Construction Management and Economics (January 2006) 24, 81–96
Expert elicitation and Bayesian analysis of construction
contract risks: an investigation
FRANCIS K. ADAMS*
School of Construction, College of Science & Technology, The University of Southern Mississippi, Box #5138,
Hattiesburg, MS 39406, USA
Received 25 November 2004; accepted 15 July 2005
Formal risk analysis techniques applied in managing construction project risks tend to focus on risks that lend
themselves to ‘objective’ methods of economic analysis. Although subjective probabilities and Bayesian
methods are applied successfully in other industries to manage ‘subjective’ risks similar to those encountered in
construction contracts, very little is reported on the application of such methods for analysing risks in
construction contracts. An investigation has been carried out into using subjective expert opinions and Bayesian
methods in construction contract risk analysis. The elicitation of expert opinions about the risk of encountering
adverse ground conditions on construction sites is examined. Prior distributions of expert opinions about the
risk form the critical component in the Bayesian analysis of risk. The conclusion of this is that although
construction professionals have difficulty estimating intermediate and tail values of probability distributions,
elicitation techniques can be used to develop prior distributions of contract risks which, coupled with sample
information on the risks, would enable the Bayesian analysis of risks. Effective strategies for systematically
analysing significant individual contract risks often covered under an ‘arbitrary’ project contingency sum can
now be developed to enhance the risk management efforts of contractors and construction experts.
Keywords: Subjective probabilities, elicitation techniques, Bayesian analysis, risk analysis, Delphi techniques
Introduction
In terms of the broad approaches by which risks are
analysed, construction project risks can be broadly
classified as either objective or subjective. Risks that are
purportedly analysed by the actual observation or
calculation of their occurrence and impact on a project
are often described as ‘objective’ risks. Analyses of
‘objective’ risks are quantitative in nature and often
structured in probabilities. They involve experimental
evidence, long-term experience, or complicated analytical calculations that describe actual or potential risks.
Risks that are assessed based on beliefs about the risks
rather than ‘objective’ recorded risk data are often
referred to as ‘subjective’ risks. Analyses of ‘subjective’
risks are often qualitative and based on the analyst’s
knowledge and experience of the risks and the process
* E-mail: francis.adams@usm.edu
by which the analyst selects and organizes such knowledge and experiences into meaningful patterns. The
majority of construction contract risks are subjective;
there are often insufficient historical data to enable
their ‘objective’ analysis.
The use of rigorous analytical techniques for
objective risks in construction is well reported in the
literature. However, reports of empirical work on the
application of similar rigor to contract risks such as
payment delays, adverse ground conditions, etc., is
scant. Evidence suggests that such risks are often
analysed in a somewhat arbitrary manner.
Contractors tend to resort to the addition of a single
arbitrary percentage cost contingency to give their
overall impression of the total risk rather than assessing
the risks that they are asked to carry. However,
applications of analytical rigor to similar risks in other
industries point to the potential benefits that such
methods present to the construction industry. For
Construction Management and Economics
ISSN 0144-6193 print/ISSN 1466-433X online # 2006 Taylor & Francis
http://www.tandf.co.uk/journals
DOI: 10.1080/01446190500310254
82
example, subjective probability forecasting has been
used reliably, in combination with classical methods
involving objective probabilities, in short-range weather
forecasting (Murphy and Winkler, 1984). Elicitation
of expert beliefs has been used in the development of
probabilistic expert systems for the diagnosis of
congenital heart disease (Spiegelhalter et al., 1994)
and in population projection (Kadane and Wolfson,
1997). Elicitation of prior beliefs has also been
successfully used in estimating the future maintenance
costs of water treatment plants, in determining the
hydraulic conductivity of rocks for nuclear waste
repository development (O’Hagan, 1997), and in
uncertainty analysis for radiological protection
(O’Hagan and Haylock, 1997).
Subjective predictions made on the weather are
based on the forecaster’s knowledge and experience of
weather patterns in much the same way as a construction expert’s knowledge and experience of soil characteristics that lead to risks such as adverse ground
conditions drive his predictions about such risks.
Furthermore, unlike recurring events that are subject
to the laws of large numbers, most contract risks
represent rare event samples for which analysis of longrun frequency and traditional statistical approaches are
often inapplicable. Tversky (1974) argues that predictions and analysis of such subjective risks are often
based on the intuitive judgements of the decisionmaker. These intuitive judgements and estimates are
influenced by individual perceptions and biases that are
often not addressed during the analysis. Analytical
methods for construction contract risks are thus needed
to enhance risk management efficiency. Bayesian
methods, for example, enable subjective opinions about
uncertainties to be combined with sample evidence
about the risk to form posterior probability distributions of the risk. Such distributions can then be used as
input variables in the systematic analysis of the
uncertainty. The adjustment of the individual expert’s
estimate by the available sample information will lead
to a more accurate representation of the probability of
the risk. Furthermore, an appropriate design of the
elicitation method and aggregation of opinions from
multiple experts can reduce the impact of individual perceptions and biases on the estimates (Adams,
2004).
This article reports on an empirical study that
investigated the use of elicitation and Bayesian methods
in transforming expert opinions into subjective probability distributions for use as input variables in
construction contract risk analysis. Specifically, the
article discusses some of the issues involved in eliciting
expert opinions from construction experts and
addresses the issues of
Adams
(a) whether expert elicitation techniques used for
objective risk analysis can be extended to
construction contract risk analysis; and
(b) whether elicited subjective expert opinions on
construction contract risks can be transformed
into subjective prior distributions for Bayesian
analysis of the risks.
If the two tasks above can be achieved, then a more
effective and systematic strategy for contract risk
management could be developed to replace the current
practices of assigning arbitrary contingency sums or risk
premiums for the overall contract risk. This strategy
will be helpful not only to contractors who share the
great bulk of project risks, but also to construction
experts who give advice for proper project risk
management.
Assessing the risk of adverse ground
conditions
Geotechnical investigation reports provide information
on the type of soil that contractors can expect to deal
with. Nevertheless, the contractor still has to rely on the
experience of the relative occurrences of ‘adverse
ground conditions’ among different soil types, site
conditions and site history to make judgements about
the risk of adverse ground conditions on any site. For
example, assume that a geotechnical investigation
reveals potential excavation problems on the soil type
that is considered mainly gravel. The contractor will be
interested in answering the question: What is the
probability that the risk of adverse ground conditions on
the project would be encountered given the potential problems
with the mainly gravel soil?’ The research sought to apply
expert elicitation techniques and Bayesian analysis to
help answer this question. This involved three key
tasks:
(i)
developing a model for eliciting subjective
opinions of construction experts about the risk;
(ii) eliciting subjective estimates from construction
experts using the model in (i); and
(iii) developing the elicited estimates into subjective
prior probabilities for Bayesian analysis.
Bayes theorem, subjective probability and
contractual risks
Bayes theorem starts with the precept that through
frequency observations we are able to determine the
probability of an effect occurring. We are also similarly
83
Construction contract risks
able to determine the conditional probability of the
effect, given its cause, by observing the number of times
the cause had exhibited that same effect. We can then
determine the ‘reverse’ or posterior probability of the
cause from the effect (Vick, 2002). Thus if
P ½cause~probability that the cause occurs
P½effect~probability that the effect occurs
P½effectjcause~conditional probability of the effect
given the cause
given the effect,
then Bayes theorem in simple terms is stated as
P ½effect jcause:P ½cause
P ½effect ð1Þ
from which we also derive the posterior probability of the
cause from the effect as
P ½effect jcause~
P ½causejeffect :P ½effect P ½cause
P ðxÞ~P ðh1 Þ:P ðxjh1 ÞzP ðh2 Þ:P ðxjh2 Þ
X
~
P ðhi Þ:P ðxjhi Þ
ð3Þ
P ðxjh1 ÞP ðh1 Þ
P ðh1 jxÞ~ P
P ðhi Þ:P ðxjhi Þ
ð4Þ
And
P ðxjh1 Þ~
P½causejeffect~conditional probability of the cause
P ½causejeffect ~
and Bayes theorem in Equations 1 and 2 above:
ð2Þ
This reasoning may be applied mathematically to the
issue of adverse ground conditions explained above.
The risk of adverse ground conditions on a project can
be caused by a number of factors including the
geological profile of the site (soil type) and the past
use of the site (e.g. dump site, mining site, archaeological site, etc.). Suppose we represent
(a) the probabilities associated with problems with
soil type by P(h1)
(b) the probabilities associated with the other
factors or sources of the risk of adverse ground
conditions by P(h2), ….P(hn)
(c) the probabilities of adverse ground conditions
(event ‘x’) resulting from the occurrence of the
causes of adverse ground conditions by P(x|h1),
P(x|h2),…… P(x|hn)
(d) the probability that adverse ground conditions
would be caused on a project by problems with
the type of soil P(h1|x)
P
and determine
P ðhi Þ:P ðxjhi Þ, the number of times
adverse ground conditions have occurred on a specified
number of projects of similar sites over a period of time
irrespective of the cause. This is obtained from sample
evidence as the ratio of the sum of the occurrences of
adverse ground conditions on similar sites in the given
period, to the total number of similar sites over the
same period. We can determine P(h1) by how often we
find in a sample of projects with gravel soil profile that
there were problems with this soil type. We can thus
determine the following from the laws of probabilities
P ðh1 jxÞ
P
P ðhi Þ:P ðxjhi Þ
P ð h1 Þ
ð5Þ
As Equation 2 indicates, Bayes theorem requires that
we know something about the posterior probability that
we seek even before bringing the sample evidence into
play. Bayesians argue on the basis of Bernoulli’s
theorem and similar reasoning, that the prior in
Equation 2 is a subjective probability (Vick, 2002). The
argument here is that one can always start with a belief
regarding the probability of an outcome (prior probability), and increase the degree of belief about the
value of the probability by revising the probability
assessments as new information become available. In
line with the postulates of subjective probabilities, this
approach does not attempt to specify what probability
is ‘correct’, but accepts all self-consistent or ‘coherent’
assessments of an observer as admissible evidence, as
long as the individual feels that they are consistent
with his or her belief. By eliciting expert estimates
for P(x|h1), the probability of encountering
adverse ground conditions given a gravel soil profile,
we can thus determine P(h1|x) using Bayesian
methodology.
In their study on judgemental forecasting however,
Wright and Ayton (1987) were surprised to find the
lack of significant relations between coherence and
forecasting performance (calibration) since the two
ways of evaluating the adequacy of a forecaster are
logically related. A measure is calibrated if, for all
events assigned a probability encoding p, the proportion that actually occurs, or is true, is in fact p (Wallsten
and Budescu, 1983). Wright and Ayton (1987) therefore argue that while an incoherent forecaster cannot be
well calibrated, it does not follow that consistency or
coherence necessarily produces good calibration. The
key issue here then is that for the estimates to be
meaningful, the forecaster has to be well calibrated.
Wallsten and Budescu (1983) demonstrated in their
study on probability encoding by experts that exceedingly high calibration can be demonstrated by experts
when encoding subjective probabilities about events
with which they are familiar, whereas a similar degree
of goodness has rarely been demonstrated by nonexperts in the field. Substantive experts required to
84
encode subjective probabilities within their areas of
competence are thus considered to be calibrated.
The use of Bayesian methods has however, not been
without critics. Mak (1995), for example, argues that
the Bayesian assumptions of mutual exclusivity,
exhaustive hypothesis and conditional independence
of evidence in hypothesis do not always hold.
Furthermore, the Bayesian view does not allow one to
distinguish uncertainty from ignorance in that one
cannot tell whether the degree of belief was directly
calculated from evidence or indirectly inferred from an
absence of evidence. Mak (1995) further argues that
because the single degree of belief is represented by a
point estimate, it is difficult to verify its accuracy.
Phillips (1973) and Chau (1995) argue however, that
the issues of vagueness and dependence arise due to the
human inability to handle complex events and systems.
Reliability of the estimates decreases as the event/subsystem increases in size and complexity. Thus, by
decomposing complex events/sub-systems into simple
units, making judgements about the simple units and
then reassembling the pieces using the laws of probability, we can confidently arrive at consistent and
meaningful probabilities regarding the original complex
events. Chau (1995) further argues that construction
estimators’ estimates are not random ‘guess-timates’
but are based on experiences that include historical
facts that may not necessarily be recorded systematically in the estimators’ minds. Furthermore, the
issues of bias due to differences in individual perceptions and range of experiences can be reduced through
group estimating techniques such as the Delphi
technique.
A model for eliciting subjective probabilities
of contractual risks
Based on published work on elicitation and heuristics,
including the works of Tversky (1974), Tversky and
Kahneman (1974), Chelsey (1975), Spetzler and Von
Holstein (1975), Kahneman et al. (1982), Hertz and
Thomas (1984), Chapman and Ward (1997) and Vick
(2002), a model for eliciting subjective estimates of
contractual risks was developed for the present study.
The outline of the model, which describes the process
and methods used for eliciting subjective estimates for
the study, is summarized in Table 1.
The model represents an idealized view of the
approach that might be implemented by a corporation
with sufficient resources. The goal of the study reported
here was however different from the corporate setting.
As an investigative research, there is a need to
determine by a ‘pilot’ study whether the model is likely
Adams
to be successful and whether it can be made more
successful by adaptation. In such circumstances, it is
desirable to be more flexible with the approach in order
to examine these questions. Hence, the study did not
directly implement the model but took essential
elements of the model to explore how they would
function.
Methods and techniques for eliciting
subjective estimates from experts
Approaches to expert elicitation may be described as
Individual or Group Assessments. In the Individual
Assessment approach, expert beliefs are elicited from
the individual using an assessment technique that
allows either self-elicitation or interviewer-elicitation.
In self-elicitation, each subject elicits their own
estimates either alone or within a group setting. In
interviewer-elicitation, a trained assessor elicits the
probabilities from the individual or group of individuals. Ashton and Ashton (1985) discovered that
generally, weighted aggregates of subjective individual
estimates are more accurate than the individual
estimates that comprised the aggregates. The aggregate
estimates are also better when the weights applied to
the estimates incorporate the relative accuracy of the
individuals involved. Also, much of the total gain in
forecast accuracy attributable to aggregation can be
achieved by combining a small number of individual
forecasts.
The Interacting Group, the Nominal Group and the
Delphi Group Assessments are the three main
approaches to Group Assessments. In the Interacting
Group approach, an initial group discussion on the
qualitative property to be measured is followed by a
group estimate. In the Nominal Group approach,
individuals make their initial estimates. This is followed
by a group discussion on the subject and estimates, and
the revision or confirmation of the individual estimates
to reach a group estimate (Chelsey, 1975; Lock, 1987).
Traditional Delphi techniques involve bringing
together individuals who then make independent
estimates about the issue in question. The estimates
are then aggregated by a central group who then
provide feedback on the group results to the individuals. The individuals subsequently confirm or revise
their estimates until either a group consensus is reached
or a satisfactory group variance level is achieved
(Robson, 1993). De Wit and Meyer (1994) describe
the following revised Delphi methodology used in
macro-environmental analysis:
(i)
identifying recognized experts in the area of
interest;
85
Construction contract risks
Table 1
A model for eliciting subjective probabilities of contractual risks
Phase
Preliminaries
Purpose(s)
Prepare for Process
Define the risk Problem
Develop Elicitation/Assessment
Schedule/Questions
Expert Selection
Expert Elicitation
Set up appointments for elicitation/mail
Assessment Schedule
Have Experts formulate and encode their
estimates
Analysis of Subjective
Judgements
Assign numerical probability values to
expert judgements
Assign numerical probability values to
aggregate values of elicited
judgement
Process steps
N Confirm need for Elicitation exercise
N Appoint, brief and train Probability Assessor/
Facilitator
N Establish Elicitation Objectives and Approach
N Establish Process budget for time, cost and
human resources
N Confirm project definition
N Clarify uncertainty and clearly define risk(s) for
which prior estimates are being sought
N Decompose risks and define decomposed risks if
necessary
N Obtain sample evidence for risk(s)
N Define questions using the relative likelihood’ and
Direct Response methods
N Define questions using a continuous variable
scaling technique and Direct Response methods
N Determine appropriate professional categories
N Determine appropriate industrial sector of
expertise
N Determine Extent of relevant professional
expertise
N Establish target expert group
N Obtain actual experts through prequalification
N Introduce the Assessor/Facilitator
N Explain the purpose of the elicitation
N Leave the elicitation schedule or arrange an
appointment for the elicitation interview
N Discuss Feedback processes and their possible
further involvement in the process.
N Motivating the subject by establishing rapport and
investigating the subject’s biases.
N Structuring the uncertain quantity by having it
clearly defined and explained to the expert.
N Conditioning the subject by making the subject
think fundamentally about his judgement and to
avoid any of his cognitive biases.
N Encoding or quantifying the probability judge
ments, and
N Verifying the responses by checking for consistency
and seeing if the subject believes his results.
N Obtain estimates of full range of risk attributes
through smoothing and scaling of expert estimates
N Convert smoothed estimates into coherent prob
abilities that sum up to unity
N Map and define probability distribution
N Define appropriate weighting for aggregation of
estimates
N Aggregate estimates using selected weighting
N Obtain estimates of full range of risk attributes
through smoothing and scaling of aggregated
estimates
N Convert smoothed estimates into coherent prob
abilities that sum up to unity
N Map and define probability distribution
86
(ii)
(iii)
(iv)
Adams
seeking their co-operation and participation;
providing the experts with an initial position
paper on the status of the issue; and
eliciting the opinions of each expert through
personal interview(s).
Although the nominal group approach is considered
superior to the other group approaches (Chelsey, 1975;
Gustafson et al., 1973), it is most appropriate where the
individuals can be brought together to discuss the risk
concerned and the estimates given. The high expense
and impracticality of getting all the experts involved in a
group setting made this approach unfeasible for the
research. A hybrid consisting of the individual assessment method, the revised Delphi group approach and a
vignette technique was therefore adopted for this study.
Traditional vignette techniques present short stories
about hypothetical characters in specified circumstances to which the interviewee is invited to respond
(Finch, 1987). The vignette used in this research
consisted of a brief description of a construction project
to provide a background to the set of questions that the
experts were invited to respond to. The responses
sought were the experts’ estimates of the relative
likelihood of occurrences of risk of adverse ground
conditions on a set of projects similar to the one
described in the vignette.
For this research, step (iii) of the revised Delphi
approach consisted of mailing a semi-structured interview/questionnaire schedule (the elicitation schedule)
that had a fixed set of questions to which the preselected experts were to respond. In consideration of
what the normal practice is, the experts were encouraged to consult other colleagues or experts in clarifying
their opinions about the probabilities. Also, since the
elicitation schedule allowed both self-elicitation and
interviewer-elicitation, experts were free to complete
and mail or fax their responses if they so preferred. The
mailing of the schedule was followed by a preelicitation phone discussion within seven days of
mailing. The objective of this follow-up phone call
was threefold. First, it was to confirm the receipt of the
elicitation schedule. Second, it was to provide detailed
information and explanation on the research and the
elicitation schedule to ensure that each expert had a
depth of understanding similar to what they would have
in a traditional Delphi approach. Third, it was to
ensure that each expert actually did reflect on the issues
raised in advance of any elicitation interview. The
following additional steps were completed following
step (iv) of the revised Delphi approach:
(i)
aggregating the individual expert opinions to
form a group opinion;
(ii) providing feedback to experts. The objective
was to seek consensus among the group
regarding the most appropriate distribution
form for the risk; and
(iii) reaching a final group consensus. To achieve
group consensus in the absence of bringing all
respondents together in one place, each respondent was asked, after completion of their
questionnaire/interview schedule, how they
would view their own responses in the light of
the group aggregate that would emerge from the
study. The options were for the experts to
maintain their original individual estimates,
adjust the estimates in view of the group
aggregate, or accept the group aggregate as
being more accurate estimates about the risks.
The purpose of this approach to arriving at the
group consensus was to reduce ‘respondent
fatigue’ by minimizing the number of times that
a respondent was contacted by the researcher
on the same issue. All respondents indicated
that they would accept the group aggregate as
being more accurate estimates about the risks.
In their view, the group aggregate was the best
reflection of the collective experience of the
experts about such rare risks.
Encoding methodology and response
techniques
Questions posed during elicitation may require subjects
to respond either directly by providing numbers or
indirectly by choosing between simple alternatives.
Direct Response Techniques include the use of
cumulative probability and fractiles in which subjects
are asked to assign either the cumulative probability at
a given value, or the value corresponding to a
probability. Indirect Response Techniques require the
subject to choose between simple alternatives or bets.
This study employed direct response techniques by
asking open-ended belief questions that sought direct
estimates of probabilities from experts regarding the
occurrence of adverse ground conditions among
hundred typical projects described in the vignette.
Two methods of encoding subjective expert opinions
were also investigated. The first set of questions used a
‘relative likelihood’ method aimed at eliciting direct
estimates of probabilities to form the extremes and the
key intermediate values of the subjective prior probability distribution of the risk (Moore and Thomas,
1976; Chapman and Ward, 1997). The method
consists of four steps. First, estimates from the experts
about the risk are elicited in the following manner:
87
Construction contract risks
(i)
(ii)
(iii)
(iv)
the minimum value of the risk;
the maximum value of the risk;
the most likely or modal value of the risk; and
the modal value is assigned likelihood rating
units that represent the highest possible rating
for the risk (assume this rating is 60 units).
Key intermediate values of the risk are then obtained by
eliciting the following:
(i)
(v)
a value for the risk greater than the modal
value that is half as likely to occur as the modal
value (i.e. a likelihood rating of 30 units);
(ii)
(vi) a value for the risk smaller than the modal
value that is half also as likely to occur as the
modal value (i.e. a likelihood rating of 30
units);
(iii)
(vii) a value for the risk greater than the modal
value that is a quarter as likely to occur as the
modal value (i.e. a likelihood rating of 15
units); and
(iv)
(viii) a value for the risk smaller than the modal
value that is quarter also as likely to occur as
the modal value (i.e. a likelihood rating of 15
units).
In developing the questionnaire schedule, central bias
and anchoring were minimized by first eliciting the
extremes of the distribution (Budescu and Wallsten,
1987; Cooper and Chapman, 1987). This approach
also ensures the display of sufficient spread in the
distribution for the risk variable (Ranasinghe and
Russell, 1993). Although experts’ estimates were
expected to lie within a certain range, respondents
were not confined to specific response categories but
allowed to express their true opinions on what reflects
their reality.
The second step involves smoothing the elicited
estimates to ‘normalize’ the data and obtain likelihood
ratings for all the other possible variable values. The
values elicited from the experts are plotted on a Scatter
Diagram and a smooth curve drawn though the various
points. The likelihood rating values of all other possible
values of the risk are then obtained from the graph.
Thirdly, each rating value is scaled using the sum of all
the rating values to form probabilities that sum to unity.
The minimum and maximum values of the risk need
not have zero probabilities. Finally, the probabilities are
plotted to obtain the probability distribution of the
smoothed estimates of the experts, which thus represent their belief functions.
The second approach to opinion encoding employed
a continuous variable scaling technique (see Figure 1).
Experts were asked to indicate a point on a linear
probability scale (from 0 to 1, where 05never and
15certain) representing a value that closely represented
Figure 1
Continuous variable scaling technique
their degree of belief regarding a range of occurrence of
adverse ground conditions on a hundred similar
projects. The objectives for using the two approaches
were to provide a check on the consistency of the
experts’ responses, and to evaluate which method
construction experts found relatively easier to use.
This evaluation would advise the refinement of the
elicitation model.
Characteristics of the survey respondents
According the findings of Simonton (1996) and the
analysis of Vick (2002) on the development of
engineering expertise, it would appear that engineering
experts reach the height of their expertise between the
career ages of 10 and 33, which corresponds to
chronological ages of thirty-five and fifty-three.
Against this background, and in view of the specialist
nature of construction contract risks and the relative
infrequency of such risks, respondents were selected
from construction experts based on a minimum of ten
years of industrial experience. For this pilot research,
all the experts were initially sampled randomly from the
United Kingdom (UK) using directories such as the
Chartered Building Company’ Directory, the Contractors’
File and the Consultants’ File. Telephone and fax
surveys were then used to identify qualifying and
interested participants. A total of 160 experts comprising 40 each of quantity surveyors, project managers,
construction managers and contract managers were
selected. The breakdown of the responses from the 160
questionnaires sent to the selected professionals is given
in Table 2. The ‘other’ category in Table 2 represents
88
Table 2
Adams
Profile of the survey sample
Profession
Construction managers
Project managers
Quantity surveyors
Contracts managers
Othersa
Total respondents
Number selected
Number responding
Percentage responding
40
40
40
40
0*
160
2
4
18
1
4
29
5.00%
10.00%
45.00%
2.50%
10.00%
18.13%
a
The ‘Other’ category therefore refers to professionals such as directors of companies, property developers and legal consultants who felt that
their current job functions did not fit accurately into any of the four main categories indicated on the questionnaire.
respondents who no longer worked in any of the four
main professional categories originally selected.
As Table 2 shows, the majority of respondents were
either quantity surveyors or project managers. This
may be reflective of the fact that as one of the primary
repositories of construction cost and risk information,
quantity surveyors are best placed to provide the
required information. Although the effective response
rate of 18% appears small, it is consistent with survey
responses within the UK construction industry
(Simister, 1994; Baker and Smith, 1999; Burchett
et al., 1999). It is also not surprising for a questionnaire
survey (Nachmias and Nachmias, 1981). The low
response rate from construction managers was mainly
attributed to either inexperience or lack of time. These
were also the main reasons given for non-response by
the other 131 survey subjects who were unable to
participate in the study. Two facts explain this reason.
The first is that in view of the relative infrequency of
contractual risks, experts would need to have been in
the field that provides them with experience of the risks
for significant number of years for them to be able to
make informed judgements about the risks. Secondly,
for most non-responses, the questionnaire was completed by a junior staff member in the original expert’s
company due to lack of time on the part of the selected
expert. The problem was that the average experience
among such junior staff members (as revealed by the
Figure 2 Respondents by years of experience
average years of experience of the non-respondents)
was between 2–5 years.
With the exception of two respondents who were
construction managers, all the respondents had more
than 10 years of industrial experience (94% had more
than 15 years of construction experience), and over
80% had more than 10 years of experience in their
current profession within construction (see Figure 2).
This high percentage of highly experienced respondents
is very significant in the light of the works of Simonton
(1996) and Vick (2002) and lends further support to
the credibility of the information obtained. The annual
turnovers of almost 70% of the respondents were less
than five million pounds (41.4% had turnovers less
than £1 million, 27.6 % between £1 million and
£5 million, 13.8% between £16 million and £25 million, 6.9% between £26 million and £50 million, and
10.3% over £50 million). This contradicts the belief
that formal risk management approaches could only be
afforded by larger companies due to perceived extra
cost of implementing such systems.
Research results and discussion
Table 3 and Appendix 1 present the results of the
relative likelihood approach (aggregated for the various
categories of experts). Figure 3 presents the probability
density functions based on the aggregated estimates. A
number of inconsistencies in the estimates can be seen
from the analyses, particularly with regard to tail
estimates. For example, the average estimates from
the Project Managers indicate a minimum possible
value of 5.67, while an average relative likelihood rating
of 15 units was also given to the occurrence value of
5.67 by the same group. A similar situation is true of
construction managers and contract managers. These
inconsistencies perhaps confirms the difficulty that
construction professionals have in estimating intermediate and tail values of a probability distribution,
and the choice of the triangular distribution for most
analytical work in construction estimating. Raftery
(1994) argues that in dealing with subjective definitions
89
Construction contract risks
Table 3
Direct estimates of the relative likelihoods of encountering adverse conditions
PDF measure
of risk
Minimum
number
Maximum
number
Most likely
number (A)
Higher number
half as likely
as ‘A’
Lower number
half as likely
as ‘A’
Higher number
a quarter as
likely as ‘A’
Lower number a
quarter as
likely as ‘A’
Rating
Mean values of relative estimates per profession
Respondents’
aggregate
Construction
managers
Project
managers
Quantity
surveyors
Contracts
managers
Others
0
11.91
7.50
5.67
14.97
20.00
5.33
0
37.86
37.50
29.00
41.60
42.00
30.00
60
23.04
17.50
14.00
25.94
30.00
20.75
30
29.42
27.50
17.00
34.87
–
19.67
30
16.96
15.00
8.75
20.00
25.00
11.25
15
33.57
30.00
21.50
41.18
42.00
23.00
15
13.81
7.50
5.67
16.59
22.00
11.25
Note: – means no mid-point estimates were given by the Contracts Managers.
Figure 3 PDFs for the risk of encountering adverse ground conditions (the graphs are based on the ‘relative likelihoods’
method. The Triangular distribution is based on the minimum, maximum and modal values of the Group Aggregate)
90
of probability, the distributions selected should be
relatively easy to understand. They should also have
clear cut-off points since most estimators can say
reasonably clearly that the cost or time for a particular
variable will never exceed a fixed maximum nor be less
than fixed minimum value. However, the findings of the
current research do not support the use of the
triangular distribution for the analysis of construction
contract risks. For the sake of comparison, the
triangular distribution of the group aggregate based
on the minimum, maximum and modal values of the
Group Aggregate is also given in Figure 3. The author
of this article contends that while the criteria set out by
Raftery (1994) for the choice of distributions are sound
guidelines, it is equally important that experts are given
the opportunity to express their true beliefs as fully as
possible without introducing any analyst biases into the
elicitation process by presupposing a form of distribution. Furthermore, it is possible to elicit as much detail
as possible about the distribution forms that represent
the expert’s true beliefs without the need for the expert
having an advanced knowledge of statistics.
Estimates from experts who did not belong to the
four main professional categories were so inconsistent
with each other that no meaningful distribution could
be derived from them. This highlights the importance
of making the selection of ‘substantive’ experts an
essential pre-condition for the elicitation. It also
confirms that the estimates given by the experts from
the main categories are genuine and that the inconsistencies shown in their estimates are not the result of
guesswork, but that of genuine difficulty the experts
have in providing probability estimates for tail values. It
is also worth noting that the numbers of occurrences of
adverse ground conditions given by all the experts fall
within the range 3–42, providing an indication of the
range of likely values to consider for preliminary
decision making purposes. Moreover, although the
probability values given by the probability density
functions from the various categories differ from each
other, the shapes of the curves are fairly similar to each
other. This indicates that the general problem representations for the risk among the experts are very
similar, the differences arising perhaps from differences
in their experiences regarding the extremes of the
occurrences. Aggregation of expert opinions will therefore capture a problem representation that truly reflects
the collective knowledge and experience of the experts,
and therefore provide a more accurate distribution
form for the risk.
Table 4, Figure 4 and Appendix 2 present the results
from the second series of questions that applied a
continuous variable scaling technique to encode
responses. While the actual estimates and distributions
from the two sets of questions display some
Adams
inconsistencies, the distribution forms are evident and
generally consistent throughout the professions. The
results presented in Figure 3 are considered more
accurate as the relative likelihood method is more
efficient in reducing bias errors in the elicitation process
(Ranasinghe and Russell, 1993).
Conclusions
The main conclusion of this article is that Bayesian
methods can indeed be applied to the analysis of
construction contract risks. By combining theoretical
requirements with practical considerations in the
elicitation process, we can elicit expert opinions about
construction contract risks and transform these into
subjective prior probability distributions of the risk.
This will combine with sample information on the risk
in Bayesian fashion to arrive at a posterior distribution
that can then be utilized as an input variable to formal
risk analysis. The significance of this result is that it
provides an empirical basis for the development of
more effective strategies for the systematic analysis and
management of construction contract risk. Such
strategies will be helpful not only to contractors who
share the great bulk of project risks, but also to
construction experts who give advice for appropriate
risk management and enhanced project performance.
The application of such strategies will also have the
ultimate benefit of enhanced project performance for
the project owner, and improve the productivity of the
industry as a whole.
The effectiveness of the elicitation model used is
supported by two factors. First, it effectively captured the
problem representations of the various groups of experts,
as seen in the similarity of the shapes of the distributions.
Second, the questioning and response methods
employed enabled most of the experts to self-elicit their
own beliefs in a manner that allowed the easy transformation of the estimates into subjective probability
distributions. Although the model did not completely
overcome the difficulties faced by some construction
experts in assigning extreme and intermediate values of
subjective probability estimates, the issue does not
appear to be a failing of the model. Previous research
suggesting that experts in some other fields do not have
this problem perhaps point to the need for the preparation of construction professionals in the applications of
probabilities in construction. Developments in mathematical and scientific theories and advancements in
modern technology present many innovative solutions to
construction problems that are currently addressed in
much less optimal ways. Thus, rather than shying away
from certain aspects of statistics and mathematics, the
91
Construction contract risks
Table 4
Estimates of the likelihoods of Adverse Conditions using the Scaling Technique
As many
occurrences of
adverse ground
conditions as:
0
5
25
50
75
95
100
Mean Values of Estimates Per Profession
Respondents’
Aggregate
Construction
Managers
Project
Managers
Quantity
Surveyors
Contracts
Managers
Others
12.96
57.17
42.88
20.79
8.87
5.93
3.95
12.50
27.50
57.00
18.50
6.00
3.50
0.00
2.67
88.00
47.00
24.33
8.00
3.67
0.33
15.13
49.71
39.40
32.13
18.00
20.47
18.40
1.00
88.00
35.00
19.00
6.00
1.00
1.00
33.50
32.67
36.00
10.00
6.33
1.00
0.00
Figure 4 PDFs for the risk of encountering adverse ground conditions (using the scaling technique)
industry and academic institutions should perhaps
incorporate these aspects into professional training in
the industry to enable the industry to better benefit from
such developments and advancements.
References
Adams, F.K. (2004) The management of risks in international infrastructural projects, PhD thesis, The University
of Edinburgh, Scotland, UK.
Ashton, H.A. and Ashton, R.H. (1985) Aggregating subjective forecasts: some empirical results. Management
Science, 31(12), 1499–508.
Baker, S., Ponniah, D. and Smith, S. (1999) Risk response
techniques currently employed for major projects.
Construction Management & Economics, 17, 205–13.
Budescu, D.V. and Wallsten, T.S. (1987) Subjective estimation of precise and vague uncertainties, in Wright, G. and
Ayton, P. (eds), Judgmental Forecasting, John Wiley & Sons,
New York, pp. 63–82.
Burchett, J.F., Rao Tummala, V.M. and Leung, H.M. (1999)
A worldwide survey of current practices in the management
of risks within electrical supply projects. Construction
Management & Economics, 17, 77–90.
Chapman, C. and Ward, S. (1997) Project Risk Management:
Processes, Techniques and Insights, John Wiley & Sons,
Chichester.
92
Chau, K.W. (1995) Monte Carlo simulations of construction
costs using subjective data. Construction Management &
Economics, 13, 369–83.
Chesley, G.R. (1975) Elicitation of subjective probabilities: a
review. The Accounting Review, L, 323–37.
Cooper, D.F. and Chapman, C.B. (1987) Risk Analysis for
Large Engineering Projects: Models, Methods and Cases,
John Wiley & Sons, Chichester.
De Wit, B. and Meyer, R. (1994) Strategy: Process, Content,
Context, West Publishing Company, St Paul.
Finch, J. (1987) The vignette technique in survey research.
Sociology, 21(1), 105–14.
Gustafson, D.H., Shukla, R.K., Delberg, A. and
Walster, G.W. (1973) A comparative study of differences
in subjective likelihood estimates made by individuals,
interacting groups, Delphi groups and nominal groups.
Organizational Behaviour and Human Performance, 280–91.
Hertz, D.B. and Thomas, H. (1984) Practical Risk Analysis:
An Approach Through Case Histories, John Wiley and Sons,
Chichester.
Kadane, J.B. and Wolfson, L.J. (1997) Experiences in
elicitation. The Statistician, 46, (4), 1–17.
Kahneman, D., Slovic, P. and Tversky, A. (1982) Judgment
Under Uncertainty: Heuristics and Biases, Cambridge
University Press, Cambridge.
Lock, A. (1987) Integrating group judgments in subjective
forecasts, in Wright, G. and Ayton, P. (eds), Judgmental
Forecasting, John Wiley & Sons, New York.
Mak, S. (1995) Risk analysis in construction: a paradigm shift
from hard to soft approach. Construction Management &
Economics, 13, 385–92.
Moore, P.G. and Thomas, H. (1976) Anatomy of Decisions
Penguin Books, London.
Murphy, A.H. and Winkler, R.L. (1984) Probability forecasting in meteorology. Journal of the American Statistical
Association, 79(387), 489–500.
Nachmias, C. and Nachmias, D. (1981) Research Methods in
the Social Sciences, Edward Arnold, London.
O’Hagan, A. (1997) Eliciting expert beliefs in substantial
practical applications. The Statistician, 46(4).
O’Hagan, A. and Haylock, R.G. (1997) Bayesian uncertainty
analysis and radiological protection, in Barnett, V. and
Adams
Turkman, K.F. (eds), Statistics for the Environment 3,
Pollution Assessment and Control, Wiley, Chichester,
pp. 109–28.
Phillips, L.D. (1973) Bayesian Statistics for Social Scientists,
Thomas Nelson & Sons, London.
Raftery, J. (1994) Risk Analysis in Project Management, E &
FN Spon, London.
Ranasinghe, M. and Russell, A.D. (1993) Elicitation of
Subjective probabilities for economic risk analysis: an
investigation. Construction Management & Economics, 11,
326–40.
Robson, C. (1993) Real World Research, Blackwell, Oxford.
Simonton, D. (1996) Creative expertise: a lifespan developmental perspective, in Ericsson, K. (ed.), The Road to
Excellence: The Acquisition of Expert Performance in the Arts
and Sciences, Sports and Games, Erlbaum, Mahwah, NJ,
pp. 227–53.
Spetzler, C. and Staël Von Holstein, C.A.S. (1975)
Probability encoding in decision analysis. Management
Science, 22(3).
Spiegelhalter, D.J., Harris, N.L., Bull, K. and
Franklin, R.C.G. (1994) Empirical evaluation of prior
beliefs about frequencies: methodology and a case study in
congenital heart disease. Journal of the American Statistical
Association, 79(387), 489–500.
Tversky, A. (1974) Assessing uncertainty. Journal of the Royal
Statistical Society, Series B, 36(2), 148–59.
Tversky, A. and Kahneman, D. (1974) Judgment under
uncertainty: heuristics and biases., Science, 185, 1124–31.
Vick, S. (2002) Degrees of Belief - Subjective Probability and
Engineering Judgement, ASCE Press, Virginia.
Wallsten, T.S. and Budescu, D.V. (1983) Encoding subjective probabilities: a psychological and psychometric
Review. Management Science, 29(2), 151–73.
Ward, S.C., Chapman, C.B. and Curtis, B. (1991) On the
allocation of risk in construction projects. International
Journal of Project Management, August, 140–7.
Wright, G. and Ayton, P. (1987) The psychology of
forecasting, in Wright, G. and Ayton, P. (eds),
Judgmental
Forecasting,
John
Wiley
&
Sons,
New York.
93
Construction contract risks
Appendix 1
Scaled estimates and assessed probabilities for the occurrence of adverse ground conditions (relative
likelihood method)
Relative likelihood (smoothed)
Number of
occurrences
Construction Project
Quantity Contracts
of adverse
managers managers surveyors managers
ground
conditions
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
0.0
1.5
3.5
5.5
8.0
10.0
12.9
16.0
20.3
24.0
28.0
32.0
38.0
44.5
50.0
55.0
58.0
59.0
59.0
58.5
56.5
53.2
50.5
46.8
43.0
39.0
35.2
32.0
29.0
25.2
21.2
18.0
15.2
13.3
12.0
11.2
10.8
10.2
10.0
9.8
9.5
9.3
9.1
9.0
8.9
8.7
8.5
8.2
8.0
0.0
2.0
4.6
7.0
9.5
12.4
16.0
21.0
26.0
31.5
38.0
45.0
52.0
57.0
60.0
55.0
41.0
30.0
25.0
21.0
18.0
16.0
14.2
13.1
12.1
11.5
11.0
10.6
10.2
10.0
9.9
9.8
9.6
9.4
9.2
9.0
8.9
8.8
8.6
8.4
8.2
8.0
7.9
7.7
7.6
7.4
7.3
7.2
7.0
0.0
0.5
1.3
2.0
3.0
4.0
4.8
5.3
6.2
7.0
7.8
8.8
9.6
10.5
11.5
16.6
15.5
17.0
20.0
25.0
30.0
36.0
43.0
50.0
55.0
59.0
60.0
59.0
56.5
53.0
49.2
45.2
40.9
36.6
32.5
29.5
26.5
23.2
20.4
18.2
16.5
15.2
14.2
13.5
13.0
12.6
12.2
11.8
11.5
0.0
0.5
1.0
1.5
2.3
2.8
3.3
4.0
4.5
5.0
5.4
6.0
6.6
7.2
8.0
8.4
9.0
9.8
10.3
11.0
12.0
13.0
15.0
18.0
24.0
30.0
37.0
45.0
52.0
57.5
60.0
57.3
50.0
42.0
35.0
30.0
26.6
24.2
22.1
20.1
18.6
17.3
16.1
15.2
14.5
14.0
13.2
13.0
12.6
Assessed probability
Group
aggregate
0.0
1.0
1.8
2.5
3.0
4.0
5.0
5.5
6.4
7.4
8.0
9.0
10.5
12.0
16.0
20.0
25.0
30.0
35.8
42.0
48.8
54.5
58.5
60.0
59.0
55.5
49.5
43.5
38.0
32.2
27.5
23.5
19.5
16.5
13.6
11.8
11.0
10.2
10.0
9.8
9.5
9.3
9.1
9.0
8.9
8.7
8.5
8.2
8.0
Construction
managers
Project
managers
Quantity
surveyors
Contracts
managers
Group
aggregate
0.000
0.001
0.002
0.004
0.006
0.007
0.009
0.011
0.014
0.017
0.020
0.023
0.027
0.032
0.035
0.039
0.041
0.042
0.042
0.041
0.040
0.038
0.036
0.033
0.030
0.028
0.025
0.023
0.021
0.018
0.015
0.013
0.011
0.009
0.008
0.008
0.008
0.007
0.007
0.007
0.007
0.007
0.006
0.006
0.006
0.006
0.006
0.006
0.006
0.000
0.002
0.004
0.007
0.009
0.012
0.016
0.020
0.025
0.031
0.037
0.044
0.051
0.056
0.058
0.054
0.040
0.029
0.024
0.020
0.018
0.016
0.014
0.013
0.012
0.011
0.011
0.010
0.010
0.010
0.010
0.010
0.009
0.009
0.009
0.009
0.009
0.009
0.008
0.008
0.008
0.008
0.008
0.008
0.007
0.007
0.007
0.007
0.007
0.000
0.000
0.001
0.002
0.003
0.004
0.005
0.005
0.006
0.007
0.008
0.009
0.009
0.010
0.011
0.016
0.015
0.017
0.019
0.024
0.029
0.035
0.042
0.049
0.054
0.057
0.058
0.057
0.055
0.052
0.048
0.044
0.040
0.036
0.032
0.029
0.026
0.023
0.020
0.018
0.016
0.015
0.014
0.013
0.013
0.012
0.012
0.011
0.011
0.000
0.000
0.001
0.001
0.002
0.003
0.003
0.004
0.004
0.005
0.005
0.006
0.006
0.007
0.008
0.008
0.009
0.010
0.010
0.011
0.012
0.013
0.015
0.018
0.023
0.029
0.036
0.044
0.051
0.056
0.058
0.056
0.049
0.041
0.034
0.029
0.026
0.024
0.022
0.020
0.018
0.017
0.016
0.015
0.014
0.014
0.013
0.013
0.012
0.000
0.001
0.002
0.002
0.003
0.003
0.004
0.005
0.005
0.006
0.007
0.008
0.009
0.010
0.014
0.017
0.021
0.025
0.030
0.036
0.041
0.046
0.050
0.051
0.050
0.047
0.042
0.037
0.032
0.027
0.023
0.020
0.017
0.014
0.012
0.010
0.009
0.009
0.008
0.008
0.008
0.008
0.008
0.008
0.008
0.007
0.007
0.007
0.007
94
Adams
(Continued)
Relative likelihood (smoothed)
Number of
occurrences
Construction Project
Quantity Contracts
of adverse
managers managers surveyors managers
ground
conditions
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
80
81
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
Total
7.9
7.8
7.6
7.4
7.2
7.0
6.8
6.7
6.5
6.4
6.2
6.1
5.9
5.8
5.6
5.5
5.3
5.2
5.0
4.9
4.7
4.6
4.4
4.2
4.1
3.9
3.8
3.6
3.5
3.3
3.0
2.9
2.9
2.7
2.6
2.4
2.3
2.1
2.0
1.8
1.7
1.5
1.4
1.2
1.1
0.9
0.8
0.6
0.5
0.3
0.2
0.0
1,412.0
6.9
6.8
6.6
6.5
6.4
6.2
6.1
6.0
5.8
5.7
5.6
5.4
5.3
5.2
5.0
4.9
4.7
4.6
4.5
4.3
4.2
4.1
3.9
3.8
3.7
3.5
3.4
3.3
3.1
3.0
2.7
2.6
2.6
2.5
2.3
2.2
2.0
1.9
1.8
1.6
1.5
1.4
1.2
1.1
1.0
0.8
0.7
0.6
0.4
0.3
0.2
0.0
1,026.7
11.2
10.9
10.7
10.3
10.1
9.9
9.7
9.5
9.3
9.1
8.8
8.6
8.4
8.2
8.0
7.8
7.6
7.3
7.1
6.9
6.7
6.5
6.3
6.0
5.8
5.6
5.4
5.2
5.0
4.8
4.3
4.1
4.1
3.9
3.7
3.5
3.3
3.0
2.8
2.6
2.4
2.2
2.0
1.7
1.5
1.3
1.1
0.9
0.7
0.5
0.2
0.0
1,026.7
12.4
12.1
11.9
11.6
11.4
11.1
10.9
10.7
10.4
10.2
9.9
9.7
9.5
9.2
9.0
8.7
8.5
8.2
8.0
7.8
7.5
7.3
7.0
6.8
6.6
6.3
6.1
5.8
5.6
5.3
4.9
4.6
4.6
4.4
4.1
3.9
3.6
3.4
3.2
2.9
2.7
2.4
2.2
2.0
1.7
1.5
1.2
1.0
0.7
0.5
0.3
0.0
1,026.7
Assessed probability
Group
aggregate
Construction
managers
Project
managers
Quantity
surveyors
Contracts
managers
Group
aggregate
7.9
7.8
7.6
7.4
7.2
7.0
6.8
6.7
6.5
6.4
6.2
6.1
5.9
5.8
5.6
5.5
5.3
5.2
5.0
4.9
4.7
4.6
4.4
4.2
4.1
3.9
3.8
3.6
3.5
3.3
3.0
2.9
2.9
2.7
2.6
2.4
2.3
2.1
2.0
1.8
1.7
1.5
1.4
1.2
1.1
0.9
0.8
0.6
0.5
0.3
0.2
0.0
1,179.5
0.006
0.006
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.004
0.004
0.004
0.004
0.004
0.004
0.004
0.004
0.004
0.004
0.003
0.003
0.003
0.003
0.003
0.003
0.003
0.003
0.003
0.002
0.002
0.002
0.002
0.002
0.002
0.002
0.002
0.002
0.002
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.000
0.000
0.000
0.000
0.000
1.000
0.007
0.007
0.006
0.006
0.006
0.006
0.006
0.006
0.006
0.006
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.004
0.004
0.004
0.004
0.004
0.004
0.004
0.004
0.003
0.003
0.003
0.003
0.003
0.003
0.003
0.003
0.002
0.002
0.002
0.002
0.002
0.002
0.002
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.000
0.000
0.000
0.000
1.000
0.011
0.011
0.010
0.010
0.010
0.010
0.009
0.009
0.009
0.009
0.009
0.008
0.008
0.008
0.008
0.008
0.007
0.007
0.007
0.007
0.007
0.006
0.006
0.006
0.006
0.005
0.005
0.005
0.005
0.005
0.004
0.004
0.004
0.004
0.004
0.003
0.003
0.003
0.003
0.003
0.002
0.002
0.002
0.002
0.001
0.001
0.001
0.001
0.001
0.000
0.000
0.000
1.000
0.012
0.012
0.012
0.011
0.011
0.011
0.011
0.010
0.010
0.010
0.010
0.009
0.009
0.009
0.009
0.009
0.008
0.008
0.008
0.008
0.007
0.007
0.007
0.007
0.006
0.006
0.006
0.006
0.005
0.005
0.005
0.004
0.004
0.004
0.004
0.004
0.004
0.003
0.003
0.003
0.003
0.002
0.002
0.002
0.002
0.001
0.001
0.001
0.001
0.000
0.000
0.000
1.000
0.007
0.007
0.006
0.006
0.006
0.006
0.006
0.006
0.006
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.004
0.004
0.004
0.004
0.004
0.004
0.004
0.004
0.003
0.003
0.003
0.003
0.003
0.003
0.003
0.002
0.002
0.002
0.002
0.002
0.002
0.002
0.002
0.002
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.000
0.000
0.000
0.000
1.000
95
Construction contract risks
Appendix 2
Scaled estimates and assessed probabilities for the occurrence of adverse ground conditions
(continuous variable scaling method)
Number of
occurrences
of adverse
ground
conditions
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
Relative likelihood (smoothed)
Construction Project Quantity Contracts
managers managers surveyors managers
13
16
19
22
25
28
29
30
32
33
35
36
38
40
41
42
44
45
47
48
50
51
53
54
56
57
55
54
52
51
49
48
46
45
43
42
40
39
37
36
34
33
31
30
28
27
25
24
22
3
20
37
54
71
88
86
84
82
80
78
76
74
72
70
68
65
63
61
59
57
55
53
51
49
47
46
45
44
43
43
42
41
40
39
38
37
36
35
34
34
33
32
31
30
29
28
27
26
15
22
29
36
43
50
49
49
48
48
47
47
46
46
45
45
44
44
43
43
42
42
41
41
40
40
39
39
39
38
38
38
37
37
37
37
36
36
36
35
35
35
34
34
34
34
33
33
33
1
18
36
53
71
88
85
83
80
77
75
72
69
67
64
62
59
56
54
51
48
46
43
40
38
35
34
34
33
32
32
31
31
30
29
29
28
27
27
26
25
25
24
23
23
22
22
21
20
Assessed probability
Group
aggregate
13
21
30
39
48
57
56
56
55
54
54
53
52
51
51
50
49
49
48
47
47
46
45
44
44
43
42
41
40
39
39
38
37
36
35
34
33
32
31
30
30
29
28
27
26
25
24
23
22
Construction
managers
Project
managers
Quantity
surveyors
Contracts
managers
Group
aggregate
0.006
0.007
0.008
0.009
0.011
0.012
0.012
0.013
0.014
0.014
0.015
0.016
0.016
0.017
0.018
0.018
0.019
0.019
0.020
0.021
0.022
0.022
0.023
0.023
0.024
0.025
0.024
0.023
0.023
0.022
0.021
0.021
0.020
0.019
0.019
0.018
0.017
0.017
0.016
0.015
0.015
0.014
0.013
0.013
0.012
0.011
0.011
0.010
0.009
0.001
0.007
0.012
0.018
0.024
0.029
0.029
0.028
0.027
0.027
0.026
0.025
0.025
0.024
0.023
0.022
0.022
0.021
0.020
0.020
0.019
0.018
0.018
0.017
0.016
0.016
0.015
0.015
0.015
0.014
0.014
0.014
0.014
0.013
0.013
0.013
0.012
0.012
0.012
0.011
0.011
0.011
0.011
0.010
0.010
0.010
0.009
0.009
0.009
0.005
0.007
0.009
0.012
0.014
0.016
0.016
0.016
0.016
0.015
0.015
0.015
0.015
0.015
0.015
0.014
0.014
0.014
0.014
0.014
0.014
0.014
0.013
0.013
0.013
0.013
0.013
0.013
0.013
0.012
0.012
0.012
0.012
0.012
0.012
0.012
0.012
0.012
0.012
0.012
0.011
0.011
0.011
0.011
0.011
0.011
0.011
0.011
0.011
0.000
0.007
0.014
0.021
0.028
0.035
0.034
0.033
0.032
0.031
0.030
0.028
0.027
0.026
0.025
0.024
0.023
0.022
0.021
0.020
0.019
0.018
0.017
0.016
0.015
0.014
0.014
0.013
0.013
0.013
0.013
0.012
0.012
0.012
0.012
0.011
0.011
0.011
0.011
0.010
0.010
0.010
0.010
0.009
0.009
0.009
0.009
0.008
0.008
0.005
0.008
0.012
0.016
0.019
0.023
0.022
0.022
0.022
0.022
0.021
0.021
0.021
0.020
0.020
0.020
0.020
0.019
0.019
0.019
0.018
0.018
0.018
0.018
0.017
0.017
0.017
0.016
0.016
0.016
0.015
0.015
0.015
0.014
0.014
0.013
0.013
0.013
0.012
0.012
0.012
0.011
0.011
0.011
0.010
0.010
0.010
0.009
0.009
96
Adams
(Continued)
Number of
occurrences
of adverse
ground
conditions
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
Total
Relative likelihood (smoothed)
Construction Project Quantity Contracts
managers managers surveyors managers
21
19
18
18
17
17
16
16
15
15
14
14
13
13
12
12
11
11
10
10
9
9
8
8
7
7
6
6
6
6
6
5
5
5
5
5
5
5
5
4
4
4
4
4
4
4
4
3
2
1
1
0
2,322
25
25
24
23
23
22
21
21
20
19
19
18
17
17
16
15
15
14
13
13
12
11
11
10
9
9
8
8
8
7
7
7
7
6
6
6
6
6
5
5
5
5
4
4
4
4
4
3
2
1
1
0
3,001
32
32
31
31
30
30
29
29
28
28
27
26
26
25
25
24
24
23
22
22
21
21
20
20
19
19
18
18
18
18
19
19
19
19
19
19
19
19
20
20
20
20
20
20
20
20
21
20
20
19
19
19
3,069
20
19
18
18
17
17
16
16
15
15
14
14
13
13
12
12
11
11
10
10
9
9
8
8
7
7
6
6
6
5
5
5
5
5
4
4
4
4
4
3
3
3
3
3
2
2
2
2
2
2
2
2
2,532
Assessed probability
Group
aggregate
Construction
managers
Project
managers
Quantity
surveyors
Contracts
managers
Group
aggregate
21
21
20
20
19
19
18
18
17
17
16
16
15
15
15
14
14
13
13
12
12
11
11
10
10
9
9
9
9
9
8
8
8
8
8
8
8
7
7
7
7
7
7
6
6
6
6
6
5
5
4
4
2,520
0.009
0.008
0.008
0.008
0.008
0.007
0.007
0.007
0.007
0.006
0.006
0.006
0.006
0.005
0.005
0.005
0.005
0.005
0.004
0.004
0.004
0.004
0.003
0.003
0.003
0.003
0.003
0.003
0.002
0.002
0.002
0.002
0.002
0.002
0.002
0.002
0.002
0.002
0.002
0.002
0.002
0.002
0.002
0.002
0.002
0.002
0.002
0.001
0.001
0.001
0.000
0.000
1.000
0.008
0.008
0.008
0.008
0.008
0.007
0.007
0.007
0.007
0.006
0.006
0.006
0.006
0.006
0.005
0.005
0.005
0.005
0.004
0.004
0.004
0.004
0.004
0.003
0.003
0.003
0.003
0.003
0.003
0.002
0.002
0.002
0.002
0.002
0.002
0.002
0.002
0.002
0.002
0.002
0.002
0.002
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.000
0.000
0.000
1.000
0.011
0.010
0.010
0.010
0.010
0.010
0.010
0.009
0.009
0.009
0.009
0.009
0.008
0.008
0.008
0.008
0.008
0.008
0.007
0.007
0.007
0.007
0.007
0.006
0.006
0.006
0.006
0.006
0.006
0.006
0.006
0.006
0.006
0.006
0.006
0.006
0.006
0.006
0.006
0.006
0.006
0.006
0.007
0.007
0.007
0.007
0.007
0.007
0.006
0.006
0.006
0.006
1.000
0.008
0.008
0.007
0.007
0.007
0.007
0.006
0.006
0.006
0.006
0.006
0.005
0.005
0.005
0.005
0.005
0.004
0.004
0.004
0.004
0.004
0.003
0.003
0.003
0.003
0.003
0.002
0.002
0.002
0.002
0.002
0.002
0.002
0.002
0.002
0.002
0.002
0.002
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
1.000
0.008
0.008
0.008
0.008
0.008
0.007
0.007
0.007
0.007
0.007
0.006
0.006
0.006
0.006
0.006
0.006
0.005
0.005
0.005
0.005
0.005
0.004
0.004
0.004
0.004
0.004
0.004
0.004
0.003
0.003
0.003
0.003
0.003
0.003
0.003
0.003
0.003
0.003
0.003
0.003
0.003
0.003
0.003
0.003
0.003
0.002
0.002
0.002
0.002
0.002
0.002
0.002
1.000