**4.2.7 Cost Risk Response Efficiency (CRRE)**

The cost risk response efficiency (CRRE) measures the efficiency of the actual cost impact (ACI) vs the forecast cost impact (FCI) at a particular point during the project period. However, the FCI, ACI, and actual response cost (ARC) show different tendencies in their changes. In general, the three curves begin at 0, approach their peaks three-quarters of the way through construction, and return to 0 at the completion of the project. The scale of the changes in the curves is largest for FCI, but the changes in the ACI and ARC are about equal. Figure 3 illustrates the tendency in the change of the forecast vs actual cost impact and response cost. The difference between the FCI and the ACI becomes the CIV, and the difference between the ACI and the ARC becomes the CRRV.

As shown in Figure 3, the CRRE at a particular point during the project period can be obtained by dividing the CIV by the ARC. It can be expressed as Equation (7).

$$\text{CRRE} = \text{CIV/ARC} \tag{7}$$

where, CRRE: Cost Risk Response Effective CIV: Cost Impact Variance ARC: Actual Response Cost

Risk Performance Index and Measurement System 237

**4.2.9 Relationship between Contingency Reserve (CR) and Actual Risk Cost (ARC)**  The relationship between the contingency reserve (CR) and the actual risk cost (ARC) can be

As the project proceeds, the contingency reserve at the project start (CR0) will decrease and the contingency reserve at the project completion (CR100) becomes 0. On the other hand, the actual response cost at the project start (ARC0) is 0, but as the project proceeds, the actual response cost will increase and the cumulative sum of actual response cost at the project completion (ARC100) matches the contingency reserve at the project start (CR0). Figure 4

Fig. 4. Relationships between Contingency Reserve (CR) and Actual Risk Cost (ARC).

ARC*n* at the specified project time *n* is explained in Table 9.

From Figure 4, the interpretation method of CR*n* and ARC*n* at a specified project time *n* is as follows. First, if CR0 = CR*n* + ARC*n*, that is, if the sum of the contingency reserve and actual response cost is equal to the contingency reserve at the project start (CR0), we can determine that the contingency reserve at the specified project time is appropriate. Second, if CR0 > CR*n* + ARC*n*, that is, if the sum of the contingency reserve and actual response cost is less than the contingency reserve at the project start (CR0), we can determine that project risks are decreasing and the contingency reserve at the specified project time should be reduced because it is too high. Third, if CR0 < CR*n* + ARC*n*, that is, if the sum of the contingency reserve and actual response cost is greater than the contingency reserve at the project start (CR0), we can determine that project risks are increasing and that the contingency reserve at the specified project time should be increased because it is too low. The analysis of CR*n* and

Index Description SRRE > 1 Schedule Risk Response Efficiency is good. SRRE =1 Schedule Risk Response Efficiency is nothing SRRE < 1 Schedule Risk Response Efficiency is bad

Table 8. SRRE Analysis.

generally defined as follows.

shows the relationship between CR and ARC.

Fig. 3. Relationships between Forecasted/Actual Cost Impact and Response Cost.

The analysis of the CRRE can be performed as follows. First, if the CRRE is greater than 1, it shows an excellent condition for the CRRE because the ARC is greater than the CIV. Second, if the CRRE is 1, there is no CRRE because the CIV is the same as the ARC. Third, if the CRRE is less than 1, the CRRE shows a bad condition because the CIV at that point is greater than the ARC. The analysis of the CRRE is explained in Table 7.


Table 7. CRRE Analysis.

#### **4.2.8 Schedule Risk Response Efficiency (SRRE)**

The schedule risk response efficiency (SRRE) measures the efficiency of the actual schedule impact (ASI) vs the forecast schedule impact (FSI) at a particular point during the project period. The difference between the FSI and the ASI becomes the SIV, and the difference between the ASI and the ARD becomes the SRRV. The SRRE at a particular point during the project can be obtained by dividing the CIV by the ARD. It can be expressed as Equation (8).

$$\text{SRRE} = \text{SIV/ARD} \tag{8}$$

where, SRRE : Schedule Risk Response Effective SIV : Schedule Impact Variance ARD : Actual Response Days

The analysis of the SRRE can be performed as follows. First, if the SRRE is greater than 1, it shows an excellent condition in the SRRE because the ARD is greater than the SIV. Second, if the SRRE is 1, there is no SRRE because the SIV is the same as the ARD. Third, if the SRRE is less than 1, the SRRE shows a bad condition because the SIV at that point is greater than the ARD. The analysis of the SRRE is explained in Table 8.


Table 8. SRRE Analysis.

236 Advanced Topics in Measurements

Fig. 3. Relationships between Forecasted/Actual Cost Impact and Response Cost.

than the ARC. The analysis of the CRRE is explained in Table 7.

**4.2.8 Schedule Risk Response Efficiency (SRRE)** 

ARD. The analysis of the SRRE is explained in Table 8.

SRRE : Schedule Risk Response Effective

SIV : Schedule Impact Variance ARD : Actual Response Days

Table 7. CRRE Analysis.

where,

Index Description CRRE > 1 Cost Risk Response Efficiency is good. CRRE =1 Cost Risk Response Efficiency is nothing CRRE < 1 Cost Risk Response Efficiency is bad

The analysis of the CRRE can be performed as follows. First, if the CRRE is greater than 1, it shows an excellent condition for the CRRE because the ARC is greater than the CIV. Second, if the CRRE is 1, there is no CRRE because the CIV is the same as the ARC. Third, if the CRRE is less than 1, the CRRE shows a bad condition because the CIV at that point is greater

The schedule risk response efficiency (SRRE) measures the efficiency of the actual schedule impact (ASI) vs the forecast schedule impact (FSI) at a particular point during the project period. The difference between the FSI and the ASI becomes the SIV, and the difference between the ASI and the ARD becomes the SRRV. The SRRE at a particular point during the project can be obtained by dividing the CIV by the ARD. It can be expressed as Equation (8).

SRRE = SIV/ARD (8)

The analysis of the SRRE can be performed as follows. First, if the SRRE is greater than 1, it shows an excellent condition in the SRRE because the ARD is greater than the SIV. Second, if the SRRE is 1, there is no SRRE because the SIV is the same as the ARD. Third, if the SRRE is less than 1, the SRRE shows a bad condition because the SIV at that point is greater than the

#### **4.2.9 Relationship between Contingency Reserve (CR) and Actual Risk Cost (ARC)**

The relationship between the contingency reserve (CR) and the actual risk cost (ARC) can be generally defined as follows.

As the project proceeds, the contingency reserve at the project start (CR0) will decrease and the contingency reserve at the project completion (CR100) becomes 0. On the other hand, the actual response cost at the project start (ARC0) is 0, but as the project proceeds, the actual response cost will increase and the cumulative sum of actual response cost at the project completion (ARC100) matches the contingency reserve at the project start (CR0). Figure 4 shows the relationship between CR and ARC.

Fig. 4. Relationships between Contingency Reserve (CR) and Actual Risk Cost (ARC).

From Figure 4, the interpretation method of CR*n* and ARC*n* at a specified project time *n* is as follows. First, if CR0 = CR*n* + ARC*n*, that is, if the sum of the contingency reserve and actual response cost is equal to the contingency reserve at the project start (CR0), we can determine that the contingency reserve at the specified project time is appropriate. Second, if CR0 > CR*n* + ARC*n*, that is, if the sum of the contingency reserve and actual response cost is less than the contingency reserve at the project start (CR0), we can determine that project risks are decreasing and the contingency reserve at the specified project time should be reduced because it is too high. Third, if CR0 < CR*n* + ARC*n*, that is, if the sum of the contingency reserve and actual response cost is greater than the contingency reserve at the project start (CR0), we can determine that project risks are increasing and that the contingency reserve at the specified project time should be increased because it is too low. The analysis of CR*n* and ARC*n* at the specified project time *n* is explained in Table 9.

Risk Performance Index and Measurement System 239

Fig. 5. Qualitative Risk Performance Measurement Table.


Table 9. CRn and ARCn Analysis.

#### **4.3 Risk performance measurement tables**

It is necessary to produce a format that verifies the risk factors existing in a mega project and their influences by analyzing the RPIs and calculation results proposed in this study. Thus, we classified the performance indexes into qualitative aspects that measure the risk performance as indexes, and quantitative aspects that measure risks in monetary amounts. We therefore propose the Qualitative Risk Performance Measurement Table and Quantitative Risk Performance Measurement Table, which can verify each risk factor and the results of the measurement as shown in Figures 5 and 6, respectively.

The Qualitative Risk Performance Measurement Table, in Figure 5, configures the forecast risk value (FRV) and residual risk value (RRV), which can be used as criteria for presenting the RPIs as columns that are calculated on a reference day, and shows the results of the calculation of the CRPI and SRPI based on this table. The Quantitative Risk Performance Measurement Table, in Figure 6, configures the FCI/FSI, ACI/ASI, and ARC/ARD, which can be used as criteria for presenting the risk performance as columns that are calculated on a reference day, and demonstrates the results of the calculation of the CIV/SIV, CRRV/SRRV, and CRRE/SRRE based on this table. It is evident that these risk performance measurement tables help the project manager to judge the scale, influence, and response efficiency of the various risk factors included in the mega project.

#### **4.4 Risk performance measurement example**

Figures 5 and 6 show the calculation of risk performance using existing housing redevelopment data. These examples nicely illustrate the theoretical and practical value, as well as the validity, of the risk performance measurement model proposed in this paper. The risk performance measurements in Figures 5 and 6 are evaluated every three months.

A qualitative risk performance measurement for the 'Low rate of apartment sales' on two risk factors is shown in Figure 5. Ratings on the probability scale and cost impact scale for April 1, 2010 were 4 and 5, respectively. Therefore, the forecasted cost risk value (FCRV) was calculated to be 20. Also, the rating on the schedule impact scale was 2, yielding a forecasted schedule risk value (FSRV) of 8. The residual risk values of the 'Low rate of apartment sales' were determined for the base date of July 1, 2010. With this reevaluation, the probability scale and cost impact scale values were lowered to 3 and 2, respectively, making the residual cost risk value (RCRV) 6. On the other hand, because the schedule impact scale value increased to 4, the residual schedule risk value (RSRV) is 12. Using the FCRV, FSRV, RCRV, and RSRV numbers in Equation (1), the cost risk performance index (CRPI) is 0.7. Using Equation (2), the schedule risk performance index (SRPI) is –0.5. A CRPI


Fig. 5. Qualitative Risk Performance Measurement Table.

project time should be reduced because it is too much.

project time should be increased because it is too low

It is necessary to produce a format that verifies the risk factors existing in a mega project and their influences by analyzing the RPIs and calculation results proposed in this study. Thus, we classified the performance indexes into qualitative aspects that measure the risk performance as indexes, and quantitative aspects that measure risks in monetary amounts. We therefore propose the Qualitative Risk Performance Measurement Table and Quantitative Risk Performance Measurement Table, which can verify each risk factor and

The Qualitative Risk Performance Measurement Table, in Figure 5, configures the forecast risk value (FRV) and residual risk value (RRV), which can be used as criteria for presenting the RPIs as columns that are calculated on a reference day, and shows the results of the calculation of the CRPI and SRPI based on this table. The Quantitative Risk Performance Measurement Table, in Figure 6, configures the FCI/FSI, ACI/ASI, and ARC/ARD, which can be used as criteria for presenting the risk performance as columns that are calculated on a reference day, and demonstrates the results of the calculation of the CIV/SIV, CRRV/SRRV, and CRRE/SRRE based on this table. It is evident that these risk performance measurement tables help the project manager to judge the scale, influence, and response

Figures 5 and 6 show the calculation of risk performance using existing housing redevelopment data. These examples nicely illustrate the theoretical and practical value, as well as the validity, of the risk performance measurement model proposed in this paper. The risk performance measurements in Figures 5 and 6 are evaluated every three months. A qualitative risk performance measurement for the 'Low rate of apartment sales' on two risk factors is shown in Figure 5. Ratings on the probability scale and cost impact scale for April 1, 2010 were 4 and 5, respectively. Therefore, the forecasted cost risk value (FCRV) was calculated to be 20. Also, the rating on the schedule impact scale was 2, yielding a forecasted schedule risk value (FSRV) of 8. The residual risk values of the 'Low rate of apartment sales' were determined for the base date of July 1, 2010. With this reevaluation, the probability scale and cost impact scale values were lowered to 3 and 2, respectively, making the residual cost risk value (RCRV) 6. On the other hand, because the schedule impact scale value increased to 4, the residual schedule risk value (RSRV) is 12. Using the FCRV, FSRV, RCRV, and RSRV numbers in Equation (1), the cost risk performance index (CRPI) is 0.7. Using Equation (2), the schedule risk performance index (SRPI) is –0.5. A CRPI

Project risks are decreasing or Contingency Reserve at the specified

Project risks are increasing or Contingency Reserve at the specified

Index Description

the results of the measurement as shown in Figures 5 and 6, respectively.

efficiency of the various risk factors included in the mega project.

**4.4 Risk performance measurement example** 

CR0 > CRn + ARCn

CR0 < CRn + ARCn

Table 9. CRn and ARCn Analysis.

**4.3 Risk performance measurement tables** 

CR0 = CRn + ARCn Contingency Reserve at the specified project time is proper


Fig. 6. Quantitative Risk Performance Measurement Table.

Risk Performance Index and Measurement System 241

between 0 and 1 indicates that the cost risk has been effectively controlled, or the residual cost risks are smaller than the forecasted cost risks, as illustrated in Table 4. However, when the SRPI is less than 0, as it is in this case, the schedule risk has not been effectively controlled, or the residual schedule risks are higher than the forecasted schedule risks (see Table 4). This analysis of the CRPI and SRPI numbers tells the project team that they should

Figure 6 shows the results of a quantitative risk performance measurement for the same risk item, the 'Low rate of apartment sales.' With respect to cost risk, the forecasted cost risk impact (FCI) based on a previous forecast date was quantitatively determined to be 200,000,000 won, whereas the actual cost impact (ACI) as determined from the base date was 150,000,000 won. Thus, using Equation (3), we can see that the cost impact variance (CIV) is 50,000,000 won. A CIV of 50,000,000 won indicates that the cost risk response was effective, or cost risk has decreased, as shown in Table 5. Also, because the actual response cost (ARC) on the base date was 30,000,000 won, Equation (5) tells us that the cost risk response variance (CRRV) is 120,000,000 won, which means that the cost risk response strategies are good, as is shown in Table 6. Furthermore, using Equation (7), the cost risk response efficiency (CRRE) is calculated to be 1.67, and anything above 1 indicates good CRRE, as shown in Table 7. For schedule risk, the forecasted schedule risk impact (FSI) based on a previous forecast date was quantitatively determined to be 65 days, whereas the actual schedule impact (ASI) based on a base date was 80 days. Thus, using Equation (4), the schedule impact variance (SIV) is –15 days. An SIV less than 0 indicates that the schedule risk response was not effective, or the schedule risk has increased (see Table 5). Also, because the actual response days (ARD) value on the base date was 86 days, Equation (6) yields a schedule risk response variance (SRRV) of –6 days. An SRRV less than 0 means that the schedule risk response strategies are bad, as shown in Table 6. Furthermore, using Equation (8), we can see that the schedule risk response efficiency (SRRE) is –0.17, and

focus on controlling the schedule risk of the 'Low rate of apartment sales.'

anything less than 0 indicates poor SRRE (see Table 8).

**5. Conclusion** 

**4.5 Value and validity of risk performance index and measurement system** 

considering project risks during the project performance measurement.

method proposed in this study can be summarized as follows.

Generally, project risk management includes risk identification, analysis, and response at a project-specific time. The traditional EVMS cannot conduct the project performance measurement considering the project uncertainties and risks integrated with the cost and schedule. However, the risk performance indexes and measurement system proposed in this paper account for changing project risks, the evaluation of residual risk values, and the efficiency of risk response strategies by periodically comparing previous forecasted risk performance variables with those at a base date—risk performance indexes are calculated every three months rather than at one project-specific point in time. Furthermore, the measurement system integrates the traditional EVMS and risk management concepts by

This chapter has proposed risk performance indexes to improve the efficiency of the general performance measurement for mega projects by extending the existing cost/schedule-based performance measurement system. The expected effects of the risk performance index

Fig. 6. Quantitative Risk Performance Measurement Table.

between 0 and 1 indicates that the cost risk has been effectively controlled, or the residual cost risks are smaller than the forecasted cost risks, as illustrated in Table 4. However, when the SRPI is less than 0, as it is in this case, the schedule risk has not been effectively controlled, or the residual schedule risks are higher than the forecasted schedule risks (see Table 4). This analysis of the CRPI and SRPI numbers tells the project team that they should focus on controlling the schedule risk of the 'Low rate of apartment sales.'

Figure 6 shows the results of a quantitative risk performance measurement for the same risk item, the 'Low rate of apartment sales.' With respect to cost risk, the forecasted cost risk impact (FCI) based on a previous forecast date was quantitatively determined to be 200,000,000 won, whereas the actual cost impact (ACI) as determined from the base date was 150,000,000 won. Thus, using Equation (3), we can see that the cost impact variance (CIV) is 50,000,000 won. A CIV of 50,000,000 won indicates that the cost risk response was effective, or cost risk has decreased, as shown in Table 5. Also, because the actual response cost (ARC) on the base date was 30,000,000 won, Equation (5) tells us that the cost risk response variance (CRRV) is 120,000,000 won, which means that the cost risk response strategies are good, as is shown in Table 6. Furthermore, using Equation (7), the cost risk response efficiency (CRRE) is calculated to be 1.67, and anything above 1 indicates good CRRE, as shown in Table 7. For schedule risk, the forecasted schedule risk impact (FSI) based on a previous forecast date was quantitatively determined to be 65 days, whereas the actual schedule impact (ASI) based on a base date was 80 days. Thus, using Equation (4), the schedule impact variance (SIV) is –15 days. An SIV less than 0 indicates that the schedule risk response was not effective, or the schedule risk has increased (see Table 5). Also, because the actual response days (ARD) value on the base date was 86 days, Equation (6) yields a schedule risk response variance (SRRV) of –6 days. An SRRV less than 0 means that the schedule risk response strategies are bad, as shown in Table 6. Furthermore, using Equation (8), we can see that the schedule risk response efficiency (SRRE) is –0.17, and anything less than 0 indicates poor SRRE (see Table 8).

#### **4.5 Value and validity of risk performance index and measurement system**

Generally, project risk management includes risk identification, analysis, and response at a project-specific time. The traditional EVMS cannot conduct the project performance measurement considering the project uncertainties and risks integrated with the cost and schedule. However, the risk performance indexes and measurement system proposed in this paper account for changing project risks, the evaluation of residual risk values, and the efficiency of risk response strategies by periodically comparing previous forecasted risk performance variables with those at a base date—risk performance indexes are calculated every three months rather than at one project-specific point in time. Furthermore, the measurement system integrates the traditional EVMS and risk management concepts by considering project risks during the project performance measurement.
