Relative Frequency Histograms Research Articles

Probability distribution functions for the ultimate strength of X-joints with collar plates in compressive load at room and fire conditions

In this paper, the results of performing finite element (FE) analysis on 360 tubular X-joints reinforced with collar plates have been used to propose a probability distribution model for ultimate strength at ambient and fire conditions. As far as the authors know, no study has been conducted on the probability distribution of the ultimate strength in X-joints with collar plates. Consequently, according to the reinforced X-joints, a total of ultimate capacity data sets was generated. The FE models were validated and compared with 35 experimental tests and numerical models. Also, in the present FE models, the welds connecting the plates to the chord member were created. Moreover, the contacts between the outer surfaces of the chord member and the inner surfaces of the reinforcing plates were modeled. In addition, nonlinear material and geometry properties were applied. In the following step, twelve theoretical probability density functions (PDFs) were fitted to relative frequency histograms of five databases. The maximum likelihood method was applied to determine the parameters of each distribution. Investigating the goodness-of-fit according to the Kolmogorov-Smirnov, Anderson Darling, and Chi-square tests showed that the Generalized Petro distribution is the best for the ultimate capacity values in collar plate retrofitted X-joints at ambient and different fire conditions. In the following step, six fully defined theoretical PDFs and cumulative distribution functions (CDFs) were established. Also, probability-probability graphs indicated that the proposed theoretical probability distributions are near the given data sets.

Probability distribution models for the ultimate strength of tubular T/Y-joints reinforced with collar plates at room and different fire conditions

In this research work, the simulation results of 360 T/Y-joints reinforced with collar plates have been used to propose theoretical probability distribution models for the ultimate capacity at ambient and fire conditions. So far, no study has been carried out on the probability distribution of ultimate strength in joints with collar plates at room or elevated temperature. Therefore, according to the reinforced T/Y-joint models, which were verified with 18 tests, a total of ultimate capacity data sets was produced. In the FE models, the welds along the collar/brace intersection and between the chord and collar have been generated. Also, the Augmented Lagrange method was applied as the contact algorithm for solving the contact between the collar and chord. In the next step, 13 theoretical probability density functions (PDFs) were fitted to the relative frequency histograms of the databases. For obtaining the parameters of each distribution, the maximum likelihood (ML) method was utilized. Assessing the goodness-of-fit based on the Kolmogorov-Smirnov and Anderson Darling tests indicated that the Johnson SB distribution is the best for the ultimate capacity values in the T/Y-joints reinforced with collar plates at 20, 400, 600, and 800 °C. But, for the reinforced joints at 200 °C, the Inverse Gaussian (3P) distribution is the best. In the next step, five fully defined theoretical PDFs were proposed for the collar plate reinforced T/Y-joints at room and different high temperatures. Probability difference and probability-probability graphs indicated that the proposed theoretical probability distributions are well near the given data sets.

Probabilistic analysis of the ultimate strength of tubular X-joints stiffened with outer ring at ambient and elevated temperatures

In this research work, the results of performing 540 FE analyses on the tubular X-joints stiffened with external ring at ambient and different high temperatures have been applied to propose probability distribution models for the ultimate capacity. As per the authors’ knowledge, so far, no study has been carried out on the probability distribution of ultimate strength in tubular joints at room or high temperatures. Therefore, according to the stiffened X-joint FE models, a set of ultimate strength sample databases was generated. In the next step, 12 different probability density functions (PDFs) were fitted to the relative frequency histograms of the samples. For determining the parameters of every distribution, the maximum likelihood method was applied. Evaluating the goodness-of-fit according to the Chi-squared and Kolmogorov-Smirnov tests demonstrated that the Generalized extreme value distribution is the finest one for the ultimate strength values in the tubular X-joints stiffened with the external ring at ambient and different elevated temperatures. However, the mean, the standard deviation, and shape parameters of the proposed distributions in the different temperatures are different. In the final step, five fully defined PDFs were proposed for the stiffened joints at room and high temperatures.

Development of a probability distribution model for the SCFs in tubular X-connections retrofitted with FRP

In this study, results of performing 324 FE analyses on 108 circular hollow section (CHS) X-connections with fiber reinforced polymer (FRP) have been used to derive a probability distribution model for SCFs in the retrofitted joints under axial, IPB, and OPB loads. As far as the authors are aware, no study has been conducted on the probability distribution of SCFs in X-connections with FRP. However, the probability distribution models are essential for the reliability-based analysis and design of offshore structures. Therefore, based on the retrofitted X-connection FE models which were verified with several experimental tests, a set of SCF sample databases was generated. In these SCF sample databases, different FRP properties (layer number and material) and connection geometry (β, τ, and γ) are included. 10 various probability density functions (PDFs) were fitted to the relative frequency histograms of the SCF samples. For obtaining the parameters of each distribution, the maximum likelihood method was used. Assessing the goodness-of-fit based on the Chi-squared and Kolmogorov-Smirnov tests shown that the Log-normal distribution is the best one for the maximum SCF values in CHS X-connections retrofitted with FRP subjected to axial load. In addition, the Log-logistic and Generalized Extreme Value distributions were set as the governing probability function for the retrofitted X-connections under IPB and OPB loads, respectively. In the last step, five fully defined PDFs were established for the maximum SCFs in CHS X-joints retrofitted with FRP under three various types of loadings.

Probabilistic analysis of the SCFs in tubular T/Y-joints reinforced with FRP under axial, in-plane bending, and out-of-plane bending loads

The stress concentration factor (SCF) is one of the most important parameters in the fatigue reliability analysis of tubular offshore structures. This parameter exhibits remarkable scatter which calls for more emphasis in accurately computing the SCFs for determining the fatigue life. As per the authors’ knowledge, no study has been conducted on the probability distribution of SCFs in tubular joints with FRP. Therefore, in this study, results of performing 288 FE analyses on 96 T/Y-joints with FRP have been used to propose a probability distribution model for SCFs in the FRP-reinforced joints subjected to axial, IPB, and OPB loads. According to the T/Y-connection FE models which were validated with several experimental tests, a set of SCF sample databases was generated. 11 various probability density functions (PDFs) were fitted to the relative frequency histograms of the SCF samples. For determining the parameters of every distribution, the maximum likelihood method was applied. Evaluating the goodness-of-fit according to the Chi-squared and Kolmogorov-Smirnov tests indicated that the Weibull distribution is the best one for the maximum SCF values in tubular T/Y-connections retrofitted with FRP under axial load. Also, the Gamma distribution was set as the governing probability function for T/Y-joints with FRP under IPB and OPB loads. In the final step, five fully defined PDFs were proposed for the maximum weld SCFs of in T/Y-joints with FRP under three different types of loadings.

Aerosol physico–optical–radiative characterization and classification during summer over Ny-Ålesund, Arctic

ABSTRACT With an aim to study the year-to-year changes in physical, optical, and radiative properties of polar aerosols, special observation campaigns were conducted during three consecutive summers of 2010, 2011 and 2012 over Ny-Ålesund (78.9°N, 11.9°E, 42 m AMSL), Arctic, employing a ground-based Multi-channel Solar-radiometer (MICROTOPS II Sun- photometer). In the present study, the columnar Aerosol Optical Depth (AOD) at λ = 500 nm and the Angstrom exponent (α) data sets are used to analyse the daily mean AOD and α by using a liner regression (best-fit) method. The results highlight that the columnar aerosol optical depth (mean AOD@500 nm for the study period) is 0.144 ± 0.05. Signature of secondary aerosol formation through marine sources based on variation in two wavelength AODs is also studied. These columnar AOD measurements over the study region are found to be in good agreement within experimental limitations with the synchronous MODIS satellite derived values. The 3 years’ α mean value is found to be 0.797 ± 0.328 within the range of 0.01–1.4. The frequency of occurrence and relative frequency histograms of α exhibited two modes centred at around 1.2 and 0.8. The primary and secondary modes reveal that the marine aerosols in the study region are mixed type, and they contribute about 44%, with the accumulation particles alone contributing about 31%. We found a close correspondence between aerosol optical properties and local meteorological conditions over the experimental location. The aerosol radiative forcing estimations revealed higher negative aerosol radiative forcing (indicating cooling) at Bottom-of-the-Atmosphere (BOA) and positive radiative forcing (indicating warming) in the Atmosphere (ATM) and Top-of-the-Atmosphere (TOA) during 2012 as compared to those obtained during 2010 and 2011, which is consistent with the observed AOD and α. The airmass back-trajectory model analysis also showed intrusion of anthropogenic aerosols from neighbouring regions into the study region, particularly during the year 2012.

Monte Carlo Simulation-Based Uncertainty Integration into Rock Particle Shape Descriptor Distributions

The particles within the rock samples are present in extensive ranges of shapes and sizes, and their characterization and analysis exist with a considerable diversity. The prior research works have appraised the significance of the particle shape types and their effects on the geotechnical structures and deficiencies by evaluating the uncertainty-related rock particle shape descriptors (PSDs). In this work, the Monte Carlo simulation (MCS) is used in order to present a framework to integrate the inherent uncertainty associated with PSDs. A tabletop microscope is used to measure the primary particle shape distribution for the sandstone samples. An open-source processing tool, ImageJ, is used in order to analyze PSDs. The probabilistic distribution of PSDs is acquired using MCS according to the relative frequency histogram of the input parameters. Additionally, a probabilistic sensitivity analysis is performed in order to evaluate the importance of the input parameters in PSDs. The sensitivity analysis results demonstrate that the major axis and area are the most influential parameters involved. The simulation results obtained have revealed that the proposed framework is capable of integrating the inherent uncertainties related to the particle shape.

Aerosol climatology and determination of different types over the semi-arid urban area of Tehran, Iran: Application of multi-platform remote sensing satellite data

In this study, the combination of multiple satellite data was used to improve the assessments of aerosol properties including the aerosol optical depth, Angstrom exponent, UV aerosol index, and single scattering albedo over a semi-arid urban area during the period from 2008 to 2017. The data sets were derived from MODIS and OMI. The critical threshold values for each of the aerosol properties have been defined according to the previous studies to determine different aerosol types.Results of long term analysis of aerosol properties show that all parameters present a distinct monthly variation. A slightly increasing trend is detected for aerosol index values and this indicates the presence of more absorbing aerosols in recent years. There also is an obvious, consistent cooling effect of aerosols based on the variation of single scattering albedo. The aerosol optical depth relative frequency histogram shows a wide range of values with a maximum of about 40% around the range of 0.3 which is generally higher than some other polluted cities in the world. However, the Angstrom exponent peak around 0.8 likely means the dominance of aerosols in coarse mode.The results of the determination of different aerosol type show that, right after the mixed type aerosols, the urban/industrial aerosol type is the second-highest contributor to the aerosol composition and that it is followed by dust aerosols. On the other hand, maritime aerosols and smoke, present in less than 5% of the days studied, do not have a significant contribution. Seasonal analysis of different aerosol types indicates the dominance of large absorbing aerosols, i.e. dust during summertime, and small aerosols with non-absorbing properties, i.e. urban/industrial aerosols, mostly during cold seasons.

Monte Carlo simulation (MCS)-based uncertainty analysis of rock mass quality Q in underground construction

Uncertainties in a rock mass quality measure are due largely to the inherently heterogeneous nature of the rock mass itself. Traditional deterministic methods for the assessment of rock mass quality are not based upon a complete understanding of these inherent uncertainties, which can result in adverse impact on overall design performance. To address this problem, a Monte Carlo simulation (MCS)-based uncertainty analysis framework is proposed in this study to probabilistically quantify the uncertainties in the Q-system of rock mass classification. The proposed framework is then implemented in a highway tunnel case study. The probability distribution of the Q-value is obtained using the MCS technique in which the relative frequency histograms of the input parameters are used to probabilistically assess the rock mass properties and responses with appropriate empirical correlations. The probabilistic estimates of the rock mass properties are also adopted as the input for a finite element model for probabilistic evaluation of the excavation-induced tunnel displacement. In addition, a probabilistic sensitivity analysis is conducted to rank the relative importance of the input parameters in the Q-system according to the regression coefficients, Spearman’s rank-order correlation coefficients, contributions to variance and effects on output mean. The effects of the distribution types of uncertain input parameters in the Q-system are also examined. The proposed framework is shown to be capable of systematically assessing the uncertainty in the rock mass quality measure before construction as well as providing insightful information for the probabilistic evaluation of the ground response and support performance of underground structures. Although applied specifically to the Q-system, the proposed probabilistic framework should also be applicable to other rock mass classification systems.

Quantifying Wet Muck Entry Risk for Long-term Planning in Block Caving

Wet muck entry is one of the major geotechnical risks associated with long-term production goals in cave mining. The objective of this research is to quantify the effect of the main risk variables related to wet muck entry in an effort to prioritize and confront these variables accordingly. Logistic regression modeling was carried out using mine data from Pipa Norte Mine (PNM) and Sur Andes Pipa Mine (SPM), both located at El Teniente Mine. A confusion table was employed to calibrate the model, while a scatter plot and an error relative frequency histogram were used to validate it. The results indicated that ore draw and environmental conditions are the main risk variables associated with wet muck entry. The aforementioned metrics show an acceptable agreement between mine and modeled data. Hence, we used these results to create a statistically significant predictive model, which may be useful for the risk evaluation of numerous long-term plans. Based on optimal calibrated conditions, the predictive model is a powerful instrument not only to identify high-risk zones susceptible to wet muck entry but also to make long-term preventive decisions, which could lead in mitigating the risks of wet muck entry in cave mines.

Economical thermal-RGB imaging system for monitoring agricultural crops

In this study, a low-cost thermal-RGB imager was developed for use in agricultural crop monitoring applications. It is weatherproof, and has a geo-referencing capability along with a power management panel that allows unattended field deployment of the systems for crop monitoring over extended period of time. The imager is made up of single-board Linux-based computer integrated with RGB and thermal imaging modules. The imager can be configured as FTP server to allow data transfer to/from a client computer. Developed was also the custom image-processing algorithm which overlays, aligns thermal and RGB images, and mask for the thermal image to remove the soil background and shaded leaves. The algorithm outputs are the average temperature of sunlit leaves and canopy coverage. Prior to field validation, the performance of ten thermal modules and four fully assembled RGB-thermal imagers were assessed under laboratory conditions. In the spring of 2017, two imagers were mounted on a center pivot retrofitted with Medium Elevation Spray Application (MESA) and Low Elevation Spray Application (LESA) systems in a mint field near Toppenish, WA. The thermal modules showed an accuracy of ±2.4 °C on average over a range of 0–50 °C of a blackbody target. Although accurate for larger canopies, the imperfect alignment of RGB and thermal images introduced significant errors in the calculations of sunlit leaves surface temperature in images with small canopy coverage. Further investigations revealed that the first peak of thermal image relative frequency histogram could be a more accurate representative of sunlit leaf surface temperature. Overall, the amended image-processing algorithm was able to successfully extract canopy surface temperature and percent canopy cover from a wide range of images captured during the crop growing season. The current design of imager allows for creating a network of imaging units in the field to obtain real-time surface temperature data from plant canopies. The system has the potential to be used for creating evapotranspiration and prescription maps in real-time, and irrigation scheduling.

МЕТОДИЧЕСКИЕ АСПЕКТЫ КРОССКОРРЕЛЯЦИОННОГО АНАЛИЗА ЭЭГ, "Российский физиологический журнал им. И.М. Сеченова"

В статье рассматриваются методические аспекты применения корреляционного анализа при изучении ЭЭГ человека в состоянии покоя. Исследуются причины, по которым выборочный коэффициент корреляции Пирсона r между отдельными отведениями ЭЭГ не является прямым индикатором наличия или отсутствия взаимосвязи между активностью различных областей головного мозга. Приводятся примеры гистограмм относительных частот величин r для различных испытуемых, показывающие ошибочность использования усредненных по испытуемым значений r при оценке возможной взаимосвязи между различными ЭЭГ-сигналами. Показано, что межиндивидуальное сходство между векторами r, составленными из однотипных наборов выборочных коэффициентов корреляции Пирсона, оказывается более информативным, поскольку при его оценке может происходить частичная коррекция смещения полученных оценок r, в результате которой проявляется смысл корреляции в понимании Ж. Кювье, а именно в соразмерности или пропорциональности, активности различных областей головного мозга у разных испытуемых в состоянии покоя

Reliability Estimation of Parameters of Helical Wind Turbine with Vertical Axis.

Due to the prolonged use of wind turbines they must be characterized by high reliability. This can be achieved through a rigorous design, appropriate simulation and testing, and proper construction. The reliability prediction and analysis of these systems will lead to identifying the critical components, increasing the operating time, minimizing failure rate, and minimizing maintenance costs. To estimate the produced energy by the wind turbine, an evaluation approach based on the Monte Carlo simulation model is developed which enables us to estimate the probability of minimum and maximum parameters. In our simulation process we used triangular distributions. The analysis of simulation results has been focused on the interpretation of the relative frequency histograms and cumulative distribution curve (ogive diagram), which indicates the probability of obtaining the daily or annual energy output depending on wind speed. The experimental researches consist in estimation of the reliability and unreliability functions and hazard rate of the helical vertical axis wind turbine designed and patented to climatic conditions for Romanian regions. Also, the variation of power produced for different wind speeds, the Weibull distribution of wind probability, and the power generated were determined. The analysis of experimental results indicates that this type of wind turbine is efficient at low wind speed.

Summary about Optimal Power Flow of Power System with Wind Farm Iteration

Integrated wind farms exert a growing influence in the economic operation of power system. Wind power is a form of intermittent and random energy. This paper introduces a model including the error in wind power forecasts using a probability or relative frequency histogram. Compared with the deterministic OPF, the proposed model allows the coordination of wind andthermal power while accounting for the expected penalty cost for not using all available wind power and the expected cost of calling up power reserves because of wind power shortage.Simulation results are presented for cases where the forecasting error histogram is eitherderived from historical data or estimated by a bimodal normal distribution.

Can Power Laws Help Us Understand Gene and Proteome Information?

Proteins are biochemical entities consisting of one or more blocks typically folded in a 3D pattern. Each block (a polypeptide) is a single linear sequence of amino acids that are biochemically bonded together. The amino acid sequence in a protein is defined by the sequence of a gene or several genes encoded in the DNA-based genetic code. This genetic code typically uses twenty amino acids, but in certain organisms the genetic code can also include two other amino acids. After linking the amino acids during protein synthesis, each amino acid becomes a residue in a protein, which is then chemically modified, ultimately changing and defining the protein function. In this study, the authors analyze the amino acid sequence using alignment-free methods, aiming to identify structural patterns in sets of proteins and in the proteome, without any other previous assumptions. The paper starts by analyzing amino acid sequence data by means of histograms using fixed length amino acid words (tuples). After creating the initial relative frequency histograms, they are transformed and processed in order to generate quantitative results for information extraction and graphical visualization. Selected samples from two reference datasets are used, and results reveal that the proposed method is able to generate relevant outputs in accordance with current scientific knowledge in domains like protein sequence/proteome analysis.

Distribution of Temporomandibular Joint Vibration Transfer to the Opposite Side

A vibration produced when a displaced temporomandibular disc reduces during opening can transfer some of its energy from the ipsilateral joint to the contralateral joint. The objective of this study was to measure what percentage of the ipsilateral vibration is transferred to the contralateral joint. The study included the temporomandibular joint (TMJ) vibrations of 144 (informed consent) subjects, (113 F, 31 M), with reducing displaced discs (DDR). Vibrations from 165 joints were recorded bilaterally with BioJVA (BioResearch Associates, Inc. Milwaukee, WI). In each case, any contralateral vibration was analyzed to verify that it was caused by the ipsilateral joint. The contralateral amplitude was divided by the ipsilateral amplitude and multiplied by 100 to produce a percentage of transfer. The percentage values (0-100%) were used to create a Relative Frequency Histogram with 20 classes (1-5%, 6-10%, 11-15%, etc.). The Relative Frequency Histogram graph revealed a three-mounded distribution of the percentage of transfer. One mound fell between 5 and 34 percent, one between 35 and 69 percent and the third between 70 and 98 percent. The appearance of a three-mounded distribution suggests that there may be three different failure modes leading to TMJ internal derangements. Alternatively, it may be that failure of the disc’s stabilizing ligaments leads to three different internal derangement conditions that are in some way distinct. The evidence of apparent tri-modality in this vibration data distribution suggests that there may be three different failure modes of disc displacement with reduction (e.g., anterior, anteromedial, and medio-lateral disc displacement). If so, identifying them could allow for a more detailed description of DDR. Therefore, further investigation of this ‘tri-modal’ distribution should be undertaken.

A probability distribution model for stress concentration factors in multi-planar tubular DKT-joints of steel offshore structures

The stress concentration factor (SCF) is one of the most important parameters in the fatigue reliability analysis of steel offshore structures. This parameter exhibits considerable scatter which calls for greater emphasis in accurately computing the SCFs for predicting the fatigue life of these structures. As far as the authors are aware, no comprehensive research has been carried out on the probability distribution of SCFs in tubular joints, especially multi-planar ones, which cover the majority of practical applications. What has been used so far as the probability distribution of SCFs in the reliability analysis of offshore structures is mainly based on assumptions and limited observations, especially in terms of distribution parameters. In the present paper, results of performing FE analysis on 81 steel multi-planar tubular DKT-joints have been used to propose a probability distribution model for SCFs along the weld toe of the central brace under axial loads. Based on the multi-planar DKT-joint FE models which are verified against experimental results and the predictions of Lloyd's Register (LR) equations, a set of SCF sample databases was constructed. 15 different probability density functions (PDFs) were fitted to the relative frequency histograms of the SCF samples. The maximum likelihood method was used to determine the parameters of each distribution. Standard goodness-of-fit tests led to the conclusion that the Inverse Gaussian distribution is the best probability model for the peripheral distribution of SCFs along the weld toe and the Birnbaum–Saunders distribution is the best one for the maximum value of weld toe SCF.

A Method for the Selection of Exploration Areas for Unconformity Uranium Deposits

The method we propose employs two analyses: (1) exploration simulation and risk valuation and (2) portfolio optimization. The first analysis, implemented by the investment worth system (IWS), uses Monte Carlo simulation to integrate a wide spectrum of uncertain and varied components to a relative frequency histogram for net present value of the exploration investment, which is converted to a risk-adjusted value (RAV). Iterative rerunning of the IWS enables the mapping of the relationship of RAV to magnitude of exploration expenditure, X. The second major analysis uses RAV vs. X maps to identify that subset (portfolio) of areas that maximizes the RAV of the firm’s multiyear exploration budget. The IWS, which is demonstrated numerically, consists of six components based on the geologic description of a hypothetical basin and project area (PA) and a mix of hypothetical and actual conditions of an unidentified area. The geology is quantified and processed by Bayesian belief networks to produce the geology-based inputs required by the IWS. An exploration investment of $60 M produced a highly skewed distribution of net present value (NPV), having mean and median values of $4,160 M and $139 M, respectively. For hypothetical mining firm Minex, the RAV of the exploration investment of $60 M is only $110.7 M. An RAV that is less than 3% of mean NPV reflects the aversion by Minex to risk as well as the magnitude of risk implicit to the highly skewed NPV distribution and the probability of 0.45 for capital loss. Potential benefits of initiating exploration of a portfolio of areas, as contrasted with one area, include increased marginal productivity of exploration as well as reduced probability for nondiscovery. For an exogenously determined multiyear exploration budget, a conceptual framework for portfolio optimization is developed based on marginal RAV exploration products for candidate PAs. PORTFOLIO, a software developed to implement optimization, allocates exploration to PAs so that the RAV of the exploration budget is maximized. Moreover, PORTFOLIO provides a means to examine the impact of magnitude of budget on the composition of the exploration portfolio and the optimum allocation of exploration to PAs that comprise the portfolio. Using fictitious data for five PAs, a numerical demonstration is provided of the use of PORTFOLIO to identify those PAs that comprise the optimum exploration portfolio and to optimally allocate the multiyear budget across portfolio PAs.

Intermittent wind generation in optimal power flow dispatching

A stochastic model of wind generation in an optimal power flow (OPF) dispatching program is presented. The model includes the error in wind power forecasts using a probability or relative frequency histogram. Compared with the deterministic OPF, the proposed model allows the coordination of wind and thermal power while accounting for (i) the expected penalty cost for not using all available wind power and (ii) the expected cost of calling up power reserves because of wind power shortage. The stochastic model is integrated in an extended conic quadratic OPF program in which wind driven generators are represented as induction machines. Simulation results are presented for cases where the forecasting error histogram is either derived from historical data or estimated by a bimodal normal distribution. The effect of the skewness of the error distribution on the optimal dispatch policy is studied.

Ｆｌａｔｐａｎｅｌｄｅｔｅｃｔｏｒ（ＦＰＤ）装置を使用した小児ディジタル胸部撮影における最適ヒストグラム解析の検討

Optical density of the lung area in pediatric digital chest radiography using an indirect flat panel detector (FPD) system were changed enormously by the influence of such factors as the size of lung area, gas of retroperitoneum, and so on. Our purpose in this study was to improve the stability of lung density on output images by means of optimizing histogram analysis. Chest images of a lung phantom were taken at various X-ray tube voltages and processed using a half-type region of interest (ROI) for the lung area. The shape of the histogram obtained by two different calculation methods including frequency distribution and cumulative relative frequency were compared, and digital chest images of 110 clinical cases in our hospital were classified into three age-groups (under 6 years old, over 6 years old and under 13 years old, and over 13 years old) and their histograms were analyzed. In conclusion, it was important that to analyze the histograms of age-groups, a cumulative relative frequency histogram should be used because the influence of X-ray tube voltage was lower than the frequency distribution histogram, and stabilized lung density under 6 years old could be obtained if the value of the imaging parameter for lung density from default was 90% to 85% or 80% because the distribution of lung area and its center value were significantly lower than in those over 13 years old.