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Prognostics Metrics Classifications

A variety of prognostics metrics are used in the domains reviewed above. Depending on the end use of the prognostic information, basic accuracy and precision based metrics are transformed into more sophisticated measures. Several factors were identified that classify these metrics into different classes. In this section we attempt to enumerate some of these classifications.

Functional Classification

The most important classification is based on the information these metrics provide to fulfill specific functions. In general we identified three major categories, namely: (1) Algorithm performance metrics, (2) Computational performance metrics, and (3) Cost-benefit metrics. As evident from their names these metrics measure success based on entirely different criteria. As shown in Figure 6, the algorithmic performance metrics can be further classified into four major subcategories.

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Figure 6. Functional classification of prognostics metrics.

## End User Based Classification

Prognostics information may be used by different people for entirely different purposes. In general, end users of prognosis may be classified into the five categories shown in Table 1.

Table 1. Classification of prognostic metrics based on end user requirements.

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## Classification Based on Predicted Entity

Within PHM applications, we identified three major classes of the forms of prediction outputs and hence the corresponding metrics. Prognostics performance can be established based on different forms of the prediction outputs, e.g. future health index trajectory at tP, an RUL estimate at tP, or a RUL trajectory as it evolves with time. Some algorithms provide a distribution over predicted entities to establish confidence in predictions. Metrics to evaluate such outputs differ in form from those required for single value predictions. In other cases such a distribution is obtained from multiple UUTs, e.g., from fleet applications. The basic form of the metrics used for various categories may be similar, but the underlying information conveyed is usually different in a statistical sense. Figures 7-9 illustrate some representative examples.

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Figure 7. (a) Predictions are made in the health domain for a single UUT. A health trajectory is predicted to consider evolution of fault in the system. (b) Predictions can be in the form of distributions with associated confidence bounds.

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Figure 8. (a) Each prediction in the health domain appears as a point prediction in the RUL domain, which then may be compared with ground truth (b) RUL predictions may be obtained with corresponding confidence limits.

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Figure 9. (a) A further assessment can be made on how well an algorithm's RUL estimate evolves over time and converges to the true value as more data becomes available. (b) Such RUL trajectories may be accompanied by corresponding error bars as well.

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