente se ha detallado y validado mediante medidas. El mecanismo de pérdidas de potencia del convertidor reductor tiene que incluir las transiciones en tiempo real, lo cual es diferente del clásico modelos de pérdidas de un convertidor reductor síncrono. Este modelo estima la eficiencia del sistema y juega un papel muy importante en el proceso de optimización. Finalmente, la segunda arquitectura del amplificador de evolvente se integra con el amplificador de clase F. La medida del sistema EER prueba el ahorro de energía con el amplificador de evolvente propuesto sin perjudicar la linealidad del sistema. ABSTRACT The requirement of delivering high data rates in modern wireless communication systems results in complex modulated RF signals with wide bandwidth and high peak-to-average ratio (PAPR). In order to guarantee the linearity performance, the conventional linear power amplifiers typically work at 4 to 10 dB back-off from the maximum output power, leading to low system efficiency. The envelope elimination and restoration (EER) and envelope tracking (ET) are two promising techniques to overcome the efficiency problem. In both EER and ET, it is challenging to design efficient envelope amplifier for wide bandwidth and high PAPR RF signals. An usual approach for envelope amplifier includes a high-efficiency switching power converter operating at a frequency higher than the RF signal's bandwidth. In this case, the power loss of converter caused by high switching operation becomes unbearable for system efficiency when signal bandwidth is very wide. The solution of this problem is the focus of this dissertation that presents two architectures of envelope amplifier: a hybrid series converter with slow-envelope technique and a multilevel converter based on a multiphase buck converter with the minimum time control. In the first architecture, a hybrid topology is composed of a switched buck converter and a linear regulator in series that work together to adjust the output voltage to track the envelope with accuracy. A slow envelope generation algorithm yields a waveform with limited slew rate that is lower than the maximum slew rate of the original envelope. The buck converter's output follows this waveform instead of the original envelope using lower switching frequency, because the waveform has not only reduced slew rate but also reduced bandwidth. In this way, the linear regulator used to filter the waveform has additional power loss. Depending on how much reduction of the slew rate of envelope in order to obtain that waveform, there is a trade-off between the power loss of buck converter related to the switching frequency and the power loss of linear regulator. The optimal point referring to the lowest total power loss of this envelope amplifier is identified with the help of a precise power loss model that is a combination of behavioral and analytic loss model. In addition, the output filter's effect on the response is analyzed. An extra parallel damping filter is needed to eliminate the resonant oscillation of output filter L and C, because the buck converter operates in open loop. The second architecture is a multilevel voltage tracking envelope amplifier. Unlike the converters using multi-sources, a multiphase buck converter is employed to generate the multilevel voltage. In the steady state, the buck converter operates at complete ripple cancellation points of duty cycle. The number of the voltage levels is equal to the number of phases according the characteristics of interleaved buck converter. In the transition, a minimum time control (MTC) for multiphase converter is originally proposed and developed for changing the output voltage of buck converter between different levels. As opposed to conventional minimum time control for multiphase converter with equivalent inductance, the proposed MTC considers the current ripple of each phase based on the fixed phase shift resulting in different control schemes among the phases. The advantage of this control is that all the phase current return to the steady state after the transition so that the next transition can be triggered very soon, which is very favorable for the application of multilevel voltage tracking. Besides, the control is independent on the load condition and not affected by the unbalance of phase current. Like the first architecture, there is also a linear stage with the same function, connected in series with the multiphase buck converter. Since both steady state and transition state of the converter are not strongly related to the switching frequency, it can be reduced for wide bandwidth envelope which is the main consideration of this architecture. The optimization of the second architecture for wider bandwidth envelope is presented including the output filter design, switching frequency and the number of phases. The filter design area is restrained by fast transition and the minimum pulse of hardware. The fast transition needs small filter but the minimum pulse of hardware limitation pushes the filter in opposite way. The converter switching frequency mainly affects the minimum pulse limitation and the power loss. With lower switching frequency, the pulse width in the transition is smaller. The number of phases related to specific application can be optimized in terms of overall efficiency. Another aspect of optimization is improving control strategy. Transition shift allows tracking some parts of envelope that are faster than the hardware can support at the price of complexity. The new transition synchronization method increases the frequency of transition, allowing the multilevel voltage to be closer to the envelope. Both control strategies push the converter to track wider bandwidth envelope than the limitation of power stage. The power loss model of envelope amplifier is detailed and validated by measurements. The power loss mechanism of buck converter has to include the transitions in real time operation, which is different from classical power loss model of synchronous buck converter. This model estimates the system efficiency and play a very important role in optimization process. Finally, the second envelope amplifier architecture is integrated with a Class F amplifier. EER system measurement proves the power saving with the proposed envelope amplifier without disrupting the linearity performance.

GESTÃO DO CONHECIMENTO: UM ESTUDO SOBRE A RELAÇÃO ENTRE A LIDERANÇA TRANSFORMACIONAL, A CONVERSÃO DO CONHECIMENTO E A EFICÁCIA ORGANIZACIONAL

Este estudo teve como objetivo principal analisar a relação entre a Liderança Transformacional, a Conversão do Conhecimento e a Eficácia Organizacional. Foram considerados como pressupostos teóricos conceitos consolidados sobre os temas desta relação, além de recentes pesquisas já realizadas em outros países e contextos organizacionais. Com base nisto identificou-se potencial estudo de um modelo que relacionasse estes três conceitos. Para tal considera-se que as organizações que buscam atingir Vantagem Competitiva e incorporam a Knowledge-Based View possam conquistar diferenciação frente a seus concorrentes. Nesse contexto o conhecimento ganha maior destaque e papel protagonista nestas organizações. Dessa forma criar conhecimento através de seus colaboradores, passa a ser um dos desafios dessas organizações ao passo que sugere melhoria de seus indicadores Econômicos, Sociais, Sistêmicos e Políticos, o que se define por Eficácia Organizacional. Portanto os modos de conversão do conhecimento nas organizações, demonstram relevância, uma vez que se cria e se converte conhecimentos através da interação entre o conhecimento existente de seus colaboradores. Essa conversão do conhecimento ou modelo SECI possui quatro modos que são a Socialização, Externalização, Combinação e Internalização. Nessa perspectiva a liderança nas organizações apresenta-se como um elemento capaz de influenciar seus colaboradores, propiciando maior dinâmica ao modelo SECI de conversão do conhecimento. Se identifica então na liderança do tipo Transformacional, características que possam influenciar colaboradores e entende-se que esta relação entre a Liderança Transformacional e a Conversão do Conhecimento possa ter influência positiva nos indicadores da Eficácia Organizacional. Dessa forma esta pesquisa buscou analisar um modelo que explorasse essa relação entre a liderança do tipo Transformacional, a Conversão do Conhecimento (SECI) e a Eficácia Organizacional. Esta pesquisa teve o caráter quantitativo com coleta de dados através do método survey, obtendo um total de 230 respondentes válidos de diferentes organizações. O instrumento de coleta de dados foi composto por afirmativas relativas ao modelo de relação pesquisado com um total de 44 itens. O perfil de respondentes concentrou-se entre 30 e 39 anos de idade, com a predominância de organizações privadas e de departamentos de TI/Telecom, Docência e Recursos Humanos respectivamente. O tratamento dos dados foi através da Análise Fatorial Exploratória e Modelagem de Equações Estruturais via Partial Least Square Path Modeling (PLS-PM). Como resultado da análise desta pesquisa, as hipóteses puderam ser confirmadas, concluindo que a Liderança Transformacional apresenta influência positiva nos modos de Conversão do Conhecimento e que; a Conversão do Conhecimento influencia positivamente na Eficácia Organizacional. Ainda, concluiu-se que a percepção entre os respondentes não apresenta resultado diferente sobre o modelo desta pesquisa entre quem possui ou não função de liderança.

Statistical Hurdle Models for Single Cell Gene Expression: Differential Expression and Graphical Modeling

Thesis (Ph.D.)--University of Washington, 2016-06

The genetics of alcohol intake and of alcohol dependence

Background: Because alcohol has multiple dose-dependent consequences, it is important to understand the causes of individual variation in the amount of alcohol used. The aims of this study were to assess the long-term repeatability and genetic or environmental causes of variation in alcohol intake and to estimate the degree of overlap with causes of susceptibility to alcohol dependence. Methods: Data were used from three studies conducted between 1980 and 1995 on volunteer adult male and female Australian twin subjects. In each study, alcohol intake was reported both as quantity X frequency and as past-week data. Repeatability was calculated as correlations between occasions and between measures, and the effects of genes and environment were estimated by multivariate model fitting to the twin pair repeated measures of alcohol use. Relationships between mean alcohol use and the lifetime history of DSM-III-R alcohol dependence were tested by bivariate model fitting. Results: Repeatability of the alcohol intake measures was between 0.54 and 0.85, with the highest repeatability between measures within study and the lowest repeatability between the first and last studies. Reported alcohol consumption was mainly affected by genetic factors affecting all times of study and by nonshared environmental factors (including measurement error) unique to each time of study. Genes that affect alcohol intake do affect alcohol dependence, but genetic effects unique to dependence are also significant; environmental effects are largely unique to either intake and dependence. Conclusions: Nearly all the repeatable component of variation in alcohol intake is due to genetic effects. Genes affecting intake also affect dependence risk, but there are other genes that affect dependence alone. Studies aiming to identify genes that affect alcohol use disorders need to test loci and candidate genes against both phenotypes.

Nonlinear quantum optical computing via measurement

We show how the measurement induced model of quantum computation proposed by Raussendorf and Briegel ( 2001, Phys. Rev. Letts., 86, 5188) can be adapted to a nonlinear optical interaction. This optical implementation requires a Kerr nonlinearity, a single photon source, a single photon detector and fast feed forward. Although nondeterministic optical quantum information proposals such as that suggested by KLM ( 2001, Nature, 409, 46) do not require a Kerr nonlinearity they do require complex reconfigurable optical networks. The proposal in this paper has the benefit of a single static optical layout with fixed device parameters, where the algorithm is defined by the final measurement procedure.

Advantage of single-trial models for response to selection in wheat breeding multi-environment trials

An investigation was conducted to evaluate the impact of experimental designs and spatial analyses (single-trial models) of the response to selection for grain yield in the northern grains region of Australia (Queensland and northern New South Wales). Two sets of multi-environment experiments were considered. One set, based on 33 trials conducted from 1994 to 1996, was used to represent the testing system of the wheat breeding program and is referred to as the multi-environment trial (MET). The second set, based on 47 trials conducted from 1986 to 1993, sampled a more diverse set of years and management regimes and was used to represent the target population of environments (TPE). There were 18 genotypes in common between the MET and TPE sets of trials. From indirect selection theory, the phenotypic correlation coefficient between the MET and TPE single-trial adjusted genotype means [r(p(MT))] was used to determine the effect of the single-trial model on the expected indirect response to selection for grain yield in the TPE based on selection in the MET. Five single-trial models were considered: randomised complete block (RCB), incomplete block (IB), spatial analysis (SS), spatial analysis with a measurement error (SSM) and a combination of spatial analysis and experimental design information to identify the preferred (PF) model. Bootstrap-resampling methodology was used to construct multiple MET data sets, ranging in size from 2 to 20 environments per MET sample. The size and environmental composition of the MET and the single-trial model influenced the r(p(MT)). On average, the PF model resulted in a higher r(p(MT)) than the IB, SS and SSM models, which were in turn superior to the RCB model for MET sizes based on fewer than ten environments. For METs based on ten or more environments, the r(p(MT)) was similar for all single-trial models.

The effect of service evaluations on behavioral intentions and quality of life

Understanding the contribution of marketing to economic and social outcomes is fundamental to broadening the focus of marketing. The authors develop a comprehensive model that integrates the impact of service quality and service satisfaction on both economic and societal outcomes. The model is validated using two random samples involving intensive health services. The results indicate that service quality and service satisfaction significantly enhance quality of life and behavioral intentions, highlighting that customer service has social as well as economic outcomes. This is an important finding given the movement toward recognizing social and environmental outcomes, such as emphasized through triple bottom-line reporting. The findings have important implications for managing service processes, for improving the quality of life of customers, and for enhancing customers' behavioral intentions toward the organization.

Do organizational climate and competitive strategy moderate the relationship between human resource management and productivity?

This study examined whether the effectiveness of human resource management (HRM)practices is contingent on organizational climate and competitive strategy The concepts of internol and external fit suggest that the positive relationship between HRM and subsequent productivity will be stronger for firms with a positive organizational climate and for firms using differentiation strategies. Resource allocation theories of motivation, on the other hand, predict that the relationship between HRM and productivity will be stronger for firms with a poor climate because employees working in these firms should have the greatest amount of spare capacity. The results supported the resource allocation argument.

Consistency of epidemiologic estimates

Background: The epidemiology of a disease describes numbers of people becoming incident, being prevalent, recovering, surviving, and dying from the disease or from other causes. As a matter of accounting principle, the inflow, stock, and outflows must be compatible, and if we could observe completely every person involved, the epidemiologic estimates describing the disease would be consistent. Lack of consistency is an indicator for possible measurement error. Methods: We examined the consistency of estimates of incidence, prevalence, and excess mortality of dementia from the Rotterdam Study. We used the incidence and excess mortality estimates to calculate with a mathematical disease model a predicted prevalence, and compared the predicted to the observed prevalence. Results: Predicted prevalence is in most age groups lower than observed, and the difference between them is significant for some age groups. Conclusions: The observed discrepancy could be due to overestimates of prevalence or excess mortality, or an underestimate of incidence, or a combination of all three. We conclude from an analysis of possible causes that it is not possible to say which contributes most to the discrepancy. Estimating dementia incidence in an aging cohort presents a dilemma: with a short follow-up border-line incident cases are easily missed, and with longer follow-up measurement problems increase due to the associated aging of the cohort. Checking for consistency is a useful strategy to signal possible measurement error, but some sources of error may be impossible to avoid.

A self-similar array model of single-walled carbon nanotubes

To describe single-walled carbon nanotube (SWNT) arrays, we propose a self-similar array model. For isolated SWNT bundles, the self-similar array model is consistent with the classical triangular array model; for SWNT bundle arrays, it can present hierarchy structures and specify different array configurations. Based on this self-similar array model, we calculated the energetics of SWNT arrays, investigated the driving force for the formation of macroscopic SWNT arrays, and briefly discussed the hierarchy structures in real macroscopic SWNT arrays. (c) 2005 American Institute of Physics.

The return to schooling: Estimates from a sample of young Australian twins

This study uses a sample of young Australian twins to examine whether the findings reported in [Ashenfelter, Orley and Krueger, Alan, (1994). 'Estimates of the Economic Return to Schooling from a New Sample of Twins', American Economic Review, Vol. 84, No. 5, pp.1157-73] and [Miller, P.W., Mulvey, C and Martin, N., (1994). 'What Do Twins Studies Tell Us About the Economic Returns to Education?: A Comparison of Australian and US Findings', Western Australian Labour Market Research Centre Discussion Paper 94/4] are robust to choice of sample and dependent variable. The economic return to schooling in Australia is between 5 and 7 percent when account is taken of genetic and family effects using either fixed-effects models or the selection effects model of Ashenfelter and Krueger. Given the similarity of the findings in this and in related studies, it would appear that the models applied by [Ashenfelter, Orley and Krueger, Alan, (1994). 'Estimates of the Economic Return to Schooling from a New Sample of Twins', American Economic Review, Vol. 84, No. 5, pp. 1157-73] are robust. Moreover, viewing the OLS and IV estimators as lower and upper bounds in the manner of [Black, Dan A., Berger, Mark C., and Scott, Frank C., (2000). 'Bounding Parameter Estimates with Nonclassical Measurement Error', Journal of the American Statistical Association, Vol. 95, No.451, pp.739-748], it is shown that the bounds on the return to schooling in Australia are much tighter than in [Ashenfelter, Orley and Krueger, Alan, (1994). 'Estimates of the Economic Return to Schooling from a New Sample of Twins', American Economic Review, Vol. 84, No. 5, pp. 1157-73], and the return is bounded at a much lower level than in the US. (c) 2005 Elsevier B.V. All rights reserved.

GESTÃO DO CONHECIMENTO: UM ESTUDO SOBRE A RELAÇÃO ENTRE A LIDERANÇA TRANSFORMACIONAL, A CONVERSÃO DO CONHECIMENTO E A EFICÁCIA ORGANIZACIONAL

Este estudo teve como objetivo principal analisar a relação entre a Liderança Transformacional, a Conversão do Conhecimento e a Eficácia Organizacional. Foram considerados como pressupostos teóricos conceitos consolidados sobre os temas desta relação, além de recentes pesquisas já realizadas em outros países e contextos organizacionais. Com base nisto identificou-se potencial estudo de um modelo que relacionasse estes três conceitos. Para tal considera-se que as organizações que buscam atingir Vantagem Competitiva e incorporam a Knowledge-Based View possam conquistar diferenciação frente a seus concorrentes. Nesse contexto o conhecimento ganha maior destaque e papel protagonista nestas organizações. Dessa forma criar conhecimento através de seus colaboradores, passa a ser um dos desafios dessas organizações ao passo que sugere melhoria de seus indicadores Econômicos, Sociais, Sistêmicos e Políticos, o que se define por Eficácia Organizacional. Portanto os modos de conversão do conhecimento nas organizações, demonstram relevância, uma vez que se cria e se converte conhecimentos através da interação entre o conhecimento existente de seus colaboradores. Essa conversão do conhecimento ou modelo SECI possui quatro modos que são a Socialização, Externalização, Combinação e Internalização. Nessa perspectiva a liderança nas organizações apresenta-se como um elemento capaz de influenciar seus colaboradores, propiciando maior dinâmica ao modelo SECI de conversão do conhecimento. Se identifica então na liderança do tipo Transformacional, características que possam influenciar colaboradores e entende-se que esta relação entre a Liderança Transformacional e a Conversão do Conhecimento possa ter influência positiva nos indicadores da Eficácia Organizacional. Dessa forma esta pesquisa buscou analisar um modelo que explorasse essa relação entre a liderança do tipo Transformacional, a Conversão do Conhecimento (SECI) e a Eficácia Organizacional. Esta pesquisa teve o caráter quantitativo com coleta de dados através do método survey, obtendo um total de 230 respondentes válidos de diferentes organizações. O instrumento de coleta de dados foi composto por afirmativas relativas ao modelo de relação pesquisado com um total de 44 itens. O perfil de respondentes concentrou-se entre 30 e 39 anos de idade, com a predominância de organizações privadas e de departamentos de TI/Telecom, Docência e Recursos Humanos respectivamente. O tratamento dos dados foi através da Análise Fatorial Exploratória e Modelagem de Equações Estruturais via Partial Least Square Path Modeling (PLS-PM). Como resultado da análise desta pesquisa, as hipóteses puderam ser confirmadas, concluindo que a Liderança Transformacional apresenta influência positiva nos modos de Conversão do Conhecimento e que; a Conversão do Conhecimento influencia positivamente na Eficácia Organizacional. Ainda, concluiu-se que a percepção entre os respondentes não apresenta resultado diferente sobre o modelo desta pesquisa entre quem possui ou não função de liderança.

Data analysis methods in optometry. Part 5: correlation

1. Pearson's correlation coefficient only tests whether the data fit a linear model. With large numbers of observations, quite small values of r become significant and the X variable may only account for a minute proportion of the variance in Y. Hence, the value of r squared should always be calculated and included in a discussion of the significance of r. 2. The use of r assumes that a bivariate normal distribution is present and this assumption should be examined prior to the study. If Pearson's r is not appropriate, then a non-parametric correlation coefficient such as Spearman's rs may be used. 3. A significant correlation should not be interpreted as indicating causation especially in observational studies in which there is a high probability that the two variables are correlated because of their mutual correlations with other variables. 4. In studies of measurement error, there are problems in using r as a test of reliability and the ‘intra-class correlation coefficient’ should be used as an alternative. A correlation test provides only limited information as to the relationship between two variables. Fitting a regression line to the data using the method known as ‘least square’ provides much more information and the methods of regression and their application in optometry will be discussed in the next article.

EPQ Model with Imperfect Quality Raw Material

MSC 2010: 26A33, 33E12, 33C60, 44A20

Assembly accuracy analysis for small components with a planar surface in large-scale metrology

Large-scale mechanical products, such as aircraft and rockets, consist of large numbers of small components, which introduce additional difficulty for assembly accuracy and error estimation. Planar surfaces as key product characteristics are usually utilised for positioning small components in the assembly process. This paper focuses on assembly accuracy analysis of small components with planar surfaces in large-scale volume products. To evaluate the accuracy of the assembly system, an error propagation model for measurement error and fixture error is proposed, based on the assumption that all errors are normally distributed. In this model, the general coordinate vector is adopted to represent the position of the components. The error transmission functions are simplified into a linear model, and the coordinates of the reference points are composed by theoretical value and random error. The installation of a Head-Up Display is taken as an example to analyse the assembly error of small components based on the propagation model. The result shows that the final coordination accuracy is mainly determined by measurement error of the planar surface in small components. To reduce the uncertainty of the plane measurement, an evaluation index of measurement strategy is presented. This index reflects the distribution of the sampling point set and can be calculated by an inertia moment matrix. Finally, a practical application is introduced for validating the evaluation index.