## Info

Production [t /m]

Figure 3.13 Residual Scatter Diagram of Energy Residues Variations

The particular value for the data set presented in Figure 3.13 is ± 183. One characteristic of SEE is that 68 % of all data points will fall within a band of ±SEE. The width of that band gives a measure of variability. If we draw these lines on our residual scatter diagram as upper and lower limit, only three values will fall outside the band. It means that if we analyze energy variability around the best-fit line and use SEE as criteria to establish significance of variation, there are only three instances that require exploration (Fig. 3.13).

In purely statistical terms, the described approach may be valid, but it does not satisfy the needs of energy/production variability evaluation related to energy performance monitoring.

If SEE is large, the range is wider. When SEE is divided by the mean energy value of the analyzed data set (1502.17 t/m from the Table 3.1), the scatter can be expressed as a percentage, which is about 12 %. This percentage represents high variability and indicates the loose control of energy in production. Therefore, the threshold for significance of variability should not be established mechanically. It must be based on knowledge of the process and the underlying energy/production relationship.

When evaluating energy performance, we are not actually interested in variability around the best-fit line, because the best-fit line represents an average of the energy/production relationship, i.e. average energy performance. We are interested in energy variability against a target that represents the best energy performance for the given production output. Another look at the scatter diagram can help us to identify three cases of best performance during the observed period (Fig. 3.14). It makes good sense for energy performance assessment to take the best-achieved performance as a reference for evaluation and as a target for future performance.

We can even calculate a new regression equation based on only three indicated points that present best performance (Fig. 3.15). The new regression equation displays changed a and b parameters:

The correlation analysis will now yield a correlation coefficient and a coefficient of determination with values close to 1, which means almost perfect correlation. As we have said before: for any data set spreadsheet software will provide statistical indicators and equations, but which one is right or the Figure 3.14 Identifying Base Line for Energy Performance Evaluation

Production [t /m]

Figure 3.14 Identifying Base Line for Energy Performance Evaluation Figure 3.15 Energy Variability Evaluation - Best Performance as Base Line

Production [t/m]

Figure 3.15 Energy Variability Evaluation - Best Performance as Base Line best for our purposes, statistics cannot decide. This can be answered based only on the knowledge and understanding of the process and the actual energy/production relationship.

In our case it is proven that the new regression equation presents a more desirable and appropriate energy/production relationship. This is why we can use it as a base or target line (equation) in order to assess past or even future energy performance, as long as the context of the underlying relationship of energy/production remains unchanged. When the material changes occur within the context, the regression equation will need to be updated.

New Regersion Equation

Upper ignificance limit