**5. Measuring road quality**

The current step involves developing a mathematical model to measure the quality of the highway depending on the values of the main criteria previously predicted by the experts.

The highway linking Basra - Nasiriyah has been divided into 28 sections, each section consisting of 10 km in length for the purpose of establishing an assessment from 1 to 9 for the six criteria that determine the efficiency of the road. Out of the total 28 surveyed sections of the highway, 25 sections were used to develop the road quality model while the other three sections were randomly excluded for later use in a cross-validation method to indicate the extent to which the inferred equation represents the actual data. The SPSS program, a software specialized in the statistical analyses, was employed to process the collected data and to find out the best representation of the quality equation based on the main criteria as independent variables. **Figure 3** depicts a screen shot for the data in the SPSS interface.


#### **Figure 3.** *Data sheet of SPSS program.*

### **5.1 Highway quality model development**

After collecting and analyzing the on-site data with the questionnaires that were conducted, there was a linear relationship between the quality of the road and the main criteria, as shown below

*Q* ¼ �0*:*688 þ 0*:*159*S* þ 0*:*198*Rc* þ 0*:*246*Sr* þ 0*:*185*C* þ 0*:*270*Gd* þ 0*:*089*E* (1)

Where: Q = Quality of the road. S = Safety. Rc = Road condition. Sr. = Services. C = Cost. Gd = Geometric design. E = Environment.

The empirical data of the excluded three expressway sections are utilized for verifying the regression model's output results and for testing its accuracy as shown in **Table 4**.

For the purpose of applying the expert weights to each of the criteria and plugging them into the Eq. (1), the equation becomes:

Qc ¼ �0*:*688 þ 0*:*159�9�S þ 0*:*198�9�Rc þ 0*:*246�7�Sr þ 0*:*185�7�C þ 0*:*270�8 ð þ �Gd 0*:*089�6�EÞ*=*9 *Qc* ¼ �0*:*688 þ 0*:*159*S* þ 0*:*176*Rc* þ 0*:*191*Sr* þ 0*:*144*C* þ 0*:*24*Gd* þ 0*:*06*E* (2)

Where: Qc is Corrected Quality.

When applying this equation to the values in **Table 2**, it is possible to use the data in the third column that represent the least acceptable values for the main criteria of road efficiency to find the least acceptable amount of road efficiency Qc as bellow:

*Development of Highways Management Systems in Iraq DOI: http://dx.doi.org/10.5772/intechopen.105852*


**Table 4.**

*Verification results for the developed equation.*

$$\begin{aligned} \mathbf{Qc} &= -0.688 + 0.159^{\circ}\mathbf{5} + 0.176^{\circ}\mathbf{4}.\mathbf{5} + 0.191^{\circ}\mathbf{3}.\mathbf{7} + 0.144^{\circ}\mathbf{4}.\mathbf{8} + 0.24^{\circ}\mathbf{4}.\mathbf{3} + 0.06^{\circ}\mathbf{4} \\ \mathbf{Qc} &= 3.5 \end{aligned}$$

Moreover, when applying the values in the first column of **Table 2**, the efficiency of the road can be found at the current conditions as bellow:

$$\begin{aligned} \mathbf{Qc} &= -0.688 + 0.159^\* 4.7 + 0.176^\* 4.3 + 0.191^\* 3 + 0.144^\* 5.5 + 0.24^\* 5.3 + 0.06^\* 4.7 \\ \mathbf{Qc} &= 3.7 \end{aligned}$$

(4)

(3)
