A control chart based on sample ranges for monitoring the covariance matrix of the multivariate processes

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

The Synthetic Control Chart Based on Two Sample Variances for Monitoring the Covariance Matrix

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Bayesian estimation of generalized exponential distribution under noninformative priors

The generalized exponential distribution, proposed by Gupta and Kundu (1999), is a good alternative to standard lifetime distributions as exponential, Weibull or gamma. Several authors have considered the problem of Bayesian estimation of the parameters of generalized exponential distribution, assuming independent gamma priors and other informative priors. In this paper, we consider a Bayesian analysis of the generalized exponential distribution by assuming the conventional non-informative prior distributions, as Jeffreys and reference prior, to estimate the parameters. These priors are compared with independent gamma priors for both parameters. The comparison is carried out by examining the frequentist coverage probabilities of Bayesian credible intervals. We shown that maximal data information prior implies in an improper posterior distribution for the parameters of a generalized exponential distribution. It is also shown that the choice of a parameter of interest is very important for the reference prior. The different choices lead to different reference priors in this case. Numerical inference is illustrated for the parameters by considering data set of different sizes and using MCMC (Markov Chain Monte Carlo) methods.

A new sampling strategy for the Shewhart control chart monitoring a process with wandering mean

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Theoretical estimation of optical absorption and photoluminescence in nanostructured silicon; an approach to improve efficiency in nanostructured solar cells

Renewable energy is growing in demand, and thus the the manufacture of solar cells and photovoltaic arrays has advanced dramatically in recent years. This is proved by the fact that the photovoltaic production has doubled every 2 years, increasing by an average of 48% each year since 2002. Covering the general overview of solar cell working, and its model, this thesis will start with the three generations of photovoltaic solar cell technology, and move to the motivation of dedicating research to nanostructured solar cell. For the current generation solar cells, among several factors, like photon capture, photon reflection, carrier generation by photons, carrier transport and collection, the efficiency also depends on the absorption of photons. The absorption coefficient,α, and its dependence on the wavelength, λ, is of major concern to improve the efficiency. Nano-silicon structures (quantum wells and quantum dots) have a unique advantage compared to bulk and thin film crystalline silicon that multiple direct and indirect band gaps can be realized by appropriate size control of the quantum wells. This enables multiple wavelength photons of the solar spectrum to be absorbed efficiently. There is limited research on the calculation of absorption coefficient in nano structures of silicon. We present a theoretical approach to calculate the absorption coefficient using quantum mechanical calculations on the interaction of photons with the electrons of the valence band. One model is that the oscillator strength of the direct optical transitions is enhanced by the quantumconfinement effect in Si nanocrystallites. These kinds of quantum wells can be realized in practice in porous silicon. The absorption coefficient shows a peak of 64638.2 cm-1 at = 343 nm at photon energy of ξ = 3.49 eV ( = 355.532 nm). I have shown that a large value of absorption coefficient α comparable to that of bulk silicon is possible in silicon QDs because of carrier confinement. Our results have shown that we can enhance the absorption coefficient by an order of 10, and at the same time a nearly constant absorption coefficient curve over the visible spectrum. The validity of plots is verified by the correlation with experimental photoluminescence plots. A very generic comparison for the efficiency of p-i-n junction solar cell is given for a cell incorporating QDs and sans QDs. The design and fabrication technique is discussed in brief. I have shown that by using QDs in the intrinsic region of a cell, we can improve the efficiency by a factor of 1.865 times. Thus for a solar cell of efficiency of 26% for first generation solar cell, we can improve the efficiency to nearly 48.5% on using QDs.

Bayesian estimation of multilevel item response model with missing data

This study proposed a novel statistical method that modeled the multiple outcomes and missing data process jointly using item response theory. This method follows the "intent-to-treat" principle in clinical trials and accounts for the correlation between outcomes and missing data process. This method may provide a good solution to chronic mental disorder study. ^ The simulation study demonstrated that if the true model is the proposed model with moderate or strong correlation, ignoring the within correlation may lead to overestimate of the treatment effect and result in more type I error than specified level. Even if the within correlation is small, the performance of proposed model is as good as naïve response model. Thus, the proposed model is robust for different correlation settings if the data is generated by the proposed model.^

A Note on Bayesian Estimation for the Negative-Binomial Model

2000 Mathematics Subject Classification: 62F15.

The role of parametric assumptions in adaptive Bayesian estimation.

Variants of adaptive Bayesian procedures for estimating the 5% point on a psychometric function were studied by simulation. Bias and standard error were the criteria to evaluate performance. The results indicated a superiority of (a) uniform priors, (b) model likelihood functions that are odd symmetric about threshold and that have parameter values larger than their counterparts in the psychometric function, (c) stimulus placement at the prior mean, and (d) estimates defined as the posterior mean. Unbiasedness arises in only 10 trials, and 20 trials ensure constant standard errors. The standard error of the estimates equals 0.617 times the inverse of the square root of the number of trials. Other variants yielded bias and larger standard errors.

Bayesian estimation in generalized autoregressive conditional heteroskedasticity models

Esta tesis doctoral nace con el propósito de entender, analizar y sobre todo modelizar el comportamiento estadístico de las series financieras. En este sentido, se puede afirmar que los modelos que mejor recogen las especiales características de estas series son los modelos de heterocedasticidad condicionada en tiempo discreto,si los intervalos de tiempo en los que se recogen los datos lo permiten, y en tiempo continuo si tenemos datos diarios o datos intradía. Con esta finalidad, en esta tesis se proponen distintos estimadores bayesianos para la estimación de los parámetros de los modelos GARCH en tiempo discreto (Bollerslev (1986)) y COGARCH en tiempo continuo (Kluppelberg et al. (2004)). En el capítulo 1 se introducen las características de las series financieras y se presentan los modelos ARCH, GARCH y COGARCH, así como sus principales propiedades. Mandelbrot (1963) destacó que las series financieras no presentan estacionariedad y que sus incrementos no presentan autocorrelación, aunque sus cuadrados sí están correlacionados. Señaló también que la volatilidad que presentan no es constante y que aparecen clusters de volatilidad. Observó la falta de normalidad de las series financieras, debida principalmente a su comportamiento leptocúrtico, y también destacó los efectos estacionales que presentan las series, analizando como se ven afectadas por la época del año o el día de la semana. Posteriormente Black (1976) completó la lista de características especiales incluyendo los denominados leverage effects relacionados con como las fluctuaciones positivas y negativas de los precios de los activos afectan a la volatilidad de las series de forma distinta.

Essays in Empirical Operations Management: Bayesian Learning of Service Quality and Structural Estimation of Complementary Product Pricing and Inventory Management

This dissertation contributes to the rapidly growing empirical research area in the field of operations management. It contains two essays, tackling two different sets of operations management questions which are motivated by and built on field data sets from two very different industries --- air cargo logistics and retailing.

The first essay, based on the data set obtained from a world leading third-party logistics company, develops a novel and general Bayesian hierarchical learning framework for estimating customers' spillover learning, that is, customers' learning about the quality of a service (or product) from their previous experiences with similar yet not identical services. We then apply our model to the data set to study how customers' experiences from shipping on a particular route affect their future decisions about shipping not only on that route, but also on other routes serviced by the same logistics company. We find that customers indeed borrow experiences from similar but different services to update their quality beliefs that determine future purchase decisions. Also, service quality beliefs have a significant impact on their future purchasing decisions. Moreover, customers are risk averse; they are averse to not only experience variability but also belief uncertainty (i.e., customer's uncertainty about their beliefs). Finally, belief uncertainty affects customers' utilities more compared to experience variability.

The second essay is based on a data set obtained from a large Chinese supermarket chain, which contains sales as well as both wholesale and retail prices of un-packaged perishable vegetables. Recognizing the special characteristics of this particularly product category, we develop a structural estimation model in a discrete-continuous choice model framework. Building on this framework, we then study an optimization model for joint pricing and inventory management strategies of multiple products, which aims at improving the company's profit from direct sales and at the same time reducing food waste and thus improving social welfare.

Collectively, the studies in this dissertation provide useful modeling ideas, decision tools, insights, and guidance for firms to utilize vast sales and operations data to devise more effective business strategies.

Bayesian Estimation of Small Proportions Using Binomial Group Test

Group testing has long been considered as a safe and sensible relative to one-at-a-time testing in applications where the prevalence rate p is small. In this thesis, we applied Bayes approach to estimate p using Beta-type prior distribution. First, we showed two Bayes estimators of p from prior on p derived from two different loss functions. Second, we presented two more Bayes estimators of p from prior on π according to two loss functions. We also displayed credible and HPD interval for p. In addition, we did intensive numerical studies. All results showed that the Bayes estimator was preferred over the usual maximum likelihood estimator (MLE) for small p. We also presented the optimal β for different p, m, and k.

Accuracy of working length determination using 3 electronic apex locators and direct digital radiography

Objectives. The objectives of this study were to assess the accuracy of working length determination using 3 electronic apex locators and direct digital radiography and to compare the results with those obtained using the visual method (control measurement). Study design. Twenty extracted human maxillary premolars were selected: 17 two-rooted and 3 single-rooted (total of 37 canals). Working length was measured using electronic apex locators Elements Diagnostic, Root ZX, and Just II. Subsequently, teeth were positioned in the alveolar bone of a dry skull and submitted to direct digital radiography. A variation of +/- 1 mm was considered as acceptable. Results were analyzed using the Wilcoxon and the chi(2) tests. Results. Results presented an accuracy of 94.6% for Elements Diagnostic, 91.9% for Root ZX, 73.0% for Just II, and 64.9% for direct digital radiography when considering the margin of +/- 1 mm in relation to the control measurement. Comparisons with the actual control measurements resulted in accuracy results of 13.51%, 13.51%, 10.10%, and 2.70%, respectively. Conclusions. Root ZX and Elements Diagnostic are more accurate in determining working length when compared with Just II and Schick direct digital radiography. (Oral Surg Oral Med Oral Pathol Oral Radiol Endod 2011;111:e44-e49)

Avaliação do desempenho da carta CUSCORE: estudo comparativo com a estatística CUSUM

A evolução da qualidade tem sido fundamental na monitorização de processos produtivos, quer de produtos ou de serviços, e é um conceito que está cada vez mais presente nas organizações. Actualmente existem diversas metodologias que auxiliam e contribuem para o alcance da qualidade, sendo o controlo estatístico do processo uma das que mais se destaca em contexto industrial, representada pela aplicação das cartas de controlo. As cartas de controlo são ferramentas que têm cativado o interesse das organizações que se dedicam a processos industriais modernos. No entanto, existem alguns factores, nomeadamente, a auto-correlação de dados (ocorre quando, num dado instante, uma observação depende de outras ocorridas em instantes antecedentes), que dificultam a interpretação sobre a estabilidade do processo ao nível estatístico. Neste sentido, a presente dissertação tem como objectivo apresentar um estudo comparativo entre o desempenho da carta