3. Let A- (1,2,-1),(2, 1,-1).(-1,2,1).(2,-1,1).(2,-1,-1), (2.-2,1),(-1,1,1)) (a)
ID: 3887637 • Letter: 3
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3. Let A- (1,2,-1),(2, 1,-1).(-1,2,1).(2,-1,1).(2,-1,-1), (2.-2,1),(-1,1,1)) (a) For the Pareto order on A, use the Boolean matrix representation to find the Pareto-maximal and Pareto-minimal element sets Pn(A) and Pia(A), and the Pareto greatest and least elements (if any) of A. (b) Let f : R3 R2 be defined by f(z) = (ri + ra, ra) for all x = (ri,T2,T3) E R3. Denote the Pareto order on R2 by P. You may freely use the results from the lecture that P is reflexive, transitive, and antisymmetric. Define by -a, b)la b E A. f(a)Pf(b)). (i) Determine whether satisfies the properties of reflexivity, transitivity, and i) Determine all maximal/minimal elements and greatest/least elements in A antisymmetry. with respect to ".Explanation / Answer
A Pareto chart, named after Vilfredo Pareto, is a type of chart that contains both bars and a line graph, where individual values are represented in descending order by bars, and the cumulative total is represented by the line.
The left vertical axis is the frequency of occurrence, but it can alternatively represent cost or another important unit of measure. The right vertical axis is the cumulative percentage of the total number of occurrences, total cost, or total of the particular unit of measure. Because the reasons are in decreasing order, the cumulative function is a concave function. To take the example below, in order to lower the amount of late arrivals by 78%, it is sufficient to solve the first three issues.
The purpose of the Pareto chart is to highlight the most important among a (typically large) set of factors. In quality control, it often represents the most common sources of defects, the highest occurring type of defect, or the most frequent reasons for customer complaints, and so on. Wilkinson (2006) devised an algorithm for producing statistically based acceptance limits (similar to confidence intervals) for each bar in the Pareto chart.
These charts can be generated by simple spreadsheet programs, such as Apache OpenOffice/LibreOffice Calc [1] and Microsoft Excel,[2] visualization tools such as Tableau Software,[3] specialized statistical software tools, and online quality charts generators.
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