Business Models Assignment
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Added on 2020-03-15
Business Models Assignment
Added on 2020-03-15
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1DETERMINING FLOOD FLOW RATE AT BIELSDOWN CREEK, ADVANCEDHYDROLOGICAL ANALYSIS USING PROBABILITY DISTRIBUTIONSName:Institutional AffiliationsProfessor:Course:Date:
2Table of Contents1.0 Introduction..............................................................................................................................3Fitting the flow into probability curves.......................................................................................4Normal Probability Curve.........................................................................................................5Lognormal Probability Curve...................................................................................................9Lp3 Probability Curve.............................................................................................................12Erlang, 3p Distribution Curve................................................................................................15Comparison with Non-Parametric Method...............................................................................17Logistic Probability Distribution Method..............................................................................18Recommendation for the design of the bridge just upstream of Station 204017...................20Bibliography..................................................................................................................................22Appendix........................................................................................................................................23
31.0 IntroductionThe application of business models for strategic decision-making processes should depend on the volume of the business output possible from a given process. On the same note, business engineering processes and models must only be undertaken on proven and well-known measures of output. Business models and machines can be measured to determine their outputs and throughputs. As a result, an accurate examination of the use of the business models can be undertaken. It is in the line of this that determining the flow rate of water at any river would be useful in determining the kind, size and nature of the bridge that needs to be constructed at any given causeway (Holden et al., 2006:63-5). The bridge to be constructed must be accurately measured according to the needed throughput to determine the efficiency and durability of the construction to be undertaken. According to Gordon, 2004, this is possible when the amount of water flowing in the place can be measured during the high season to determine the maximum water volume that should be considered for the development of the bridge (Gordon, 2004: 83). Further, the measurement should be undertaken in such a way that it is repeated over the course of time so that trend lines can be created based on the frequency of the measured outputs (Reynolds, 2011). Of importance further, is to develop an understanding of the probability measurements based on the water flow rate. A distribution probability curve can then be used to determine the possible volume of parameters to be modelled into the bridge structure and model. Moreover, it is important for the bridge developers to ensure to consider in the construction of the bridge with efficiency in throughput and quality delivery (Yin et al., 2010). Therefore, this paper considers the development of the understanding of the required specifications for the bridge to be developed at Bielsdown creek.
4The main aim of the paper is to help in undertaking an analytical model to be useful in determining water flow rate at Bielsdown creek. It used an advanced hydrological analysis using probability distributions and modeled using normal distribution curve. Difference approaches arehowever given to show the analysis as the probability distribution curve is developed through thenormal distribution curve, lognormal distribution curve, Lognormal 3P distribution cure, and the Erlang 3P probability distribution curve. All the analytical values are developed through the use of the Easyfit evaluation model software for normal probability distributional measures. Fitting the flow into probability curvesA probability curve is a useful tool that can help hydrological engineering developers to be able to find out the most profitable and probable way to solve the challenges that may face thedevelopment of the bridge structures (Hubka & Eder, 2012). The probability distributions would be useful in identifying the boundaries that the project would be acceptable, and the extremes that can point to a non-sustainable and unachievable project. Through the probability distributionanalysis, it would be useful for the hydrological construction engineers to define the safe values in the distribution of the parameters to be used in the construction (Avramenko & Kraslawski, 2008). The normal probability distribution curve is one such common tool that shows the probability distributions of the various elements. Key features that will be used in the definition of the probability statistics in the normal curve include the mean and the standard deviation. These parameters are useful in defining the height and the stretch of the probability distribution curve (Clauset, Shalizi, & Newman, 2009: 663-5). Notably, these two parameters have strong indication onto the type and the nature of the probability curve that can be used for the development of an understanding of the length and the value of the curve to be used in the analysis.
5However, other key features can also be used to define the nature and the values presented in the distribution curve. For instance, the symmetry of the curve can be used to definewhether the curve is skewed posted or negatively (Yue, Pilon & Cavadis, 2002: 262). A positively skewed cure would not have a normal distribution but would have the mean greater than the median and the median greater than the mode. In such a case, the curve can be describedas one that has a long tail to the right, with an exponential rise from the left. On the other hand, a negatively skewed curve would have the least mean in the measures of the central tendency, and mode still higher than the media. The curve is also described as one that has a long tail to the left with a drastic fall on the distribution of the frequencies.Other features that describe the probability statistics under the normal curve structure include the height of the curve and the breadth of the curve. Notably, the total area under the normal probability distribution curve is normally adding up to 1.0, and thus the presented values that can be used in the development of decisions for the model can only have areas that are less than one (Favre et al., 2004). Further, it is notable that in most normal curve probability distributions, 68% of the cases fall within the confidence interval of 95%, and are thus useful in making accurate strategic analysis for the data (Williams & MacKinnon, 2008: 23-4). Normal Probability CurveIn fitting the flow rate using the normal probability curve, the following parameters listedin the table shows the mean and the standard deviations for the data. DistributionParametersAB1Normalδ = 172.076 μ = 202.5δ = 168.13μ = 190.3 2Lognormalδ = 0.0607 μ = 7.596 δ = 0.05806μ = 4.9479
63Lognormal(3P)δ = 0.82643 μ = 4.5541 γ = -11.8945 δ = 0.81497μ = 5.0627γ = -11.614Erlang(3P)M = 1.65 β = 0.93782 γ =18.359 M = 1β = 0.93083γ = 16.11The data analysis fit for the development of the normal curve probability distribution is undertaken by two parameters, in which both cases are extreme factor analysis for the bridge parameters. In this case, therefore, the set A produced a mean of 190.3 and a standard deviation of 172.073 in a parametric statistical analysis. The mean and the standard deviations presented ineach of the cases shows that the hydrological construction engineers are in a position to develop a stronger case understanding of the variable that should be considered for the development of the bridge as normal. The variability of the standard deviation figures being closer to the mean denotes that the curve would be a normal curve with equal distribution of the construction parameters (Limpert, Stahel, & Abbt, 2001: 343-7). These cases presented the highest case scenario with the extreme highest parameters of the water flow rate through the bridge course. In the minimum case scenario for the normal distributions, there would be slight variations in the values presented for the analytical case. The minimum extreme case shows that the mean would be 168.13 and the standard deviation would be 190.3. These figures present the least measurements that can be presented as part of the bridge assuming that the amount of waterflow rate would be least experienced, a condition that would be experienced during the drought seasons. In line with the analysis, the following chart shows the probability distribution analysis
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