**4.1 Definition of risk performance index**

An Risk Performance Index (RPI) can assess the risk management in three-dimensional mixed-use development projects and can be combined with similar measurement systems such as that for the EVMS. The combined performance measurement index can then be used to measure the performance in the three aspects of cost/schedule/risk.

### **4.2 Definition of risk performance index**

The RPI used in this study recognizes the internal risks in a project from the point of view of risk management and quantizes those risks as schedule and cost risk values based on the estimation of each residual risk. The RPI consists of 18 detailed indexes and variables. Table 2 shows the English terms for these indexes and variables with their descriptions and abbreviations.


management only measures the visible performance in businesses, such as financial and management performance. In particular, few studies have examined the risk factors that

Therefore, it is necessary to create a performance management method related to such risk factors to help estimate these factors' influence on a project in a timely and effective manner by developing a technology that continuously manages performance in relation to the risk factors in the early stages of mega projects and that suggests strategies for responses. Thus, we define an RPI for measuring the performance related to risks in construction businesses and derive calculation techniques and measurement methods. We then propose a new performance measurement method that considers the internal risk factors that affect the success or failure of the project in the context of the conventional cost/schedule-based

An Risk Performance Index (RPI) can assess the risk management in three-dimensional mixed-use development projects and can be combined with similar measurement systems such as that for the EVMS. The combined performance measurement index can then be used

The RPI used in this study recognizes the internal risks in a project from the point of view of risk management and quantizes those risks as schedule and cost risk values based on the estimation of each residual risk. The RPI consists of 18 detailed indexes and variables. Table 2 shows the English terms for these indexes and variables with their descriptions and

No Terminology Description Abb.

7 Forecasted Cost Impact Cost Impact forecasted at the specified project time FCI

Performance Index measuring risks related to the

Performance Index measuring risks related to the

Cost Risk Value forecasted at the specified project

Cost Risk Value remaining after subtract eliminated

Schedule Impact forecasted at the specified project

Schedule Risk Value forecasted at the specified

Schedule Risk Value remaining after subtract

project cost CRPI

project schedule SRPI

time FCRV

project time FSRV

cost risk from FCRV RCRV

eliminated schedule risk from FSRV RSRV

time FSI

affect the performance management of mega projects.

**4. Risk performance index and measurement systems** 

to measure the performance in the three aspects of cost/schedule/risk.

**4.1 Definition of risk performance index** 

**4.2 Definition of risk performance index** 

approach.

abbreviations.

Index

Value

Value

Value

Impact

<sup>2</sup>Schedule Risk

<sup>1</sup>Cost Risk Performance

Performance Index

<sup>3</sup>Forecasted Cost Risk

<sup>4</sup>Forecasted Schedule Risk Value

<sup>5</sup>Residual Cost Risk

<sup>6</sup>Residual Schedule Risk

<sup>8</sup>Forecasted Schedule


Table 2. Risk Performance Indexes.

#### **4.2.1 Cost Risk Performance Index (CRPI)**

As noted in Equation (1), the cost risk performance index (CRPI) can be calculated by subtracting the residual cost risk variance (RCRV) from the forecast cost risk variance (FCRV) and dividing by the FCRV at a specific point during the business period.

$$\text{CRPI} = \text{(FCRV-RCRV)} / \text{FCRV} \tag{1}$$

where,

CRPI: Cost Risk Performance Index FCRV: Forecasted Cost Risk Value RCRV: Residual Cost Risk Value

The analysis of the CRPI can be performed as follows. First, if the CRPI is 1, then the RCRV is 0, showing the perfect elimination of the cost risk. It can also be seen that the residual risk in the project is 0, which is the best condition of the cost risk. Second, if the CRPI is greater than 0 and less than 1, it shows that the RCRV is lower than the FCRV. This means that although there are still some risks in the project, they are at a low level compared with the forecasts and so the cost risk shows a good status. Third, if the CRPI is 0, the FCRV is the same as the RCRV. Because this shows that there has been no reduction in the FCRV, it also shows no reduction in the cost risk. Fourth, if the CRPI is less than 0, it shows that the RCRV exceeds the FCRV, indicating an increase in the cost risk in the project. Table 3 shows the cost risk and its analysis method.

Risk Performance Index and Measurement System 233

The analysis of the integrated chart of the cost/schedule RPIs is as follows. First, if the CRPI and SRPI are both 1, it shows that the cost/schedule risks have been totally removed. Second, if the CRPI and SRPI are greater than 0, it shows an excellent condition in which the cost and schedule risks have all been reduced. Third, if the CRPI is greater than 0, but the SRPI is less than 0, the cost risk has decreased, but the schedule risk has increased. Fourth, if the CRPI is less than 0, but the SRPI is greater than 0, the cost risk has increased, but the schedule risk has decreased. Fifth, if the CRPI and SRPI are both less than 0, the cost risk and schedule risk have significantly increased and the project's state has deteriorated.

The cost impact variance (CIV) and schedule impact variance (SIV) verify the effective execution of the response to risks by comparing the cost/schedule impact forecast by the cost and schedule risks at a particular point with the cost/schedule impact that has actually

CIV = FCI – ACI (3)

SIV = FSI – ARI (4)

Fig. 1. Integrated Cost/Schedule Risk Performance Indexes.

**4.2.4 Cost Impact Variance (CIV), Schedule Impact Variance (SIV)** 

where,

CIV : Cost Impact Variance FCI : Forecasted Cost Impact

occurred. These can be calculated by using Equations (3) and (4), respectively.


Table 3. CRPI Analysis.

#### **4.2.2 Schedule Risk Performance Index (SRPI)**

The schedule risk performance index (SRPI) can be computed by subtracting the residual schedule risk variance (RSRV) from the forecast schedule risk variance (FSRV) and dividing by the FSRV at a specific point during the business period. The calculation formula can be expressed as Equation (2).

$$\text{SRPI} = \text{(FSRV-RSRV)/FSRV} \tag{2}$$

where,

SRPI: Schedule Risk Performance Index FSRV: Forecasted Schedule Risk Value RSRV: Residual Schedule Risk Value

The SRPI can be analyzed as follows. First, if the SRPI is 1, it shows that the RSRV is 0, indicating the perfect elimination of the schedule risk. The remaining risk in the project is 0, which shows the best condition of the schedule risk. Second, if the SRPI is greater than 0 and less than 1, it shows that the RSRV is lower than the FSRV. This means that although there are still some risks in the project, they are at a low level compared with the forecasts, indicating that the schedule risk is in an excellent state. Third, if the SRPI is 0, the FSRV is the same as the RSRV. Because this shows there is no reduction in the FSRV, it also shows no reduction in the schedule risk. Fourth, if the SRPI is less than 0, it shows that the RSRV exceeds the FSRV, indicating an increase in the schedule risk in the project. Table 4 shows the schedule risk and its analysis method.


Table 4. SRPI Analysis.

#### **4.2.3 Integrated Cost/Schedule Risk Performance Indexes**

It is obviously possible to verify the change in the cost/schedule/risk according to the measurement points of the performance index using a method in which the cost/schedule/risk performance can be presented by integrating the CRPI and SRPI in a quadrant, as illustrated in Figure 1.

CRPI = 1 Best status, residual cost risk is 0, all cost risks have been eliminated. 0<CRPI<1 Good status, residual cost risks are smaller than forecasted cost risks. CRPI = 0 Unchanged status, residual cost risks are equal to forecasted cost risks. CRPI < 0 Bad status, residual cost risks are larger than forecasted cost risks.

The schedule risk performance index (SRPI) can be computed by subtracting the residual schedule risk variance (RSRV) from the forecast schedule risk variance (FSRV) and dividing by the FSRV at a specific point during the business period. The calculation formula can be

The SRPI can be analyzed as follows. First, if the SRPI is 1, it shows that the RSRV is 0, indicating the perfect elimination of the schedule risk. The remaining risk in the project is 0, which shows the best condition of the schedule risk. Second, if the SRPI is greater than 0 and less than 1, it shows that the RSRV is lower than the FSRV. This means that although there are still some risks in the project, they are at a low level compared with the forecasts, indicating that the schedule risk is in an excellent state. Third, if the SRPI is 0, the FSRV is the same as the RSRV. Because this shows there is no reduction in the FSRV, it also shows no reduction in the schedule risk. Fourth, if the SRPI is less than 0, it shows that the RSRV exceeds the FSRV, indicating an increase in the schedule risk in the project. Table 4 shows

SRPI = 1 Best status, residual schedule risk is 0, all schedule risks have been eliminated 0<SRPI<1 Good status, residual schedule risks are smaller than forecasted schedule risks. SRPI = 0 Unchanged status, residual schedule risks are equal to forecasted schedule

SRPI < 0 Bad status, residual schedule risks are larger than forecasted schedule risks.

It is obviously possible to verify the change in the cost/schedule/risk according to the measurement points of the performance index using a method in which the cost/schedule/risk performance can be presented by integrating the CRPI and SRPI in a

**4.2.3 Integrated Cost/Schedule Risk Performance Indexes** 

SRPI = (FSRV-RSRV)/FSRV (2)

Index Description

Table 3. CRPI Analysis.

expressed as Equation (2).

SRPI: Schedule Risk Performance Index FSRV: Forecasted Schedule Risk Value RSRV: Residual Schedule Risk Value

the schedule risk and its analysis method.

Index Description

risks

quadrant, as illustrated in Figure 1.

Table 4. SRPI Analysis.

where,

**4.2.2 Schedule Risk Performance Index (SRPI)** 

Fig. 1. Integrated Cost/Schedule Risk Performance Indexes.

The analysis of the integrated chart of the cost/schedule RPIs is as follows. First, if the CRPI and SRPI are both 1, it shows that the cost/schedule risks have been totally removed. Second, if the CRPI and SRPI are greater than 0, it shows an excellent condition in which the cost and schedule risks have all been reduced. Third, if the CRPI is greater than 0, but the SRPI is less than 0, the cost risk has decreased, but the schedule risk has increased. Fourth, if the CRPI is less than 0, but the SRPI is greater than 0, the cost risk has increased, but the schedule risk has decreased. Fifth, if the CRPI and SRPI are both less than 0, the cost risk and schedule risk have significantly increased and the project's state has deteriorated.

#### **4.2.4 Cost Impact Variance (CIV), Schedule Impact Variance (SIV)**

The cost impact variance (CIV) and schedule impact variance (SIV) verify the effective execution of the response to risks by comparing the cost/schedule impact forecast by the cost and schedule risks at a particular point with the cost/schedule impact that has actually occurred. These can be calculated by using Equations (3) and (4), respectively.

$$\text{'CIV=FCI-ACI} \tag{3}$$

$$\text{ISIV} = \text{FSI} - \text{ARI} \tag{4}$$

where, CIV : Cost Impact Variance FCI : Forecasted Cost Impact

Risk Performance Index and Measurement System 235

It is possible to examine the total change in the efficiency of the response strategy for the cost/schedule/risk by integrating the CRRV and SRRV in a quadrant as shown in Figure 2. The integrated chart of the cost/schedule risk response variances can be analyzed as follows. First, if the CRRV and SRRV are both greater than 0, it shows that the efficiency of the response strategy is excellent in both cases. Second, if the CRRV is greater than 0, but the SRRV is less than 0, it shows that the efficiency of the strategy of the SRRV is poor. Third, if the CRRV is less than 0, but the SRRV is greater than 0, the efficiency of the CRRV is poor, but the efficiency of the SRRV is good. Fourth, if the CRRV and SRRV are both less than 0,

**4.2.6 Integrated Cost/Schedule Risk Response Variances** 

the efficiencies of the CRRV and SRRV are both poor.

Fig. 2. Integrated Cost/Schedule Risk Response Variance Measurement.

difference between the ACI and the ARC becomes the CRRV.

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

As shown in Figure 3, the CRRE at a particular point during the project period can be

CRRE = CIV/ARC (7)

obtained by dividing the CIV by the ARC. It can be expressed as Equation (7).

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

where, CRRE: Cost Risk Response Effective

CIV: Cost Impact Variance ARC: Actual Response Cost

ACI : Actual Cost Impact SIV : Schedule Impact Variance FSI : Forecasted Schedule Impact ASI : Actual Schedule Impact

The analysis of the CIV and SIV can be performed as explained in Table 5.


Table 5. CIV, SIV Analysis.

#### **4.2.5 Cost Risk Response Variance (CRRV), Schedule Risk Response Variance (SRRV)**

The cost risk response variance (CRRV) shows the difference between the actual cost impact and the actual response cost impact investigated at a particular point, and the schedule risk response variance (SRRV) represents the difference between the actual schedule impact and the actual response schedule impact investigated at a particular point. The calculation of these values can be carried out using Equations (5) and (6), respectively.

$$\text{CRRV} = \text{ACI} - \text{ARC} \tag{5}$$

$$\text{SRRV} = \text{ASI} - \text{ARD} \tag{6}$$

where, CRRV : Cost Risk Response Variance ACI : Actual Cost Impact ARC : Actual Response Cost SRRV : Schedule Risk Response Variance ASI : Actual Schedule Impact ARD : Actual Response Days

The analysis of the CRRV and SRRV can be performed as explained in Table 6.


Table 6. CRRV, SRRV Analysis.

CIV > 0 ACI is less than FCI, risk response has been efficient or cost risk has

CIV < 0 ACI is greater than FCI, risk response has been inefficient or cost risk

SIV > 0 ASI is less than FSI, risk response has been efficient or schedule risk

SIV < 0 ASI is greater than FSI, risk response has been inefficient or schedule

**4.2.5 Cost Risk Response Variance (CRRV), Schedule Risk Response Variance** 

The cost risk response variance (CRRV) shows the difference between the actual cost impact and the actual response cost impact investigated at a particular point, and the schedule risk response variance (SRRV) represents the difference between the actual schedule impact and the actual response schedule impact investigated at a particular point. The calculation of

CRRV = ACI – ARC (5)

SRRV = ASI – ARD (6)

The analysis of the CIV and SIV can be performed as explained in Table 5.

Index Description

been decreased.

has been increased.

has been decreased.

risk has been increased.

these values can be carried out using Equations (5) and (6), respectively.

The analysis of the CRRV and SRRV can be performed as explained in Table 6.

Index Description CRRV > 0 Cost risk response strategies are good. CRRV < 0 Cost risk response strategies are bad SRRV > 0 Schedule risk response strategies are good SRRV < 0 Schedule risk response strategies are bad

ACI : Actual Cost Impact SIV : Schedule Impact Variance FSI : Forecasted Schedule Impact ASI : Actual Schedule Impact

Table 5. CIV, SIV Analysis.

CRRV : Cost Risk Response Variance

SRRV : Schedule Risk Response Variance

ACI : Actual Cost Impact ARC : Actual Response Cost

ASI : Actual Schedule Impact ARD : Actual Response Days

Table 6. CRRV, SRRV Analysis.

**(SRRV)** 

where,
