*5.2. Results: Faults' Impact on Key Operating Parameters*

Experimental data under faulty operation and predicted data under fault-free operation were compared by calculating the arithmetic mean μ and the standard deviation σ of (1) return air temperature (TRA) and (2) return air relative humidity (RHRA). The arithmetic mean μ and standard deviation σ have been calculated by means of the following formulas:

$$\mu = \sum\_{i=1}^{N} \frac{\mathbf{d}\_i}{\mathbf{N}} \tag{16}$$

$$\sigma = \sqrt{\frac{\sum\_{i=1}^{N} (\mathbf{d}\_i - \mu)^2}{N}} \tag{17}$$

where N is the whole number of points, while di is the value at time step i of the abovementioned parameters. Table 12 compares the arithmetic mean μ and standard deviation σ during tests 5–9 (summer tests) and 14–18 (winter tests).

**Table 12.** Differences between predicted fault free data and experimental faulty data in terms of TRA and RHRA.


Table 12 also shows the percentage difference (%D) between the values of arithmetic mean and the standard deviation under faulty (predicted values) and fault free operation (experimental values) for each of the above-mentioned parameters. The percentage difference %D has been calculated by means of the following formula:

$$\% \text{D} = \frac{(\mathbb{X}\_{\text{fault},i} - \mathbb{X}\_{\text{w/o\\_fault},i})}{\mathbb{X}\_{\text{w/o\\_fault},i}} \times 100\tag{18}$$

where X is the arithmetic mean μ or the standard deviation σ of TRA or RHRA.

Table 13 summarizes the comments described above; for each of five typical faults considered and for each of four parameters, a performance index has been assigned with the following signs: "+" indicates that the fault causes substantial positive changes (greater than 20%) of %D; "-" indicates that the fault causes substantial negative changes (greater than −20%) of %D; "0" indicates that the fault causes not substantial changes (between −20% and 20%) of %D.

**Table 13.** Summary of symptoms associated to the 5 typical faults on TRA and RHRA.

