Performance metrics continuous

This Section addresses cases with a continuous performance metric, y. We identify the corresponding problem statements and results, which are compared with conventional formulations and solutions. Then Taguchi loss functions are introduced as quality cost models that allow one to express a quality-related y on a continuous basis. Next we present the learning methodology used to solve the alternative problem statements and uncover a set of final solutions. The section ends with an application case study. 

Similarly, for the case where a continuous performance metric, y, is employed, the following loss functions were defined (Saraiva and Stephanopoulos, 1992c) ... 

The solution found when the plasma etching was analyzed in terms of continuous performance metrics is also presented in Fig. 8, and is given by... 

The nature of the performance metric, y, is determined by the characteristics of the specific process under analysis. Since we are particularly interested in analyzing situations where y is related to product or process quality, it is quite common to find systems where a categorical variable y is chosen to classify and evaluate their performance. This may happen due to the intrinsic nature of y (e.g., it can only be measured and assume qualitative values, such as good, high, and low ), or because y is derived from a quantization of the values of a surrogate continuous measure of performance (e.g., y = good if some characteristic z of the product has value within the range of its specifications, and y= bad, otherwise). 

In Section IV we considered a categorical performance metric y. Although that represents a common practice, especially when y defines the quality of a product or process operation, there are many instances where system performance is measured by a continuous variable. Even when y is quality-related, it is becoming increasingly clear that explicit continuous quality cost models should be adopted and replace evaluations of performance based on categorical variables. 

Both situations with categorical and continuous, real-valued performance metrics will be considered and analyzed. Since Taguchi loss functions provide quality cost models that allow the different objectives to be expressed on a commensurate basis, for continuous performance variables only minor modifications in the problem definition of the approach presented in Section V are needed. On the other hand, if categorical variables are chosen to characterize the system s multiple performance metrics, important modifications and additional components have to be incorporated into the basic learning methodology described in Section IV. 

Given the data challenges discussed previously and the increasing use of streamlined methods, it is necessary to continuously improve the consistency and transparency of the information and the assumptions used in such tools to ensure the quality and the validity of the decisions made with the aid of LGA metrics. The inclusion of quality indicators (such as sensitivity and uncertainty analysis) will continue to be an important step to estimate the uncertainties involved in the inventory and impact models. Finally, there is a need to continuously perform peer review assessments by LGA experts, as the current LGA expertise in pharmaceuticals is very limited. When these requirements are fulfilled, LGA metrics are powerful tools to aid the decision making leading to more sustainable pharmaceutical processes. For further examples of FLASG scores and other LGA analyzes being applied, see Section 10.4.1. 

The fundamental requirement for a Variable MSA is that the data can be measured on a continuous quantitative scale. As such, a standard operational definition for the performance metrics may already exist. If not, develop a clear definition suitable for your purposes. 

Worldwide, society is increasingly risk-averse and demanding more information and improved performance from economic entities perceived as high risk. Governments and citizens around the world will expect and require an ever-higher level of process safety performance and a demonstrated commitment to continuous performance improvement. A commitment to process safety borne out by relevant and effective metrics will increasingly become part of the license to operate everywhere. 

Of all the three performance metrics discussed above, LER continues to be the most challenging metric to meet for the 22-nm nodes and beyond. 

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