12/29/2023 0 Comments Truth tables calculatorOnce the graph representing each network has been defined, it is necessary to estimate its reliability. In that sense we could consider the generated networks in this research as potential supply networks, corresponding to companies from medium to very large size. However, considering some extreme cases will provide additional understanding of the subject and facilitate the identification of the behaviour of each factor over the objective variable. This might generate some supply networks that appear unrealistic when compared to real life networks. It is important to note that to analyse the influence of the various factors under consideration, it is necessary to define different levels for each factor. As an example, Figure 1 represents two of the 81,920 network structures generated according to the factors of the experiment. Furthermore, each of the suppliers will be responsible for the shipment of one type of raw material required for the finished product. Each of the elements of the network (nodes, clusters and flows) will have an associated reliability, which is the probability that it will function without disruption when required (in the case of a cluster, a disruption would affect all the nodes in the region associated to that cluster). Given that one of the factors under analysis is the clusterisation (density) of nodes around a particular region, each warehouse is assigned to a region, for which the number of nodes assigned to it will define the density of the cluster. In this context, a certain supply network will be represented by a set of nodes (suppliers, warehouses and final customers) linked together by arrows representing the flow (transport) of products between the nodes. To analyse the reliability of man-made networks – not only supply networks, but also others such as telecom networks and social networks – modelling is usually represented using graphs (Asha and Newth, 2007). All statistical analysis was carried out with the statistical package R. Given that it is possible that different raw materials are used, the output variable will be the product of the reliabilities obtained for each product, considering that all raw materials should reach the final customer. All the factors are fixed and the model includes second order interaction terms. We conducted a balanced 2 13 full-factorial design with ten replicates, giving a total of 81,920 observations. A multi-factorial Design of Experiments (DOE) was thus performed to test differences between factors (and the presence of interactions between them) when observing the resulting supply network reliabilities. Hence a total of 13 factors have been considered, each at two levels (Table I), as usually done in exploratory analysis (Eriksson et al. Finally, we have also taken into consideration the variances in reliability of four of the variables: density variance (F5) node variance (F11), flow variance (F12) and cluster variance (F13), which could affect overall reliability. Second, we included the reliabilities of specific nodes (F8), flows (F9), and clusters (F10), as it would be expected that more reliable components would make more reliable networks. How to judge the proposition or argument is explained on the terminology screen. ![]() Below, as on the computer, it is marked within | | Note: If this procedure is followed, then the last column calculated will be the one for the main operator. On the computer, you can mark a column as having been used by changing its case. Keep in mind that each column is used only once to calculate an operator value. The final step is to calculate the values of each logical operator. The column for the final letter should contain alternating TF's.Ĥ. If there are eight, then the consecutive number is four.įor each new letter, divide the consecutive number in half. If there are four lines then the first column consists of two consecutive T's followed by two consecutive F's. Assign the same values in each column which contains the same letter. The top half of the lines are assigned T for true and the bottom half F for false. Next the basic input values are assigned to each letter. This can be done by starting at the left end of the formula and moving to the first ) and then backing up to the previous (. One way to find this operator is to pair the parentheses. It is never between a left and a right pair of ( ), , or. Second, the main operator has to be identified. The number of lines is 2 raised to the power of this number.Ģ. This number is also the number of different capital letters in the formula(s). To do this count the number of different (atomic) propositions in the formula(s) for which the table is being built. Determine the number of lines or rows in the table. ![]() There are four steps to building a truth table.ġ.
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