High medium

If there is insufficient data to describe a continuous probability distribution for a variable (as with the area of a field in an earlier example), we may be able to make a subjective estimate of high, medium and low values. If those are chosen using the p85, p50, pi 5 cumulative probabilities described in Section 6.2.2, then the implication is that the three values are equally likely, and therefore each has a probability of occurrence of 1/3. Note that the low and high values are not the minimum and maximum values. 

In the example, the first decision is whether or not to appraise. If one appraises, then there are three possible outcomes represented by the chance node the high, medium, or low STOMP. On the branches from the chance node, the estimated probability of these outcomes in noted (0.33 in each case). The sum of the probabilities on the branches... 

In this example it would therefore be justifiable to spend up to 22 million on appraisal activity which would distinguish between the high, medium, and low STOMP cases. If it would cost more than 22 million to determine this, then it would be better to go ahead without the appraisal. The decision tree has therefore been used to place a value on the appraisal activity, and to indicate when it is no longer worthwhile to appraise. 

Discriminant emalysis is a supervised learning technique which uses classified dependent data. Here, the dependent data (y values) are not on a continuous scale but are divided into distinct classes. There are often just two classes (e.g. active/inactive soluble/not soluble yes/no), but more than two is also possible (e.g. high/medium/low 1/2/3/4). The simplest situation involves two variables and two classes, and the aim is to find a straight line that best separates the data into its classes (Figure 12.37). With more than two variables, the line becomes a hyperplane in the multidimensional variable space. Discriminant analysis is characterised by a discriminant function, which in the particular case of hnear discriminant analysis (the most popular variant) is written as a linear combination of the independent variables ... 

For incompressible cake, the pressure distribution and the rate depend on the resistance of the filter medium and the permeability of the cake. Figure L8-150 shows several possible pressure profiles in the cake with increasing filtration rates through the cake. It is assumed that r /i i = 0.8 and /p//i = 0.6. The pressure at / = ri, corresponds to pressure drop across the filter medium Ap, with the ambient pressure taken to be zero. The filtration rate as well as the pressure distribution depend on the medium resistance and that of the cake. High medium resistance or blinding of the medium results in greater penalty on filtration rate. 

Objective Provide a basis to judge the relative likelihood (probability) and severity of various possible events. Risks can be expressed in qualitative terms (high, medium, low) based on subjective, common-sense evaluations, or in quantitative terms (numerical and statistical calculations). 

High, medium, or low dependence level a,ssigned to each system and the resultant conditional failure probabilities,... 

Reasons for selecting high, medium, or low dependence for each system, and... 

Pore volume High Very high Medium high High... 

Sieve Linde High High/Medium Low Good/Medium... 

Dual Flow Figure 8-68A Shell Dev. High High/Medium Low Low... 

Float Valve Figures 8-69A, 69B Nutter High Hlgh/High Medium Good... 

Ballast, Valve V-Series V-1 thru V-5 valves Figure 8-74 and 8-77 Glitsch Higher than Sieve High/High Medium Similar to Sieve Good... 

System Foaming Characteristics Allowable Clear Liquid Velocities, ft/sec High Medium Low... 

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