Abstract: This work investigates a mathematical study for traffic flow and traffic density in Kigali city roads and the data collected from the national police of Rwanda in 2012. While working on this topic, some mathematical models were used in order to analyze and compare traffic variables. This work has been carried out on Kigali roads specifically at roundabouts from Kigali Business Center (KBC) to Prince House as our study sites. In this project, we used some mathematical tools to analyze the data collected and to understand the relationship between traffic variables. We applied the Poisson distribution method to analyze and to know the number of accidents occurred in this section of the road which is from KBC to Prince House. The results show that the accidents that occurred in 2012 were at very high rates due to the fact that this section has a very narrow single lane on each side which leads to high congestion of vehicles, and consequently, accidents occur very frequently. Using the data of speeds and densities collected from this section of road, we found that the increment of the density results in a decrement of the speed of the vehicle. At the point where the density is equal to the jam density the speed becomes zero. The approach is promising in capturing sudden changes on flow patterns and is open to be utilized in a series of intelligent management strategies and especially in noncurrent congestion effect detection and control.
Abstract: Banda Sea Collision Zone (BSCZ) is the result of the
interaction and convergence of Indo-Australian plate, Eurasian plate
and Pacific plate. This location is located in eastern Indonesia. This
zone has a very high seismic activity. In this research, we will
calculate the rate (λ) and Mean Square Error (MSE). By this result,
we will classification earthquakes distribution in the BSCZ with the
point process approach. Chi-square is used to determine the type of
earthquakes distribution in the sub region of BSCZ. The data used in
this research is data of earthquakes with a magnitude ≥ 6 SR for the
period 1964-2013 and sourced from BMKG Jakarta. This research is
expected to contribute to the Moluccas Province and surrounding
local governments in performing spatial plan document related to
disaster management.
Abstract: Industries using conventional fossil fuels have an
interest in better understanding the mechanism of particulate
formation during combustion since such is responsible for emission
of undesired inorganic elements that directly impact the atmospheric
pollution level. Fine and ultrafine particulates have tendency to
escape the flue gas cleaning devices to the atmosphere. They also
preferentially collect on surfaces in power systems resulting in
ascending in corrosion inclination, descending in the heat transfer
thermal unit, and severe impact on human health. This adverseness
manifests particularly in the regions of world where coal is the
dominated source of energy for consumption.
This study highlights the behavior of calcium transformation as
mineral grains verses organically associated inorganic components
during pulverized coal combustion. The influence of existing type of
calcium on the coarse, fine and ultrafine mode formation mechanisms
is also presented. The impact of two sub-bituminous coals on particle
size and calcium composition evolution during combustion is to be
assessed. Three mixed blends named Blends 1, 2, and 3 are selected
according to the ration of coal A to coal B by weight. Calcium
percentage in original coal increases as going from Blend 1 to 3.
A mathematical model and a new approach of describing
constituent distribution are proposed. Analysis of experiments of
calcium distribution in ash is also modeled using Poisson distribution.
A novel parameter, called elemental index λ, is introduced as a
measuring factor of element distribution.
Results show that calcium in ash that originally in coal as mineral
grains has index of 17, whereas organically associated calcium
transformed to fly ash shown to be best described when elemental
index λ is 7.
As an alkaline-earth element, calcium is considered the
fundamental element responsible for boiler deficiency since it is the
major player in the mechanism of ash slagging process. The
mechanism of particle size distribution and mineral species of ash
particles are presented using CCSEM and size-segregated ash
characteristics. Conclusions are drawn from the analysis of
pulverized coal ash generated from a utility-scale boiler.
Abstract: This purpose of this paper is to present the acceptance single sampling plan when the fraction of nonconforming items is a fuzzy number and being modeled based on the fuzzy Poisson distribution. We have shown that the operating characteristic (oc) curves of the plan is like a band having a high and low bounds whose width depends on the ambiguity proportion parameter in the lot when that sample size and acceptance numbers is fixed. Finally we completed discuss opinion by a numerical example. And then we compared the oc bands of using of binomial with the oc bands of using of Poisson distribution.
Abstract: Using a set of confidence intervals, we develop a
common approach, to construct a fuzzy set as an estimator for
unknown parameters in statistical models. We investigate a method
to derive the explicit and unique membership function of such fuzzy
estimators. The proposed method has been used to derive the fuzzy
estimators of the parameters of a Normal distribution and some
functions of parameters of two Normal distributions, as well as the
parameters of the Exponential and Poisson distributions.
Abstract: This paper developed the c-Chart based on a Zero- Inflated Poisson (ZIP) processes that approximated by a geometric distribution with parameter p. The p estimated that fit for ZIP distribution used in calculated the mean, median, and variance of geometric distribution for constructed the c-Chart by three difference methods. For cg-Chart, developed c-Chart by used the mean and variance of the geometric distribution constructed control limits. For cmg-Chart, the mean used for constructed the control limits. The cme- Chart, developed control limits of c-Chart from median and variance values of geometric distribution. The performance of charts considered from the Average Run Length and Average Coverage Probability. We found that for an in-control process, the cg-Chart is superior for low level of mean at all level of proportion zero. For an out-of-control process, the cmg-Chart and cme-Chart are the best for mean = 2, 3 and 4 at all level of parameter.
Abstract: Com Poisson distribution is capable of modeling the count responses irrespective of their mean variance relation and the parameters of this distribution when fitted to a simple cross sectional data can be efficiently estimated using maximum likelihood (ML) method. In the regression setup, however, ML estimation of the parameters of the Com Poisson based generalized linear model is computationally intensive. In this paper, we propose to use quasilikelihood (QL) approach to estimate the effect of the covariates on the Com Poisson counts and investigate the performance of this method with respect to the ML method. QL estimates are consistent and almost as efficient as ML estimates. The simulation studies show that the efficiency loss in the estimation of all the parameters using QL approach as compared to ML approach is quite negligible, whereas QL approach is lesser involving than ML approach.
Abstract: “Dengue" is an African word meaning “bone
breaking" because it causes severe joint and muscle pain that feels
like bones are breaking. It is an infectious disease mainly transmitted
by female mosquito, Aedes aegypti, and causes four serotypes of
dengue viruses. In recent years, a dramatic increase in the dengue
fever confirmed cases around the equator-s belt has been reported.
Several conventional indices have been designed so far to monitor the
transmitting vector populations known as House Index (HI),
Container Index (CI), Breteau Index (BI). However, none of them
describes the adult mosquito population size which is important to
direct and guide comprehensive control strategy operations since
number of infected people has a direct relationship with the vector
density. Therefore, it is crucial to know the population size of the
transmitting vector in order to design a suitable and effective control
program. In this context, a study is carried out to report a new
statistical index, ABURAS Index, using Poisson distribution based
on the collection of vector population in Jeddah Governorate, Saudi Arabia.
Abstract: The objective of this paper is to present explicit analytical formulas for evaluating important characteristics of Double Moving Average control chart (DMA) for Poisson distribution. The most popular characteristics of a control chart are Average Run Length ( 0 ARL ) - the mean of observations that are taken before a system is signaled to be out-of control when it is actually still incontrol, and Average Delay time ( 1 ARL ) - mean delay of true alarm times. An important property required of 0 ARL is that it should be sufficiently large when the process is in-control to reduce a number of false alarms. On the other side, if the process is actually out-ofcontrol then 1 ARL should be as small as possible. In particular, the explicit analytical formulas for evaluating 0 ARL and 1 ARL be able to get a set of optimal parameters which depend on a width of the moving average ( w ) and width of control limit ( H ) for designing DMA chart with minimum of 1 ARL
Abstract: In this paper, at first we explain about negative
hypergeometric distribution and its properties. Then we use the w-function
and the Stein identity to give a result on the poisson
approximation to the negative hypergeometric distribution in terms of the total variation distance between the negative hypergeometric and
poisson distributions and its upper bound.
Abstract: In this paper, we apply and compare two generalized estimating equation approaches to the analysis of car breakdowns data in Mauritius. Number of breakdowns experienced by a machinery is a highly under-dispersed count random variable and its value can be attributed to the factors related to the mechanical input and output of that machinery. Analyzing such under-dispersed count observation as a function of the explanatory factors has been a challenging problem. In this paper, we aim at estimating the effects of various factors on the number of breakdowns experienced by a passenger car based on a study performed in Mauritius over a year. We remark that the number of passenger car breakdowns is highly under-dispersed. These data are therefore modelled and analyzed using Com-Poisson regression model. We use the two types of quasi-likelihood estimation approaches to estimate the parameters of the model: marginal and joint generalized quasi-likelihood estimating equation approaches. Under-dispersion parameter is estimated to be around 2.14 justifying the appropriateness of Com-Poisson distribution in modelling underdispersed count responses recorded in this study.
Abstract: This research investigates risk factors for defective products in autoparts factories. Under a Bayesian framework, a generalized linear mixed model (GLMM) in which the dependent variable, the number of defective products, has a Poisson distribution is adopted. Its performance is compared with the Poisson GLM under a Bayesian framework. The factors considered are production process, machines, and workers. The products coded RT50 are observed. The study found that the Poisson GLMM is more appropriate than the Poisson GLM. For the production Process factor, the highest risk of producing defective products is Process 1, for the Machine factor, the highest risk is Machine 5, and for the Worker factor, the highest risk is Worker 6.
Abstract: Reconfigurable optical add/drop multiplexers
(ROADMs) can be classified into three categories based on their
underlying switching technologies. Category I consists of a single
large optical switch; category II is composed of a number of small
optical switches aligned in parallel; and category III has a single
optical switch and only one wavelength being added/dropped. In this
paper, to evaluate the wavelength-routing capability of ROADMs of
category-II in dynamic optical networks,the dynamic traffic models
are designed based on Bernoulli, Poisson distributions for smooth
and regular types of traffic. Through Analytical and Simulation
results, the routing power of cat-II of ROADM networks for two
traffic models are determined.
Abstract: Number of breakdowns experienced by a machinery is a highly under-dispersed count random variable and its value can be attributed to the factors related to the mechanical input and output of that machinery. Analyzing such under-dispersed count observations as a function of the explanatory factors has been a challenging problem. In this paper, we aim at estimating the effects of various factors on the number of breakdowns experienced by a passenger car based on a study performed in Mauritius over a year. We remark that the number of passenger car breakdowns is highly under-dispersed. These data are therefore modelled and analyzed using Com-Poisson regression model. We use quasi-likelihood estimation approach to estimate the parameters of the model. Under-dispersion parameter is estimated to be 2.14 justifying the appropriateness of Com-Poisson distribution in modelling under-dispersed count responses recorded in this study.
Abstract: C-control chart assumes that process nonconformities follow a Poisson distribution. In actuality, however, this Poisson distribution does not always occur. A process control for semiconductor based on a Poisson distribution always underestimates the true average amount of nonconformities and the process variance. Quality is described more accurately if a compound Poisson process is used for process control at this time. A cumulative sum (CUSUM) control chart is much better than a C control chart when a small shift will be detected. This study calculates one-sided CUSUM ARLs using a Markov chain approach to construct a CUSUM control chart with an underlying Poisson-Gamma compound distribution for the failure mechanism. Moreover, an actual data set from a wafer plant is used to demonstrate the operation of the proposed model. The results show that a CUSUM control chart realizes significantly better performance than EWMA.