Control charts for the shape parameter of reflected power function distribution under classical estimators

The reflected power function distribution (RPFD) has applications in the fields of reliability engineering and survival analysis. To identify and remove the variation in different reliability processes and also to monitor the reliability of machines where the number of errors follows RPFD, we develop control charts to keep the process in control. A memory less control chart like a Shewhart control chart, and two memory-based control charts like an exponentially weighted moving average (EWMA) control chart and a hybrid exponentially weighted moving average (HEWMA) control chart are discussed and compared with each other. Proposal of these control charts is based on two different estimators, the percentile estimator (PE) and the modified maximum likelihood estimator (MMLE). This study shows that an HEWMA control chart based on PE performs better than PE-based Shewhart and EWMA control charts, as well as MMLE-based Shewhart, EWMA, and HEWMA control charts.     

The modified control charts for monitoring the shape parameter of weighted power function distribution under classical estimator

Zaka et al provided a new distribution called the Weighted Power function distribution (WPFD), which has application in reliability engineering and survival analysis. They used different estimation methods to estimate the unknown parameters of WPFD and proved that modified maximum likelihood estimator (MMLE) is best to consider for the estimation of parameters. We have constructed the memoryless and memory-based control charts based on the assumption that the distribution of the underlying process does not follow the normal distribution. In this paper, we provide modified control charts using MMLE of the shape parameter for WPFD. We develop control charts to keep the process in control when the distribution of errors of underlying process follows WPFD. We propose the modified memoryless control chart, that is, Shewhart control chart and modified memory-based control chart, that is, Exponentially weighted moving average (EWMA) and Hybrid exponentially weighted moving average (HEWMA) control charts. We have made the comparison of the proposed control charts using Monte Carlo simulation and the real-life application for both and the memoryless control charts and memory-based control charts. We see that HEWMA based on MMLE performs better as compared to other proposed control charts.     

Estimation of distribution function and distribution parameter from incomplete data

In this paper, in order to estimate the distribution parameter from incomplete data, a method based on Marquardt's least squares method used to estimate nonlinear parameters is proposed. Using the Euclid distance and the principle of nearness of fuzzy set theory, the hypothesis concerning the distribution function of a parent population is tested in the incomplete data case.     

Alternative Bayes factors: Sample size determination and discriminatory power assessment

Alternative Bayes factors are families of methods used for hypothesis testing and model selection when sensitivity to priors is a concern and also when prior information is weak or lacking. This paper deals with two related problems that arise in the practical use of these model choice criteria: sample size determination and evaluation of discriminatory power. We propose a pre-experimental approach to cope with both these issues. Specifically, extending the evidential approach of Royall (J Am Stat Assoc 95(451):760–780, 2000) and following De Santis (J Stat Plan Inference 124(1):121–144, 2004), we propose a criterion for sample size choice based on the predictive probability of observing decisive and correct evidence. The basic idea is to select the minimal sample size that guarantees a sufficiently high pre-experimental probability that an alternative Bayes factor provides strong evidence in favor of the true hypothesis. It is also argued that a predictive analysis is a natural approach to the measurement of discriminatory power of alternative Bayes factors. The necessity of measuring discrimination ability depends on the fact that alternative Bayes factors are, in general, less sensitive to prior specifications than ordinary Bayes factors and that this gain in robustness corresponds to a reduced discriminative power. Finally, implementation of the predictive approach with improper priors is discussed and possible strategies are proposed.      

Optimal cluster selection probabilities to estimate the finite population distribution function under PPS cluster sampling

The estimation of the finite population distribution function under several sampling strategies based on a PPS cluster sampling, i.e., with cluster selection probabilities proportional to size, is studied. For the estimation of population means and totals, it is well-known that this type of strategies gives good results if the cluster selection probabilities are proportional to the total of the variable under study or to a related auxiliary variable over the cluster. It is proved that, for the estimation of the distribution function using cluster sampling, this solution is not good in general and, under an appropriate criteria, the optimal cluster selection probabilities that minimize the variance of the estimation, is obtained. This methodology is applied to two classical PPS sampling strategies: sampling with replacement, with the Hansen-Hurwitz estimator, and random groups sampling with the Rao-Hartley-Cochran estimator. Finally a small simulation to compare the efficiency of this approach with other methods is presented.     

Suggested parameter to estimate the region probed by photons in laser-based measurements

Abstract

In many biomedical applications of laser radiation to estimate optical parameters in tissue, it is desirable, if not crucial, to describe the region being probed. We suggest a parameter for this purpose, based on a lattice random walk on a simple cubic lattice. It is the expected number of distinct sites visited by a random walker. This is relatively easy to compute, although higher moments are not. Detailed computations are given for a continuous-wave measurement on a semi-infinite medium bounded by an absorbing plane and for a slab geometry required to analyse transillumination experiments.     

Blurring of island size distribution function in theory of nucleation

Numerical solutions of the kinetic equation of the theory of nucleation at a constant pumping of monomers are obtained in the case of two-dimensional islands growing in a ballistic or diffusion regime on a solid surface. The island size distributions obtained in various approximations are compared. It is shown that, even in the absence of Ostwald’s ripening, an increase in the critical size leads to a radical increase in the variance, which is not taken into account in the overwhelming majority of analytical models. The blurring of the distribution as a result of an increase in the critical nucleus size almost does not influence the temporal asymptotics of the mean nucleus size. The effect of blurring is much more pronounced in the ballistic growth regime. The obtained results suggest that it is necessary to improve analytical models for determining the shape of the distribution in the growth stage for various condensing systems.

     

Hydrothermal degradation of polysaccharides in a semi-batch reactor: product distribution as a function of severity parameter

The naturally occurring polysaccharides, starch and pectic acid, were hydrothermally degraded in a semi-batch reactor coupled with a plug-flow reactor (PFR) to produce valuable chemicals including mono- and oligosaccharides over a temperature range from 160 to 240 °C at 10 MPa. The solid polysaccharide samples were solubilized in a semi-batch reactor, and the water-soluble (WS) components instantly entered the PFR in which further degradation took place. The reaction temperature and/or residence time in the PFR significantly affected the yields of oligosaccharides, monosaccharides and secondary decomposition products, and also the average molecular weight of WS components. The product distributions were expressed with severity, which combines the effects of temperature and time on the progress of the reaction, as a single reaction parameter. Using this parameter, it was found that similar product distributions were obtained at equal levels of severity. The severity parameter enabled easy interpretation of the change in product distribution for these reactions.     

Low-temperature thermoelectric power factor enhancement by controlling nanoparticle size distribution

Coherent potential approximation is used to study the effect of adding doped spherical nanoparticles inside a host matrix on the thermoelectric properties. This takes into account electron multiple scatterings that are important in samples with relatively high volume fraction of nanoparticles (>1%). We show that with large fraction of uniform small size nanoparticles (～1 nm), the power factor can be enhanced significantly. The improvement could be large (up to 450% for GaAs) especially at low temperatures when the mobility is limited by impurity or nanoparticle scattering. The advantage of doping via embedded nanoparticles compared to the conventional shallow impurities is quantified. At the optimum thermoelectric power factor, the electrical conductivity of the nanoparticle-doped material is larger than that of impurity-doped one at the studied temperature range (50-500 K) whereas the Seebeck coefficient of the nanoparticle doped material is enhanced only at low temperatures (～50 K).     

The distribution of water in degrading polyglycolide. Part I: Sample size and drug release

The effect of sample thickness on the degradation of polyglycolide (PGA) disks and on their drug release profiles is explored in this paper, and conclusions drawn about the distribution of water across a sample during degradation. The degradation process was monitored by measuring changes in the long period calculated from small angle X-ray scattering profiles, and by following changes in the pH of the buffer solutions. Drug release profiles were obtained using UV-spectrophotometry. The measurements suggest that reaction-erosion fronts form at the surface of all samples after around 7 days of degradation, and that these fronts progress through the sample at a constant rate of 0.032 mm/day. The data are consistent with a model in which drug is released quickly from the porous, hydrated regions behind the front, and reaches 100% release when the fronts meet. ©2003 Kluwer Academic Publisher     

Application of the parameter plane method to the design of a digital power system stabilizer

Abstract

Stabilization of electric power systems is examined in this paper using a digital proportional‐plus‐integral (PI) stabilizer. Parameter‐plane method is proposed for the determination of the optimal gains for the PI stabilizer. For the purposes of comparison, the least‐square‐error approach is also presented for the design of a digital PI stabilizer. The effectiveness of the proposed PI stabilizer is illustrated by the digital simulation of a single‐machine‐infinite‐bus system. It is found that the proposed stabilizer can be employed as an effective means of improving the dynamic stability of the power system.     

Bayesian approach to parameter estimation of the generalized pareto distribution

Several methods have been used for estimating the parameters of the generalized Pareto distribution (GPD), namely maximum likelihood (ML), the method of moments (MOM) and the probability-weighted moments (PWM). It is known that for these estimators to exist, certain constraints have to be imposed on the range of the shape parameter,k, of the GPD. For instance, PWM and ML estimators only exist fork>−0.5 andk≤1, respectively. Moreover, and particularly for small sample sizes, the most efficient method to apply in any practical situation highly depends on a previous knowledge of the most likely values ofk. This clearly suggests the use of Bayesian techniques as a way of using prior information onk. In the present work, we address the issue of estimating the parameters of the GPD from a Bayesian point of view. The proposed approach is compared via a simulation study with ML, PWM and also with the elemental percentile method (EPM) which was developed by Castillo and Hadi (1997). The estimation procedure is then applied to two real data sets.     

Deriving an estimate for the Fried parameter in mobile optical transmission scenarios

Measuring the Fried parameter r(0) (atmospheric optical coherence length) in optical link scenarios is crucial to estimate a receiver's telescope performance or to dimension atmospheric mitigation techniques, such as in adaptive optics. The task of measuring r(0) is aggravated in mobile scenarios, when the receiver itself is prone to mechanical vibrations (e.g., when mounted on a moving platform) or when the receiver telescope has to track a fast-moving signal source, such as, in our case, a laser transmitter on board a satellite or aircraft. We have derived a method for estimating r(0) that avoids the influence of angle-of-arrival errors by only using short-term tilt-removed focal intensity speckle patterns.     

Oxide particle size distribution function in combustion of aluminum: Quasi-steady approximation

The size distribution function for oxide particles formed in combustion of aluminum is calculated in a quasi-steady approximation. It is demonstrated that the quasi-steady approximation may be employed for aluminum particles sized 15 to 300 μm. It is observed that the conditions of combustion (temperature, pressure, oxidizer content, and size of aluminum powder particles) have a weak effect on the parameters of distribution function. The results of calculations of the parameters of oxide particles formed as a result of combustion of aluminum powder are compared with the parameters of particles formed after explosion of an explosive containing aluminum powder.     

A study to estimate crack length using the separability parameter Spb in steels

The separability property with S_pb parameter was used in this work to estimate the instantaneous crack length in pre-cracked specimens. A test matrix, pre-cracked ASTM C(T), SE(B) specimens and non-standard A(B) arc-shaped geometry was prepared. Materials were ASTM 387-Gr.22 2.25Cr-1.0Mo steel, an API Gr.N80 and HSLA welded joints. Initial and final crack lengths were measured on the crack surface and instantaneous crack length was determined by the compliance method to compare against the values of crack length estimated using the S_pb parameter. The difference between the resulting values was less than 15%Δa suggested as reference in ASTM E1820-96.     

Particle size distribution in a coagulating dusty plasma

A modified version of the classical coagulation theory in the diffusion approximation is used to study some anomalies in the behavior of the particle size distribution function. It is established that unlike a normal aerosol, in a dusty plasma the dispersion of the distribution and the average particle size may decrease with time. Pis’ma Zh. Tekh. Fiz. 25, 89–95 (August 12, 1999)     

Sample size bounding and context ranking as approaches to the HRA data problem

This paper presents a technique denoted as sub sample size bounding (SSSB) useable for the statistical derivation of context-specific probabilities from data available in existing reports on operating experience. Applications for human reliability analysis (HRA) are emphasized in the presentation of the technique. Exemplified by a sample of 180 abnormal event sequences, it is outlined how SSSB can provide viable input for the quantification of errors of commission (EOCs).