- Law for Estimation: Triangular Distribution

2015 ◽  
pp. 264-277
Keyword(s):  
Triangular Distribution

NON-NORMAL STATISTICAL TOLERANCE ANALYSIS USING ANALYTICAL CONVOLUTION METHOD

2008 ◽  
Vol 07 (01) ◽  
pp. 127-130 ◽  
Author(s):  
S. G. LIU ◽  
P. WANG ◽  
Z. G. LI
Keyword(s):  
Normal Distribution ◽  
Closed Loop ◽  
Tolerance Analysis ◽  
Accurate Method ◽  
Probability Density Functions ◽  
Triangular Distribution ◽  
Normal Distributions ◽  
Statistical Tolerance ◽  
Statistical Tolerance Analysis ◽  
Convolution Method

In statistical tolerance analysis, it is usually assumed that the statistical tolerance is normally distributed. But in practice, there are many non-normal distributions, such as uniform distribution, triangular distribution, etc. The simple way to analyze non-normal distributions is to approximately represent it with normal distribution, but the accuracy is low. Monte-Carlo simulation can analyze non-normal distributions with higher accuracy, but is time consuming. Convolution method is an accurate method to analyze statistical tolerance, but there are few reported works about it because of the difficulty. In this paper, analytical convolution is used to analyze non-normal distribution, and the probability density functions of closed loop component are obtained. Comparing with other methods, convolution method is accurate and faster.

Risk Analysis of Live Fire Shoot House Containment Systems Against Multiple Projectile Impacts

2020 ◽  
Author(s):  
Steven D. Andreen ◽  
Brad G. Davis
Keyword(s):  
Normal Distribution ◽  
Numerical Models ◽  
Single Point ◽  
Experimental Results ◽  
Risk Level ◽  
Triangular Distribution ◽  
Repeated Impact ◽  
Steel Panels ◽  
The Impact ◽  
Projectile Impacts

Abstract Many analytical and numerical models exist that can describe the effect of single projectile impacts on steel targets. These models are not adequate for the evaluation of live fire shoot house containment systems, which are subjected to repeated impact loading from small caliber projectiles over the lifetime of the structure. Models assuming perfectly rigid projectiles over-predict penetration depths. Models assuming rigid targets cannot predict any penetration, and hydrodynamic models are best suited to high velocity impacts well above the ranges of conventional ordinance. Development of sufficient analytical or numerical tools using traditional techniques would be either intractable, empirically based and unique to a given scenario, require unique material properties that are not commonly available, or require significant computational effort. Due to the limited amount of empirical data on multiple impact failure, classical reliability methods are not suitable for assessing the probability of containment system perforation. Using existing experimental results of .223 caliber ammunition against AR500 steel panels with 2-inch ballistic rubber, a commonly found protective system in these facilities, the cumulative effects of multiple projectiles were quantified to estimate the number of impacts required to perforate the target material. Impacts were simulated from normal distributions of the x and y coordinates describing the impact point using a cartesian coordinate plane. The impact resistance of the steel was also simulated from a triangular distribution to account for the variability of the experimental results. Monte Carlo Simulation was then used to estimate the expected number of impacts to cause failure at a single point on the target. Using this collective model, it was possible to determine that the distribution of the number of rounds to cause target failure approached a normal distribution. The results indicated that the mean impacts at failure was 11800 with a standard deviation of 800 impacts. Finally, targeting the allowable risk level for structural failure from the JCSS probabilistic model code from the simulated normal distribution, it was determined that the safe number of impacts was approximately 7996. Decision makers can utilize the safe number of impacts to inform training guidance for the future use of facilities and to develop effective inspection requirements. This model can also be adapted to evaluate similar training facilities and to assess how other small caliber projectile impacts would affect live fire shoot house containment systems, providing a useful tool for the design and analysis of future and the assessment of existing facilities for use with ammunition that did not exist during its design.

scholarly journals Effect of Equivalent Load Distribution on the Accuracy of Mapping the Reinforcement Load Deflection Curve in LTP

2020 ◽  
Vol 10 (17) ◽  
pp. 6127
Author(s):  
Beata Gajewska ◽  
Marcin Gajewski
Keyword(s):  
Load Distribution ◽  
Load Transfer ◽  
Single Case ◽  
Soft Soil ◽  
Triangular Distribution ◽  
Deflection Curve ◽  
Measurement Results ◽  
Equivalent Load ◽  
Load Deflection Curve ◽  
Best Fit

The formulations of tasks modelling embankments on soft soil, improved with columns and with reinforced load transfer platform (LTP), differ significantly. One of these differences is the distribution of equivalent load modelling part of the load carried by the LTP reinforcement and soft soil. This article analyses the influence of the nature of the load-modelling linear function, i.e., inverse triangular, uniformly distributed and triangular, as well as intermediate distributions. In total, 41 distributions of equivalent load were considered, and the results of the obtained deflection functions were compared with the measurement results of reinforcement deflection for 5 cases of experimental research available in the literature. A measure of the accuracy of mapping the reinforcement deflection curve was proposed as a relative error in relation to the deflection curve resulting from experimental measurements. Based on the analysis of the mapping error, it was determined that among the three commonly used distributions, the inverse triangular distribution shows the best fit in most of the analysed cases. However, not in every single case this is the distribution leading to a solution that best describes the behaviour of the geosynthetic reinforcement.

A study on the control of an automatic picking system (APS) in a warehouse

2016 ◽  
Vol 36 (4) ◽  
pp. 388-397 ◽  
Author(s):  
Woo Ram Kim ◽  
Namuook Kim ◽  
Yoon Seok Chang
Keyword(s):  
Computer Simulations ◽  
Design Methodology ◽  
Triangular Distribution ◽  
Energy Usage ◽  
Content Type ◽  
Logistics Company ◽  
Automatic Picking ◽  
Order Fulfilment ◽  
Save Energy ◽  
Practical Implications

Purpose This paper aims to explore methods of defining ejecting zones (EZs) used in automatic picking systems (APSs), particularly in A-frame APSs. An A-frame APS automatically ejects products onto a conveyor, which then brings the products to their destination. EZs are moving zones on a conveyor, and each EZ corresponds to one picking order. Products are ejected as a zone passes channels in which the products are stored. Design/methodology/approach First, three EZ types are defined, and their operations are explained. Second, picking orders are analyzed and categorized by considering the structure and the picking mechanism of an A-frame APS. In addition, picking-order instances reflecting actual data are randomly generated according to each category. Finally, the performance of the EZs is evaluated using the picking-order instances and computer simulations. Findings The results from the computer simulations suggest the EZ types suitable for use with various picking order types considering order fulfilment speed and energy usage. Research limitations/implications In this paper, the authors only adopt a triangular distribution which is considered most practical distribution in the industry. Practical implications It is believed that these results can provide managers and operators with useful guides to facilitate the effective operation of an A-frame APS. The provided ideas have been implemented at the pharmaceutical warehouse of the largest logistics company in Korea. Social implications The result shows that the proposed idea could save energy consumption and the APS have potential to save labor involvement in picking. Originality/value It is essential to define the EZs when operating an A-frame APS efficiently, but there is almost no research in this area. This paper focuses on defining EZs, as well as methods to utilize these zones.

Research of Asymmetric Quality Loss Function with Triangular Distribution

2013 ◽  
Vol 655-657 ◽  
pp. 2331-2334 ◽  
Author(s):  
Qiu Jin ◽  
Shao Gang Liu
Keyword(s):  
Mathematical Models ◽  
Loss Function ◽  
Loss Functions ◽  
Optimum Process ◽  
Triangular Distribution ◽  
Quality Loss ◽  
Quality Loss Function ◽  
Process Mean ◽  
Asymmetric Quality Loss

The asymmetric quality loss functions with the triangular distribution for determining the optimum process mean are studied. The condition of using the linear and quadratic asymmetric quality loss function in the model is considered. The eight mathematical models under an asymmetric quality loss function with the triangular distribution based on the analysis of the linear and quadratic asymmetric quality loss function are presented. Finally, the validity of models is verified by the examples.

ESTUDO COMPARATIVO ENTRE ATERRO SANITÁRIO E INCINERAÇÃO PARA GERAÇÃO DE ENERGIA EM PROJETO REGIONAL FORMADO POR UM CONSÓRCIO DE MUNICÍPIOS

2018 ◽  
Vol 33 (1) ◽  
pp. 37
Author(s):  
Benedito Luiz Martins ◽  
Alcides Lopes Leão
Keyword(s):  
Climate Change ◽  
Comparative Study ◽  
Greenhouse Gases ◽  
Solid Waste ◽  
Energy Recovery ◽  
Pollutant Emissions ◽  
Sanitary Landfill ◽  
Triangular Distribution ◽  
Atmospheric Pollutant ◽  
International Panel

O objetivo deste trabalho é realizar um estudo sobre um projeto regional com 39 municípios para análise comparativa para destinação dos rejeitos dos resíduos sólidos urbanos em um incinerador e disposição em um aterro sanitário com captação do biogás, considerando a possibilidade de recuperação energética em ambos os sistemas, bem como a comparação com relação à emissão de gases de efeito estufa e poluentes atmosféricos.  Para realização deste estudo foram adotadas as seguintes metodologias: caracterização gravimétrica das frações de resíduos sólidos produzidas na região; cálculo de captação do biogás com recuperação energética utilizando a equação elabora pelo IPCC - International Panel on Climate Change, com distribuição triangular da produção do metano gerado ao longo dos anos pela degradação lenta e rápida dos resíduos; e recuperação de energia em sistema de incineração. Os resultados mostraram que o sistema de incineração tem eficiência em 3,2 vezes maior para a produção de energia em relação ao sistema de aterro sanitário, o qual emite gases de efeito estufa 2,9 vezes mais que o sistema de incineração. A conclusão do estudo é que a incineração leva vantagem sobre o aterro sanitário na gestão de resíduos sólidos, porque gera mais energia elétrica, emite menos gases de efeito estufa, utiliza menos área física de terra e, por ser um sistema fechado e estanque apresenta melhores condições para mitigação dos impactos ambientais negativos. PALAVRAS-CHAVE: Resíduos sólidos. Destinação. Disposição. Aterro sanitário. Incineração. Energia. Sustentabilidade. COMPARATIVE STUDY BETWEEN SANITARY LANDFILL AND INCINERATION FOR ENERGY GENERATION IN A REGIONAL PROJECT FORMED BY A CONSORTIUM OF MUNICIPALITIESABSTRACT: The objective of this work was to carry out a comparative study between sanitary landfill and incineration of urban solid waste, considering the possibility of energy recovery, as well as to compare both systems greenhouse gases and atmospheric pollutant emissions. This study was done within a regional cooperative project among 39 municipalities of central São Paulo State. The following methodologies were adopted: gravimetric characterization of solid waste fractions produced in the region; biogas capture with energy recovery using the equation elaborated by the International Panel on Climate Change (IPCC), with a triangular distribution of the methane production generated over the years by the slow and rapid waste degradation of the wastes; and energy recovery in incineration system. The results showed that the incineration system is 3.2 times more efficient for energy production than the landfill system, which emits greenhouse gases 2.9 times more than the incineration system. The conclusion of the study is that incineration takes advantage of landfill in solid waste management, because it generates more electricity, emits less greenhouse gases, uses less physical land area and, because it is a closed and watertight system, presents better conditions for mitigation of negative environmental impacts. KEYWORDS: Solid waste. Destination. Disposition. Landfill. Incineration. Energy. Sustainability.

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