Performance Pareto Analysis

It is also important to record properly the corrective action performed for Pareto analysis to further enhance the corrective action procedure. 

Recall the vital few-trivial many rule, 20/80 rule, or Pareto s Law discussed in Chapter 2. The approach introduced here is called Pareto Analysis after Vilfredo Pareto, an Italian sociologist and economist, who is credited as the source (Kuprenas et al 1999, Rose 2005). When agreed-upon quality is not being achieved, Pareto Analysis can be used to identify the most influential causes of substandard performance so these causes can be addressed first. 

Figure 7.11 Pareto Analysis displays the relative importance of causes of poor project profitability performance so that they can be prioritized for possible correction.

When trade-offs exist, no single compound will stand out uniquely as the optimum drug for the market, ranked hrst on all measures of performance. Rather, a set of compounds will be considered that, on current knowledge, span the optimal solution to the problem. These compounds are those for which there is no other compound that offers equivalent performance across all criteria and superior performance in at least one. In multicriteria decision analysis (MCDA) terminology, they are known as Pareto-optimal solutions. This concept is illustrated by the two-criteria schematic in Figure 11.3. 

Taguchi also suggested the use of Pareto s ANOVA [12]. This technique does not require any statistical assumption so a statistical analysis of the responses cannot be performed. Figure 2.7 shows a Pareto s ANOVA table. 

After the optimization, the robustness of the Pareto front has to be assessed. For each final solution of the optimization, a simulation of 609 days is performed with the influent proposed for BSM1 LT. This influent is typical of the events which perturb the WWTPs like rains, storms and holidays. After this long-term simulation, daily means are computed for both objectives. Then, for the evaluation of the robustness, a Principal Components Analysis (PCA) of these 609 daily mean values is performed. This provides the two directions of variations. 10 and 90 percentiles of the projections of... 

Finally, Eq. (7.9) is used to calculate the score of each solution. It is obtained by subtracting the sum of all elements in the column by the sum of all elements in the row for each diagonal element. The scores are 1.231, -1.623, and 0.392 for solutions 1, 2, and 3, respectively. The solution with the highest score is the best solution. In this example, the ranking in order of preference gives solution I as the best solution, followed by solutions 3 and 2. This example was performed with only three solutions. In practice, the same analysis is performed with thousands of Pareto-optimal solutions that are generated to adequately circumscribe the entire Pareto domain. 

A similar analysis using RSM was performed for the four-objective optimization problem where the initial inoculum concentration was added to the list of objective functions. The P and NP sets of mles that were used to rank the entire Pareto domain are presented in Table 7.12. The results obtained with the 14 mles without considering relative weights were very similar to those obtained for the three-objective optimization problem (Figs. 7.10 and 7.11). The best 5% of aU solutions... 

There are numerous methods and techniques developed in areas such as safety, reliability, and quality for conducting various types of analysis [23-25]. Some of these methods and techniques can also be used to perform rail safety analysis. These methods and techniques include fault-tree analysis, hazards and operability analysis, cause-and-effect diagram, interface safety analysis, failure modes and effect analysis, and Pareto diagram. One of these approaches (i.e., fault-tree analysis) is presented below, and information on other methods and techniques is available in Chapter 4 and in the literature [23-25]. 

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