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International Journal of Electronic Business Management, Vol. 9, No. 3, pp. 220-230 (2011)
PROJECT RELIABILITY: PROBABILITY OF A PROJECT
MEETS ITS QUALITY-COST-TIME TARGET UNDER
UNCERTAINTY
Yudha Andrian Saputra1* and Ode Siti Andini Ladamay2
1
Department of Industrial Engineering
Institut Teknologi Sepuluh Nopember (ITS)
Surabaya (60111), East Java, Indonesia
2
The 10th BPBPJN
Ministry of Public Works
Jayapura (12110), Papua, Indonesia
ABSTRACT
For so long, Quality, Cost, and Time become an Iron Triangle for measuring project success.
Many researchers have investigated about Quality-Cost-Time in a Project Network under
uncertainty, particularly it focuses on single parameter (Quality/Cost/Time only) or
combination between parameters (trade off or relation between parameters). Knowing the
probability to meet these three targets is important, especially during the project planning.
Management can gain information insights about the confidence level to meet the target and
potential risk in the future. However, none of the previous research has combined these three
parameters under uncertainty. If we define quality as: 1) a standard or requirement to be met
with failed and successful probability; 2) it has consequences or impact on additional cost
and/or additional time for nonconformity; and 3) the time and cost have their own relationship
and form of uncertainty, here our proposed method to evaluate probability of a project whether
it met its Quality-Cost-Time target under uncertainty. We call this as Project Reliability. A
Monte Carlo Simulation and Generalized Activity Network are utilized. A numerical example
is provided to support and validating the propose method.
Keywords: Quality-cost-time, Generalized Activity Network, Monte Carlo Simulation,
Uncertainty
1. INTRODUCTION
*
Quality, cost and time have become indicators
for measuring project success. These three parameters
are called as The Iron Triangle [1]. An assessment
before running the project is important for measuring
capability to meet these three constraints. A set of
action plans can be set up by the management in the
planning stage as preventive or response based on the
assessment result.
In details, several authors have investigated the
Iron Triangle, particularly focus on single criteria
(Quality/Cost/time only) or for combination, e.g.:
relation between criteria. In the field of Project
duration, we found a lot of discussion to overcome
PERT weakness and oversimplified in Williams [21],
Lu and Rizk [15], Lee and Arditi [14], and Huang and
Wang [12]. In terms of Project Cost, Elkjaer [11] and
Chou, J.S. [6] proposed different methodology to
assess project cost and uncertainties. Chan [5]
discusses about time and cost relationship in Malaysia
*
Corresponding author: [email protected]
case studies based on Bromilow equation. In Project
Quality, Burati et al. [4] conducts a research in 9
industrial fast track and record the amount of cost that
associated with non-conformities.
The idea of comprehensive evaluation of
Quality-Cost-Duration under uncertainty was stated
by Kidd [13] Kidd suggested the usability of VERT
not only for estimating duration, but also for
evaluating quality/performance and cost integrative
using an indicator called as Reliability. Unfortunately,
the discussion was only stopped at single or
interaction time-cost parameters. The most nearby
result can be found in Babu and Suresh [2] and
Tareghian and Taheri [18] which discusses
optimization and trade off of Quality-Cost-Duration
evaluation under deterministic assumption. However,
we
can’t
find
any
scholars
proposed
Quality-Cost-Duration evaluation under uncertainty.
This research can be applied in the Project
Planning stages. After an organization; e.g.: a
contractor, awarded a contract to perform a project
within specific quality-cost-duration; and a planning
already established; then the question would be how
Y. A. Saputra and O. S. A. Ladamay: Project Reliability
confidence (probability) we are with the performance
of this project to meet the target of The Iron Triangle.
To answer this question, we must be able to model the
Quality-Cost-Time in a Project Network.
Now if: 1) The environment under uncertainty;
2) The Project Reliability defines as the probability to
meet the total cost and total time/duration target, and
pass all the Quality/Standard required by the Project;
3) The Quality/Standard has some uncertainty about
successful and failed. If failed, there are some
additional process/consequences with some additional
time and cost; thus, this research proposes a
comprehensive methodology on how to evaluate a
project planning under a network rules and
uncertainty to find its probability to meet the
Quality-Cost-Time target. The reliability indicator
will become an important consideration for
management to set a preventive action to protect the
achievement of the targets as the basis of System
Safety and further Risk Analysis.
2. THE PROPOSED IDEA
Our Proposed idea for calculating the Project
Reliability is simple. The idea is shown in the Figure
1. The basic idea is similar with calculating the
Probability to meet duration in PERT methodology.
We just need to transform the Quality, Cost and Time
and its relationship from beginning activities until end
activities and to aggregate the result based on each
parameter rule. Then, each aggregate is compared
with its target.
If all aggregate can meet the target, we can say
that the project is success (Index = 1). On other hand,
if at least one target can’t be met, the project is fail
(Index=0). By repeating this experiment for X trials
we can collect how many numbers of successes and
how many numbers of fails. The portion of success
comparing to the number of trials is the value of
Project Reliability. For this purpose, we can easily
utilize Monte Carlo Simulation approach.
The problem here, we have to deal with 3
parameters in each activity. Those 3 parameters have
relationship each other and form an uncertainty. For
Cost and Time relationship maybe it’s not a big
problem since many references already discussed
about this issue [5,6,19]. For Quality-Time and
Quality-Cost, the relationship forms depend on how
we define the quality on this model. If quality is
defined as an index as discussed in Babu and Suresh
[2], the problem maybe in the practical point of view
and how to translate each Quality definition in each
activity into an index that ‘apple to apple’. Rather
than using this definition, we would like to use
another definition of quality that was already defined
by Burati etal. [4]. This definition later on drive us to
use and did little bit modification on the Project
Network proposed by Dawson and Dawson [10]
221
called Generalized Activity Network. By this
modification,
we
can
transform
each
Quality-Cost-Time from beginning to the end
activities of the project easily. The detail development
of our proposed idea is shown in subsection 2.1 and
2.2.
2.1 Quality-Cost-Time (Iron Triangle) Relationship
This section is trying to explain about the basic
concept of cost and time relationship, the quality
definition, and the quality association with the
additional cost and/or time due to failed to meet the
quality level. Based on those concepts, we can
develop a conceptual model of Quality-Cost-Time
relationship in section 2.2.
2.1.1 Cost and Time Relationship
Bromilow [3] propose an idea on how to model
total time and total cost relationship. They developed
an equation based on historical data aimed to predict
the construction time in form of the formula: T=KCB.
T is the duration of construction; C is the final cost of
building in millions of dollars adjusted to constant
labour and material prices; K is a constant describing
the general level of time performance for an
Australian $1 million project and B is a constant
describing how the time performance is affected by
project size as measured by cost. This equation then
tested by Chan [5] for Malaysia case studies.
Although it was developed for the total cost and
total time in a project, this method can be used to
develop activity cost and time relationship if there is
any similar experience in the past (historical data).
How if there is no historical data? In this situation,
then we must rely on the subjective estimation by an
experienced Project Manager. A good approach was
provided by Taylor and Davis [19]. Taylor and Davis
[19] assumed that the activity duration followed the
beta/constant distribution and the cost is deterministic
which consists of set up cost and variable cost. The set
up cost is independent to the time, but the variable
cost is dependent on how many days spent in each
activity (where the time is random variable).
Sometimes each activity has only one of either set up
or variable cost, or both. It’s conditional situation,
depend on the cost perception in each activity.
The illustration given by Taylor and Davies [19]
maybe is the most probable methods during the
planning stages, which is the time and cost both are
random variable or the cost is a function of time
(dependent on time). About the form of distribution,
the time and cost actually have free form, depend on
the case. Most of the case assumes it followed Beta
Distribution due to the PERT logic. Actually, a
planner may substitute the time distribution with any
continuous distribution form i.e.: normal, exponential,
triangular, or a discrete distribution form i.e.: Poisson,
discrete uniform, etc. [13]. The concept of setup and
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International Journal of Electronic Business Management, Vol. 9, No. 3 (2011)
variable cost can also be improved. Let’s say an
activity consists of procurement and installation, then
we can separate the cost of the activity into 2 part,
fixed cost for procurement with certain days (due to
contractual issue) and variable cost for installation
UNCERTAIN
ENVIRONMENT
Time
process with uncertain days. Another improvement
form that might occur that we can imagine can
describe as Figure 2.
Project Reliability:
Pr { Project Perform over or equal to the target }
Duration <=
x days
Quality
Target
(and form)
Cost
How to transforming Time, Cost and Quality value
from beginning to end of project network and
aggregating each target
Do the QualityCost-Time
relationship
requires special
form of Project
Network?
Cost <= y
US$
Meet Quality
Target
B
A
D
E
C
Figure 1: The framework of the proposed Idea
A c t iv it ie s
PDF
G ra p h
A / D u ra tio n
P o is s o n ( 2 8 , a n d T r u n c a te ( 2 6 ,3 1 ) )
B / D u ra tio n
D is c r e t e ( { 1 4 ,1 5 ,1 7 ,1 8 ,1 9 ,2 0 ,2 1 ,1 6
} ,{ 0 .1 ,0 .1 ,0 .1 5 ,0 .2 ,0 .1 ,0 .0 1 ,0 .0 5 ,0
.2 }
C / D u ra tio n
P o is s o n ( 2 7 , a n d T r u n c a te ( 2 0 ,3 4 ) )
D / D u ra tio n
D is c r e t e U n if o r m ( { 8 ,9 ,1 0 ,1 1 ,1 2 } )
E / D u r a t io n
D is c r e t e ( { 1 7 ,2 0 ,2 5 } ,{ 0 .2 ,0 .5 ,0 .3 } )
TIME/
TIME/
DURATION
DURATION
COST
COST
Name
Package (Fabrication, procurement,
delivery, etc.) Charged
A dditional Cost / day
Activity A
Triangular(900,1000,1300) for 1st 20
days. Cost of fabrication/procurement
E3
of the items of A. The duration is
fixed, but the cost is uncertain
Activity B
Material cost will follow normal
distribution (2400,200)
Activity C
The material cost would follow uniform
distribution (900, 1200) independent
E5
to the time/duration
Activity D
Activity E
E4
Each day activity D will be charged in
cost following Normal Distribution
(180,40)
0
The 1st 15 days the cost for
fabrication/procurement will somehow
fall in Triangular (400,620,900)
After fabrication/procurement, the rest
activity A is installation. It required
some days, uncertain. The cost required
per day is following Normal
Distributionl(200,40)
For each installation days the cost will
be charged following Normal distribution
(100,15) / days
E7
the next after 15 days, the project cost
will be charged following uniform
distribution (300,350) / day
Figure 2: Various time and cost relationship form
2.1.2 Quality Definition and its Association with
Time and Cost
In this paper, we define Quality as
"conformance to established requirements." This
definition provides a basis for measurement, i.e.: the
requirements are either met or not met [4]. For
non-conformities, it is called as Deviation. Deviation
includes changes to the requirements that results in
rework, as well as products or results that do not
conform to all specification requirements, but do not
require rework [7].
In Burati et al. [4] the quality is a representative
of the scope of project, which is defined in earlier and
it’s completed with the associated cost. Absolutely, we
can see this situation as a Bernouli trials with the
probability to meet a quality level as a successful
process (with value of p) and a probability to fail meet
quality level as failure process (1-p=q). Now, how if
Y. A. Saputra and O. S. A. Ladamay: Project Reliability
223
there is any failure process (non-conformities)? From
the literature review, there are some corrective actions,
i.e.:
• Reprocessing (loop the process again). It might
charge us additional cost and additional time to the
original/baseline process, due to we must repeat
the process [10].
• Rework or repair. It might charge us also some
additional cost and time. In most situations, the
amount is lower than original process, but in some
case, it probable to have additional time and cost
higher than the original process [4,17]
When we try to enrich another possibility about
what happen if we fail to meet the quality, we found
another situation, i.e.:
• In some project, the extreme consequences of
non-conformities sometimes made the project fail
[19]. If this happen, it might charge us cost but not
time.
• In product design, failed to meet a standard have
means activating another scenario or alternative
pathways to develop a product with lower level
quality [20]. Some pharmaceutical industry
experiencing with this situation when they develop
their product. This situation might charge us some
additional cost and time.
• In practical, we also found there is a situation that
non-conformity still might be accepted by the
project owner but it is charged by some penalty (In
some management or IT project, Burati et al. [4]).
2.1.3 The Conceptual Model of Quality-Cost-Time
Relationship under Uncertainty
Therefore, the relationship between the
Quality-Cost-Time can be described in Figure 3. We
start the discussion with a standard process which
consist of baseline time and baseline cost (as
described in 2.1.1). If the process have quality
requirement, then a Quality Checking (Meet or not
meet with the requirement) mechanism is required (as
described in 2.1.2). If the result can meet the
requirement (success=p) means we can go thorughly
the next process. If the result fails (q=1-p), then the
next question is what kind of corrective actions is
needed or any consequences for this situation (one
from five possibilities as discussed in 2.1.2).
Whatever the corrective actions/consequences, it
would charge us some additional time and/or cost.
Moreover, the Figure 3 is representing our
conceptual model for Quality-Cost-Time relationship.
The time is represented by the baseline time and
additional time if the QC process indicates failure to
meet quality requirement. Cost is represented by cost
function and additional cost if QC process indicates
failure to meet quality requirement. And the quality is
represented by a QC mechanism with success and
failure probability and a set of options for corrective
actions/consequences for failure situation.
Figure 3: Quality-cost-time relationship model
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International Journal of Electronic Business Management, Vol. 9, No. 3 (2011)
2.2 Modification on Generalized Activity Network
as the Project Network to Accommodate the
Quality-Cost-Time Relationship
Our next question is how we select an
appropriate project network to accommodate the
transferring process of Quality-Cost-Time from
beginning to the end activity in the project. Standard
AoA or AoN can’t accommodate our relationship
model in Figure 3. We need a probabilistic branching
from the arch/node. For this purpose, we try to use the
Generalized Activity Network proposed by Dawson
and Dawson [9,10].
Initially, GAN is developed by introducing
probabilistic branching between activities in AoA type,
which is explicitly identified the uncertainties and
possibilities within a project's scope. There are 2
applications of GAN have been created over the year.
First is Graphical Evaluation and Review Technique
(GERT) in 1966 and second is Venture Evaluation
Review Technique (VERT) in 1967.
After so long, Dawson and Dawson [8]
criticized and made some clarification on previous
GAN. They showed some ambiguity and complexity
of previous GAN and identified it as the reason why
GAN never been established as famous
project-management techniques. By the provision of a
clearer definition of the GAN structure, they stated
that the generalized activity network should be prove
as the next logical step that managers can make in
planning ever more complex development projects. In
their clarification, they still use Activity on Arch
(AoA) as the form of network.
In 1995, Dawson and Dawson tried to propose a
modification of GAN (Activity on Arch based) to
Generalized Activity on Node Network. They claimed
that since the weakness of PERT to handle complex
project planning and managing uncertainties, GAN
have the ability to deal with that situation.
Unfortunately, GAN did not become familiar for some
Project Managers due to its limitation with Activity on
Arch (AoA) form. Dependency logic in GAN is hard
to understand in AoA form. On the other hand, most
of Project Managers are familiar with Activity on
Node (AoN) form as basis for famous PERT. Thus,
Dawson and Dawson tried to modify their previous
Develop Software
Triangular (4,8,12)
Implement
Beta (5,20,80)
clarification on GAN in the form of Generalized
Activity on Node Network.
Again, in 1998, Dawson and Dawson proposed
extensions of GAN to existing software tools to
specify and manage such uncertainties that would be
easy to learn and use. A survey has shown that if these
extensions were available, commercial and
government organizations would regularly use them.
Now, how was exactly their proposed idea on the
reform of GAN? Here, some of their proposed idea
and why their proposed idea matches with our
requirement
to
modeling
Quality-Cost-Time
relationship as we shown in Figure 3.
In two next figures (Figure 4 and 5), Dawson
and Dawson proposed a concept of looping. Some
activities may be performed more than once. Dawson
and Dawson [10] defined this type of activity can
occur if either alternatives input are specified or if the
task exists in a task loop. The probability may change
in each looping process. The simple example that was
used in Dawson and Dawson is “test and fix example”.
The test and fix example is a type of rework or repair
activity, which is an activity performed when the test
is failed (Figure 4). Another type of loop is
re-processing, which is if a test is failed, the project
must repeat some process before the test with same
duration and cost estimation as in the first looping
(Figure 5).
Figure 4: Example of rework/repair (Test and fix
looping process)
Test
Fixed (1)
0.4, 0.6, 0.8, 1
Maintenance
Triangular(0,5,200)
0.6, 0.4, 0.2, 0
Figure 5: Example of re-processing (Test process, if fail it back again to develop software process)
From figure 4 and 5, clearly we can get an
example on how rework/repair and reprocessing can
be accommodated in GAN. But how about the other 3
failure meet quality situation as we discussed in
subsection 2.1.2? How about the extensions form of
rework/repair and reprocessing above? We try to
make some modification of GAN proposed by
Y. A. Saputra and O. S. A. Ladamay: Project Reliability
225
Dawson and Dawson [9,10] to fit and adjust the
concept with our problem.
2.2.1 Rework Process
The Figure 6 shows a simple project network
consists of 2 processes, A and B. Activity A have
quality requirement, while B does not. Activity A and
B have basic time and cost function. For activity A, a
QC mechanism is performed (1B) to check does the
process (1A) have met the quality requirement. In first
attempt of QC, it has probability of success 0.8 and
probability to failure 0.2. If the 1A result passes the
QC test (1B), the Project can go to the next process
(Process B). If fail, the Project must be performed an
additional process. In the example, the additional
process type is rework (1C). An additional cost and
time due to the rework is charged to the total cost and
total duration.
Next, after performing the rework, the looping
process goes back to the QC test. In second attempt,
the process would never be failed; because during the
rework process there is a certainty to guarantee the
process to meet the standard of quality.
2.2.2 Stop the Project and the Extension the
Number of Looping in Rework Process
If the planner does not have certainty in number
of looping as shown in Figure 6, the planner can
modify this process. The looping process in Dawson
and Dawson [10] just assumed it allowed repeating
until X times, with probability of success at X-th trials
is certain (p=1). There is some potential improvement
about the concept of looping. Our propose concept of
looping is presented in Figure 7.
From figure 7 in process A, the QC test is
conducted with probability of success 0.9. The
maximum loop is unlimited. So in this type of activity,
the looping will continue until the first success occurs.
From the same figure in process B, the looping is
limited only for 3 times. In each QC test, the
successful probability is similar (0.9). If the process
can’t pass the QC test, then the project is terminated
(failed).
Figure 7: Extension of the looping process in GAN
2.2.3 Accepted at Below Quality Standard with
Some Penalties
Figure 8a shows a condition of accepted the
non-conforming with penalty cost as the
consequences. After the process 3a completed, the QC
test will be performed. If the QC test indicate a grade
= 100 (p=0.25), then the process succeeds. If the QC
test indicates a grade < 100 (q=0.75, with grade value
somewhere between 90-99.99%), the result is
accepted but penalty cost must be added by following
a specific function. The Additional cost due to penalty
must also be added to the total of project cost.
(a)
(b)
Figure 8: GAN for acceptance non- conforming by
add penalty cost (a) and reprocessing (b)
Figure 6: Simple project network with rework process
2.2.4 Re-processing
Figure 8b show the figure of re-processing.
After 4a completed, QC test is performed (4b). If
successful, it can go to the fifth process. If fails, the
process will loop back repeat the 4a process with
same time and cost probability distribution. The
number of looping in re-processing can be extended in
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International Journal of Electronic Business Management, Vol. 9, No. 3 (2011)
term of limited and unlimited looping, similar as
rework process in Figure 7.
2.2.5 Activating new path/scenario
The last model is activating new path/scenario
as shown in Figure 9. In the 9(a), the basic/main
process actually only process 1 (A) and process 3
(Assembly). Due to QC Checking mechanism on
process A, the process can’t go directly to process 3.
If fails the QC test at 1B, it will activate process 2
(Process B). Additional time and cost is required. The
new path will be: 1-2-3. The probability of success
passes the QC test at 1B is 0.7 and the failure
probability is 0.3. It’s also possible that the path will
have different ending point due to the difference of
quality output. This situation is possible in product
development project case. The situation is described
at Figure 9(b).
The alternative modification shown from Figure
6 until 9 are the most possible situation in the project.
Definitely there are any other improvement
possibilities to enrich the scenario based on each case
or PM’s creativity. However, we have given the basic
concept.
Figure 9: Activating new path or scenario for GAN
3. NUMERICAL EXAMPLE
A manufacturer awarded a contract to do a
project fabrication spare part called X-123. The scope
of job was shown in the Figure 10. The contract
agreed at 75 days and $575,000.00. 4 of 5 activities
above have QC mechanism. The activities with QC
mechanism are: Engineering Design, Process A,
Process B, and Process C. Engineering Design and
Process A have reworking additional process, Process
B has penalty additional process, and process C has
re-processing. The actual duration, success and failure
in QC test, and the cost of each activity is uncertain. If
the target passes all the process and its required
quality target, completion time <= 75 days and
spending budget <=$520,000.00 ($55,000.00 for
profit allocation), how to the probability meet these
targets?
ProcessAA
Process
Assembly
Assembly
ProcessBB
Process
ProcessCC
Process
Engineering
Engineering
Design
Design
Figure 10: Activity on node the fabrication of x-123
A small team is formed to develop a project
plan. The team consists of some experience
planner/PM. After conducting a detail assessment
based on past performance data and makes some
subjective probability, the form of uncertainty in this
project is shown in Figure 11. The management is
confidence to start the project if the reliability is
greater than 90%. The penalty cost will occur if the
completion time of the project is over than 75 days.
The penalty is 1/1000 to the total contract
($575,000.00) and must be added to the total project
cost. In the example, time is discretized. The process
B applies penalty cost which is followed the quality
function.
For conducting the experiment, we use @Risk
software from Palisade Decision Tools [16]. The
simulation is conducted for 15 replications, each
consist of 5000 iterations. After conducting the
experiment by applying a Monte Carlo Simulation,
here are some important statistics.
We found that the Probability of the Project will
complete less than equal to 75 days and under US$
520,000.00 is around 0.847770 ≤ µPr ≤ 0.853880
(95% Confidence Interval). This parameter indicates
the Project reliability is below the target (90%).
Y. A. Saputra and O. S. A. Ladamay: Project Reliability
227
0.20
0.15
0.10
0.05
0.00
-0.05
-0.10
Figure 11: The project network planning (modified of GAN) for x-123
Figure 12: Tornado diagram for the risk factors of the x-123 Project
Another important statistics i.e.: 1) Probability
to complete the project <= 75 days itself is 0.868,
while perform below the budget target is 0.938. 2)
The Project cost will follow normal distribution with
Φ US$(453,206; 44,097); 3) 15.41% of total cost and
16.66% the total duration is happened due to
non-conformity (Quality issue).
The
next
important
information
for
management is which factor has the big contribution
to the value of Project Reliability. For this purpose,
we develop a sensitivity analysis by conducting a
Tornado Diagram from each uncertainty variable. The
result is showed in Figure 12. Tornado diagram from
a sensitivity analysis display a ranking of the input
distributions (the risks events) which impact an
output (Project Reliability). Inputs that have the
largest impact on the distribution of the output will
have the longest bars in the diagram and located at
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International Journal of Electronic Business Management, Vol. 9, No. 3 (2011)
the top. From the Figure 12, we can understand the
Risk Profile from each variable in the project to the
comprehensive Quality-Cost-Time target which is
represented by Project Reliability. Further Risk
Analysis may be required as Post Project Reliability
Analysis.
5.
6.
4. CONCLUSION
This research has shown about how and the
importance of comprehensive evaluation on the Iron
Triangle (Quality-Cost-Duration) in a project under
uncertainty situation. We introduce an index called as
Project Reliability. By modeling the quality as a
success/failure process, Project Reliability becomes
an index of measurement to evaluate the probability
of project completion within the time and cost target
and passes the entire QC requirements.
Even maybe looks so complex and lead the
managers have a little base on their estimate due to a
vague value of probability, all the proposed method
above still become important and worth to conduct.
Understanding the nature of all possibilities and
accommodating the risks in decision is worth in
managing the project. Finally, we have developed a
comprehensive overview about measuring of success
probability regarded with Iron Triangle. Moreover,
numerical example is provided to show how the
implementation of the proposed concept above. Is
this approach worth to be applied? The answer is
similar as Dawson and Dawson [10]. In many high
cost and risk project, which is a comprehensive
evaluation required (i.e.: Product Development
Feasibility Project Proposal), this approach is
important to be applied as input for decision making,
i.e.: running the project normally, run with some
further decision/consideration, or stop the project.
7.
8.
9.
10.
11.
12.
REFERENCES
1.
2.
3.
4.
Atkinson, R. A., 1999, “Project management:
Cost, time and quality, two best guesses and a
phenomenon, its time to accept other success
criteria,” International Journal of Project
Management, Vol. 17, No. 6, pp. 337-342.
Babu, A. J. G. and Suresh, N., 1996, “Theory
and methodology: Project management with
time, quality, and cost considerations,” Journal
of Operational Research, Vol. 88, pp. 320-327.
Bromilow, F. J., 1974, “Measurement and
scheduling of construction time and cost
performance in the building industry,” The
Chartered Builder 10.
Burati Jr., J. L., Farrington, J. J. and Ledbetter,
W. B., 1992, “Causes of Quality deviations in
Design and Construction,” Journal of
13.
14.
15.
16.
Construction Engineering and Management,
Vol. 118, No. 1, pp. 34-49
Chan, A. P. C., 2001, “Time-cost relationship of
public
sector projects
in
Malaysia,”
International Journal of Project Management,
Vol. 19, pp. 223-229.
Chou, J. S., 2010, “Cost simulation in an
item-based project involving construction
Engineering and management,” International
Journal
of
Project
Management,
doi:10.1016/j.ijproman.2010.07.010
Davis, K., Ledbetter, W. B. and Burati Jr., J. L.,
1989, “Measuring design and construction
quality costs,” Journal of Construction
Engineering and Management, Vol. 115, No. 3,
pp. 385-400.
Dawson, C. W. and Dawson, R. J., 1994,
“Clarification of node representation in
generalized activity networks for practical
project management,” International Journal of
Project Management, Vol. 12, No. 2, pp. 81-88.
Dawson, C. W. and Dawson, C. J., 1995,
“Generalised activity-on-the-node networks for
managing uncertainty in project,” International
Journal of Project Management, Vol. 13, No. 6,
pp. 353-362
Dawson, R. J. and Dawson, C. W., 1998,
“Practical proposals for managing uncertainty
and risk in project planning,” International
Journal of Project Management, Vol. 16, No. 5,
pp. 299-310.
Elkjaer, M., 2000, “Stochastic budget
simulation,” International Journal of Project
Management,Vol. 18, No. 2, pp. 139-147.
Huang, J. W., and Wang, X. X., 2009, “Risk
analysis of construction schedule based on
PERT and MC simulation,” In: International
Conference on Information Management,
Innovation Management and Industrial
Engineering, ICIII 2009, pp. 150-153.
Kidd, J. B., 1987, “A comparison between
VERT program and other methods of Project
Duration Estimation,” Omega, Vol. 15, No. 2,
pp129-134.
Lee, D. E. and Arditi, D., 2006, “Automated
statistical analysis in stochastic project
scheduling
simulation,”
Journal
of
Construction Engineering and Management
Vol. 132, No. 3, pp. 268-277.
Lu, M. and AbouRizk, S.M., 2000, “Simplified
CPM/PERT simulation model,” Journal of
Construction Engineering and Management,
Vol. 126, No. 3, pp. 219-226.
Palisade Corporation, 2009, Guide to using
@RISK: Risk Analysis and Simulation Add-In
for Microsoft® Excel, Palisade Corp., New
York, USA.
Y. A. Saputra and O. S. A. Ladamay: Project Reliability
17.
18.
19.
20.
21.
Project Management Institute, 2008, A guide to
the Project Management Body of Knowledge
(PMBOK® Guide) (4th Edition), PMI Inc.,
Penssylvania, USA.
Tareghian, H. R. and Taheri, S. H., 2006, “On
the discrete time, cost, and quality trade-off
problem,”
Applied
Mathematics
and
Computation, Vol. 181, pp. 1305-1312.
Taylor, III. B. W. and Davis, K. R., 1978,
“Evaluating
time/cost
factors
of
implementation via GERT simulation,” Omega,
Vol. 6, No. 3, pp. 257-266.
Ulrich, K. T. and Eppinger, S. D., 2008,
Product Design and Development (4th edition),
Mc Graw Hill, New York, USA.
Williams, T., (1999), “Towards realism in
network simulation,” Omega, Vol. 27, No.3, pp.
305-314.
229
ABOUT THE AUTHORS
Yudha Andrian Saputra is a Lecturer at Department
of Industrial Engineering at Institut Teknologi
Sepuluh Nopember (ITS) Surabaya, Indonesia. He
received his Bachelor Degree (in Industrial
Engineering) from ITS Surabaya and MBA from
Department of Industrial Management of National
Taiwan University of Science and Technology. He
has practical experience and involved on many
project management and consultancy in several
private and government institutions in Indonesia. His
research interests are: Simulation, Decision Analysis,
Risk Analysis, and Strategic Management.
Ode Siti Andini Ladamay is a staff at The 10th
BPBPJN, Ministry of Public Works Republic of
Indonesia. She has responsibility to prepare bidding
documents and monitoring several road projects in
Papua Island, East of Indonesia. She received her
Bachelor Degree (in Civil Engineering) and Master
(in Industrial Engineering) from ITS Surabaya.
(Received May 2011, revised August 2011, accepted
September 2011)
230
International Journal of Electronic Business Management, Vol. 9, No. 3 (2011)
工程可靠度：
在不確定性下工程達到品質－成本－工時目標的機率
Yudha Andrian Saputra1*、Ode Siti Andini Ladamay2
1
工業工程系
Institut Teknologi Sepuluh Nopember (ITS)
印尼東爪哇泗水市
2
印尼公共工程部
印尼巴布亞新幾內亞查亞普拉
摘要
品質、成本、與工時這三者長久以來一直是測量工程是否成功的鐵三角。許多研究探討
這三者在不確定性下的工程網路圖，大都著重探討單一指標(質量/成本/工期)或是結合多
重指標 (折衷指標間的關係)。但在工程計劃階段，滿足這三樣指標的要求是重要的。在
管理上可以得知工程計劃在一定信賴水準下，達到目標、了解潛在的不確定的因素的相
關資訊是十分有用的。然而，過去的研究並未將這三項指標結合在不確定性下作探討。
如果品質的定義如下：1) 為一可能達到的標準或條件； 2) 對於額外成本或額外工時會
有不一致性的結果及影響；3) 此外，工時和成本本身也有其關聯及其不確定性。我們提
出的驗證方法在不確定性下，檢測工程是否能夠達到其品質-成本-工期目標的機率，此即
工程可靠性。並使用蒙特卡羅模擬及一般化活動網路圖檢測。同時本文利用多個樣本支
持及驗證本文所建議的方法。
關鍵詞：品質－成本－工期、一般化活動網路圖、蒙特卡羅模擬、不確定性
（*聯絡人：[email protected]）