Answersforthequestion.pdf

Please refer to HW04_Figures.pdf attached here, also posted in Documents folder (figures and

equations also appear in our textbook). Suppose program node Nj has 10 risk events Ei (i = 1, 2,

3,…,10). Suppose each risk event’s occurrence probability and its impacts if it occurs (with four

dimensions: Cost, Schedule, Technical Performance, and Programmatic) are scored as shown on Figure

4.21.

1. Use Equation 3.68 and value functions in Figure 3.40 to approximately calculate overall impact

of each risk event. Assume equal weights among the dimensions of impact.

Generic Value Function = 𝑉(𝑥) = (1 − 𝑒
−(𝑥−𝑥𝑚𝑖𝑛 )

𝜌 )/(1 − 𝑒
−(𝑥𝑚𝑎𝑥 −𝑥𝑚𝑖𝑛 )

𝜌

Cost Value Function = 𝑉(𝑥1) =
1−𝑒

−𝑥
8.2

1−𝑒
−20
8.2

= 1.096(1 − 𝑒
−𝑥

8.2) → used to find [V(x1)] column

Schedule Value Function = 𝑉(𝑥2) =
1−𝑒

−𝑥
4.44

1−𝑒
−18
4.44

= 1.018(1 − 𝑒
−𝑥

4.44) → used to find [V(x2)] column

Risk Event

Cost Impact

($)

[x1]

Schedule Impact

(Months)

[x2]

Technical

Performance

Impact (1-5)

[x3]

Programatic

Impact (1-5)

[x4]

Value

(Cost)

[V(x1)]

Value

(Schedule)

[V(x2)]

Value

(Tech. Perf.)

[V(x3)]

Value

(Programatic)

[V(x4)]

Overall Impcat

of Risk Event

V(A)

1 12 4 4 4 0.8423 0.6045 0.60 0.79 0.7091

2 5 2 3 2 0.5003 0.3692 0.33 0.21 0.3533

3 15 12 4 5 0.9201 0.9498 0.60 1.00 0.8675

4 18 14 2 4 0.9740 0.9745 0.13 0.79 0.7178

5 12 10 5 1 0.8423 0.9109 1.00 0.00 0.6883

6 4 3 1 3 0.4231 0.5000 0.00 0.47 0.3492

7 2 1 3 1 0.2372 0.2053 0.33 0.00 0.1940

8 11 16 2 4 0.8094 0.9903 0.13 0.79 0.6806

9 4 9 5 3 0.4231 0.8839 1.00 0.47 0.6952

10 3.5 6 3 2 0.3808 0.7544 0.33 0.21 0.4198

Weight of

Impact

(w)

0.25 0.25 0.25 0.25

https://www.blackboard.odu.edu/courses/1/202030_SUMMER_ENMA724_32979/db/_10261752_1/embedded/HW04_Figures.pdf

2. Use Equation 4.1 and the value functions in Figure A to calculate the risk score measure of

each risk event. Assume equal weights in computing each risk score measure.

3. Suppose Figure 4.23 presents a portion of a capability portfolio defined as part of engineering

an enterprise system. Given the information shown, apply the risk analysis algebra in Chapter

4 to derive a risk measure as indicated. Assume λ is given by the function in Figure 4.11.

A. What is RS3.221?

𝑅𝑆3.221 = λm + (1 − λ )Average{𝑥1, 𝑥2, 𝑥3, … 𝑥𝑛 }

Where: 𝑚 = 95 ; λ = .7 ; Average = 69.125

𝑅𝑆3.221 = .7 ∗ 95 + (. 3 ) ∗ 69.125 = 87.24

B. What is RS3.222?

𝑅𝑆3.222 = λm + (1 − λ )Average{𝑥1, 𝑥2, 𝑥3, … 𝑥𝑛 }

Where: 𝑚 = 80 ; λ = .7 ; Average = 50.8

𝑅𝑆3.222 = .7 ∗ 80 + (. 3 ) ∗ 69.125 = 71.24

C. What is RS3.223?

𝑅𝑆3.223 = λm + (1 − λ )Average{𝑥1, 𝑥2, 𝑥3, … 𝑥𝑛 }

Where: 𝑚 = 50 ; λ = .5 ; Average = 28.33

𝑅𝑆3.223 = .5 ∗ 50 + (. 5 ) ∗ 28.33 = 39.17

Risk Event

Event

Probability

(%)

Overall Impact

of Risk Event

V(A)

Risk Score

[RS(E)]

1 95% 0.7091 0.8295

2 65% 0.3533 0.5017

3 55% 0.8675 0.7087

4 50% 0.7178 0.6089

5 90% 0.6883 0.7942

6 15% 0.3492 0.2496

7 25% 0.1940 0.2220

8 80% 0.6806 0.7403

9 85% 0.6952 0.7726

10 75% 0.4198 0.5849

u1 0.50

u2 0.50

D. What is RS3.22?

𝑅𝑆3.22 = λMax{𝑅𝑆3.221} + (1 − λ )Average{𝑅𝑆221, 𝑅𝑆222, 𝑅𝑆3.223}

Where: Max{𝑅𝑆3.221} = 87.24 ; λ = .7 ; Average =
87.24+71.24+39.17

3
= 65.88

𝑅𝑆3.22 = .7 ∗ 87.24 + (. 3 ) ∗ 65.88 = 80.83

E. What is RS3.2?

𝑅𝑆3.2 = λMax{𝑅𝑆3.23, 𝑅𝑆3.24} + (1 − λ )Average{𝑅𝑆21, 𝑅𝑆22, 𝑅𝑆3.23, 𝑅𝑆3.24}

Where: Max{𝑅𝑆3.23, 𝑅𝑆3.24} = Max{55,80} = 80 ; λ = .7 ; Average =
40+80.83+55+80

4
= 63.96

𝑅𝑆3.2 = .7 ∗ 80 + (. 3 ) ∗ 63.96 = 75.19

F. Briefly describe how project/program managers may use the weights in Equations

3.56 and 4.1 to make the risk algebra more meaningful and suitable.

Project managers may use weights to make the equations more relevant to their application. They can

apply their previous knowledge of the industry, project, or situation to properly elevate the severity of

each risk accordingly. The risk algebra functions include these weighted variables to reflect real life

situations and give project managers the autonomy to personalize their equations as needed.

G. Briefly describe how project/program managers may use their own λ-function to make

the risk algebra more meaningful and suitable.

Similar to the weight variables described above, the λ-function is a way for project managers to

personalize their risk algebra functions based on previous knowledge or industry standards. The λ-

function is a form of a constructed scale that is set by the company/project manager as needed to

provide the appropriate weight to risk events.