estimation and evaluation of uncertainty: a minimalist first pass approach

Estimation and evaluation of uncertainty: a minimalist ®rst passapproach

Chris Chapman, Stephen Ward*

School of Management, MSc Risk Management Programme, University of Southampton, High®eld, Southampton SO17 1BJ, UK

Received 28 September 1999; received in revised form 27 January 2000; accepted 2 February 2000

Abstract

This paper describes an approach to the estimation and evaluation of uncertainty designed for ease of use. It is designed to be

easier to use than probability impact grid based approaches, and it links qualitative approaches in this format to quantitativeapproaches. It is based on a general view of uncertainty which incorporates ambiguity as well as variability and lack of data. Aconcern for identifying sources of uncertainty is one characteristic of the approach which ¯ows from this perspective. Othercharacteristics include deliberate conservative bias to counteract persistent underestimation of uncertainty. It is set in the context

of an iterative approach to an overall uncertainty management process. The example used to illustrate the approach involvesproject duration and cost estimation for bidding purposes. 7 2000 Elsevier Science Ltd and IPMA. All rights reserved.

Keywords: Risk management; Uncertainty management; Opportunity management; Competitive bidding; Estimation and evaluation of uncer-

tainty

1. Introduction

Estimation and evaluation of uncertainty are coretasks in any process involving the management ofuncertainty in projects [1±6]. These tasks involve anumber of important objectives set out below, whichcontribute to a key aim of cost e�ective risk assess-ment.

1.1. Understanding uncertainty in general terms

Understanding uncertainty needs to go beyondvariability and available data. It needs to addressambiguity and incorporate structure and knowledge,with a focus on making the best decisions possiblegiven available data, information, knowledge, andunderstanding of structure. Attempting to understand

uncertainty from this general perspective has a numberof important implications.

1.2. Understanding sources of uncertainty

One important aspect of structure is the need tounderstand uncertainty in terms of sources of uncer-tainty, because some (not all) appropriate ways ofmanaging uncertainty are speci®c to its source.

1.3. Determining what to quantify

Distinguishing between what is usefully quanti®edand what is best treated as a condition or assumptionin terms of decision making e�ectiveness is very im-portant. Knight's classical distinction between risk anduncertainty [7] based on the availability of objectiveprobabilities is not appropriate. Subjective probabil-ities are the starting point for all quanti®cation interms of probabilities, in the `decision analysis' tra-dition [8]. At best `objective' probabilities based ondata will address only part of the uncertainty of inter-

International Journal of Project Management 18 (2000) 369±383

0263-7863/00/$20.00 7 2000 Elsevier Science Ltd and IPMA. All rights reserved.

PII: S0263-7863(00 )00016 -8

www.elsevier.com/locate/ijproman

* Corresponding author. Tel.: +44-1703-592556; fax: +44-1703-

593844.

E-mail address: [email protected] (S. Ward).

est with a less than perfect ®t between source and ap-plication, and a subjective view of the quality of cover-age and ®t is required. Knowledge gaps and the roleof organisational learning need direct explicit treat-ment.

1.4. Iterative processes

To facilitate insight and learning, uncertainty has tobe addressed in terms of an iterative process, with pro-cess objectives which change on successive passes. Aniterative approach is essential to optimise the use oftime and other resources during the uncertainty man-agement process, because initially where uncertaintylies, whether or not it matters, or how best to respondto it, are unknown. At the outset the process is con-cerned with sizing risk to discover what matters. Sub-sequent passes are concerned with re®ning assessmentsin order to e�ectively manage what matters. Finalpasses may be concerned with convincing others thatwhat matters is being properly managed. The way suc-cessive iterations are used needs to be addressed in asystematic manner. A simple one shot, linear approachis hopelessly ine�cient.

1.5. A minimalist ®rst pass at estimation and evaluation

A `minimalist' approach to the ®rst pass at esti-mation and evaluation in order to `optimise' the over-all process is critical. A `minimalist' ®rst passapproach to estimation should be so easy to use thatthe usual resistance to appropriate quanti®cationbased on lack of data and lack of comfort with subjec-tive probabilities is overcome.

1.6. Avoiding optimistic bias

The optimistic bias of most approaches to esti-mation and evaluation, which leads to systematicunderestimation of uncertainty, needs direct and expli-cit attention to manage expectations. If successive esti-mates associated with managing risk do not narrowthe perceived variability and improve the perceivedexpected cost or pro®t on average, then the earlieranalysis process is ¯awed. Very few organisations haveprocesses which meet this test. They are failing tomanage expectations. The more sophisticated the pro-cess used, the more optimistic bias damages the credi-bility of estimation and evaluation processes ingeneral.

1.7. Simplicity with constructive complexity

Simplicity is an important virtue in its own right,not just with respect to the e�ciency of a `minimalist'®rst pass approach, but because it can amplify clarity

and deepen insight. However, appropriate `constructivecomplexity' is also important, for the same reasons.Getting the best balance is partly a question of struc-ture and process, partly a question of skills which canbe learned via a process which is engineered toenhance learning.

No current approaches the authors are aware ofexplicitly address this set of objectives as a whole, withthe exception of the `simple scenario' approach [3],which the authors judge a failure with respect to objec-tive 4.

Evidence of this failure is the sustained widespreadpromotion and use of ®rst pass approaches to esti-mation and evaluation employing a probability-impactmatrix (PIM). This was deliberately accommodatedalthough not promoted in Project Risk Analysis andManagement Guide (PRAM) [2,3], because of di�er-ences of opinion amongst the working group. ThePIM approach typically de®nes `low', `medium', and`high' bands for possible probabilities and impacts as-sociated with identi®ed sources of uncertainty (usually`risks' involving adverse impacts). These bands may bede®ned as quanti®ed ranges or left wholly subjective.In either case, assessment of probabilities and impactsis a relatively crude process whereby each source ofuncertainty is assigned to a particular probability bandand a particular impact band. This limited informationabout each source of uncertainty is then usuallydiluted by using `risk indices' with common values fordi�erent probability band and impact band combi-nations. Information about uncertainty is often stillfurther obscured by the practice of adding individualrisk indices together to calculate spurious `project riskindices'. The PIM approach seems to o�er a rapid ®rstpass assessment of the relative importance of identi®edsources of uncertainty, but it delivers very little usefulinformation and even less real insight [3,9].

Even with the availability of proprietary softwareproducts such as @Risk for quantifying, displayingand combining uncertain parameters, use of PIM haspersisted (further encouraged by PIM software). Thisis surprising, but it suggests a gap between simpledirect prioritisation of sources of risk and quanti®-cation requiring the use of specialist software. In anyevent none of these PIM approaches deals directlywith the complete set of objectives set out above forestimation and evaluation.

This paper describes a `minimalist' ®rst passapproach to estimation and evaluation of uncertaintywhich addresses this gap, set in the context of anapproach which addresses all seven objectives [3]. The`minimalist' approach de®nes uncertainty ranges forprobability and impact associated with each source ofuncertainty. Subsequent calculations preserve expectedvalues and measures of variability, while explicitlymanaging associated optimistic bias.

C. Chapman, S. Ward / International Journal of Project Management 18 (2000) 369±383370

The following section outlines a `minimalist'approach to estimation and evaluation using anexample context to illustrate the `bare bones' of thewhole process. This is followed by sections which dis-cuss the rationale in terms of its iterative application,the management and shaping of expectations aboutuncertainty, and the robustness of the approach. Thesesections add ¯esh to the bones, and indicate the varietyof shapes the process can take depending on the cir-cumstances. This ¯exibility is essential in the contextof the PRAM [1±3] Focus phase, which demandsexplicit attention to tailoring a generic best practiceapproach to the particular circumstances of each appli-cation.

2. An outline of a `minimalist' approach

This section outlines the mechanics of the proposedapproach using a speci®c application to illustrate themethodology. For ease of exposition, some aspects ofthe rationale related to speci®c parts of the proposedapproach are explained in this section, but develop-ment of the rationale as a whole and exploration ofalternatives is left until following sections.

The `minimalist' approach involves the following sixsteps in a ®rst pass attempt to estimate and evaluateuncertainty:

1. Identify the parameters to be quanti®ed;2. Estimate crude but credible ranges for probability

of occurrence and impact;3. Recast the estimates of probability and impact

ranges;4. Calculate expected values and ranges for composite

parameters;5. Present results graphically (optional);6. Summarise results.

During these steps there is an underlying concern toavoid optimistic bias in the assessment of uncertainty,and a concern to retain simplicity with enough `con-structive complexity' to provide clarity and insight toguide uncertainty management.

To illustrate the proposed approach comprehen-sively, a reasonably rich example in terms of the issuesraised is helpful. Within this framework it is helpful tokeep the numbers and the details as simple as possible,to make the example easy to follow. What followsworks to these guidelines, drawing on examples dis-cussed in more detail elsewhere (pipe laying models[5,10,11], bidding [12,13]).

2.1. Example situation: estimating uncertainty for a pipelaying contract

A cost estimator with an o�shore oil and gas pipe

laying contractor is given a ``request for tender'' for a200 km pipeline to be constructed on a ®xed pricebasis, and asked to report back in a few hours with apreliminary view of the cost. Modi®cations to the esti-mator's preliminary view can be negotiated when he orshe reports, and re®nement of the analysis will be feas-ible prior to bidding. The estimator's initial analysisshould provide a framework for identifying what thethrust of such re®nements should be. The estimatorhas access to company experts and data, but the or-ganisation has no experience of formal risk manage-ment.

2.1.1. Step 1: Identify the parameters to be quanti®edThe ®rst step involves preliminaries which include

setting out the basic parameters of the situation, thecomposite parameter structure, and associated sourcesof uncertainty. Table 1 illustrates the format appliedto our example context.

The ®rst section of Table 1 identi®es the proposedparameter structure of the cost estimate in a top-downsequence. `Cost' might be estimated directly as a basicparameter, as might associated uncertainty. However,if cost uncertainty is primarily driven by other factorssuch as time as in this case, a `duration � cost rate'composite parameter structure is appropriate. Further,

Table 1

Relationships, base values, uncertainty factors and assessment modes

Composite parameter relationships

Cost = duration� cost rate (£m)

Duration = length/progress rate (months)

Progress rate = lay rate� productive days per month (km/month)

Productive days per month = 30 (1 ÿ days lost rate) (days/

month)

Basic parameters Base values

Length 200 km

Lay rate 2 km/productive day

Days lost rate 0 productive days/month

Cost rate £2.5m/month

Basic parameters Uncertainty factors Probabilistic treatment?

Length Client route change No

Other (length) No

Lay rate Barge choice No

Personnel Yes

Other (lay rate) Yes

Days lost rate Weather Yes

Supplies Yes

Equipment Yes

Buckles Yes

Lay barge sinks No

Other (days lost rate) No

Cost rate Market Yes

Other (cost rate) No

C. Chapman, S. Ward / International Journal of Project Management 18 (2000) 369±383 371

it is often useful to break `duration' down into `length/progress rate', to address more basic parameters anduncertainties within speci®c time frames. In this case itis also useful to break `progress rate' down into `layrate � productive days per month', where `lay rate're¯ects uncertainty about the length of pipe that canbe laid per day given pipe laying is feasible, and `pro-ductive days per month', the number of days in amonth when pipe laying is feasible, re¯ects a di�erentset of uncertainties. Finally, it is convenient in thiscase to express `productive days per month' in termsof days lost per month.

The second section of Table 1 provides base valuesfor all the basic parameters. The 2 km per productiveday lay rate and the £2.5m per month cost rateassumes a particular choice of lay barge which the esti-mator might regard as a conservative ®rst choice. Theestimator might anticipate later consideration of lesscapable barges with lower nominal lay and cost rates.

The third section of Table 1 identi®es sources ofuncertainty associated with each of the basic par-ameters, and asks in relation to each whether or notprobabilistic treatment would be useful.

`Length' has `client route change' identi®ed as a keysource of uncertainty, which might be de®ned in termsof client-induced route changes associated with poten-tial collector systems. Òther (length)' might refer toany other reasons for pipeline length changes, forexample, unsuitable sea bed conditions might forceroute changes. These are examples of risks which arenot sensible to quantify in probability terms becausethey are more usefully treated as basic assumptions orconditions which need to be addressed contractually.That is, the contract should ensure that responsibilityfor such changes is not borne by the contractor, sothey are not relevant to assessment of the contractor'scost. Ensuring that this happens makes listing suchrisks essential, even if in its simplest terms a standar-dised list of generic exclusions is used.

`Lay rate' identi®es `barge choice' as a factor notsuitable for quanti®cation. This is an example of avariable not suitable for probabilistic treatmentbecause it is a decision parameter usefully associatedwith assumed values and determined in a separateanalysis.

`Lay rate' is also in¯uenced by two uncertainty fac-tors which might be deemed appropriate for probabil-istic treatment because the contractor must managethem and bear ®nancial responsibility within the con-tract price. `Personnel' might re¯ect the impact on thelay rate of the experience, skill and motivation of thebarge crew, with potential to either increase ordecrease lay rate with respect to the base value. Òther(lay rate)' might re¯ect minor equipment, supply andother operating problems which are part of the pipelaying daily routine.

`Days lost rate' identi®es four uncertainty factorsusefully treated probabilistically because the operatormust own and deal with them within the contractprice. `Weather' might result in days when attemptingpipe laying is not feasible because the waves are toohigh. `Supplies' and èquipment' might involve furtherdays lost because of serious supply failures or equip-ment failures which are the contractor's responsibility.`Buckles' might be associated with `wet buckles', whenthe pipe kinks and fractures, allowing water to ®ll it,necessitating dropping it, with very serious repair im-plications. `Dry buckles', a comparatively minor pro-blem, might be part of òther (lay rate)'. In all fourcases the ®nancial ownership of these e�ects might belimited to direct cost implications for the contractor,with an assumption that any of the client's knock-oncosts are not covered by ®nancial penalties in the con-tract at this stage.

`Days lost rate' also identi®es two uncertainty fac-tors best treated as conditions or assumptions. `Laybarge sinks' might be deemed not suitable for prob-abilistic treatment because it is a force majeure eventresponsibility for which the contractor would pass onto the lay barge supplier in the assumed subcontractfor bid purposes at this stage, avoiding responsibilityfor its e�ects on the client in the main contract. Òther(days lost rate)' might be associated with catastrophicequipment failures (passed on to the subcontractor),catastrophic supply failures (passed back to the client),or any other sources of days lost which the contractorcould reasonably avoid responsibility for.

`Cost rate' might involve a `market' uncertainty fac-tor associated with normal market force variationswhich must be borne by the contractor, and usefullyquanti®ed.

`Cost rate' might also involve an òther (cost rate)'uncertainty factor placing abnormal market conditionrisks with the client, and therefore not quanti®ed.

In this example, most of the uncertainty factors trea-ted as assumptions or conditions are associated with®nancial ownership of the consequences for contrac-tual purposes. The exception is the barge choice de-cision variable. In general, there may be a number ofsuch `barge choice' decisions to be made in a project.Where and why we draw the lines between probabilis-tic treatment or not is a key uncertainty managementprocess issue, developed with further examples else-where [3].

2.1.2. Step 2: Crude but credible estimates ofprobabilities and impacts

The next step involves estimating crude but credibleranges for the probability of occurrence and the size ofimpact of the uncertainty factors which indicate `yes'to probabilistic treatment in Table 1. Table 2 illus-trates the format applied to our example context.


Table 2 is in three parts, each part corresponding to abasic parameter. All estimates are to a minimal num-ber of signi®cant ®gures, to maintain simplicity whichis important in practice as well as for example pur-poses.

The impact columns show estimated pessimistic andoptimistic scenario values, assumed for illustrative pur-poses to approximate to 90 and 10 percentile valuesrather than absolute maximum and minimum values.Extensive analysis [14] suggests the lack of an absolutemaximum, and confusion about what might or mightnot be considered in relation to an absolute minimum,makes 95±5 or 90±10 con®dence band estimates mucheasier to obtain and more robust to use. A 90±10 con-®dence band approach is chosen rather than 95±5because it better re¯ects the minimalist style and itlends itself to simple re®nement in subsequent iter-ations.

For each uncertainty factor there are two `eventprobability' columns showing the estimated range (alsoassumed to be a 90±10 percentile range), for the prob-ability of some level of impact occurring. A probabilityof 1 indicates an ever-present impact, as in the case ofpersonnel, weather or market conditions.

The `pessimistic' and `optimistic' columns indicatethe possible range for unconditional expected impactvalues given the estimates for event probability andconditional impact. The `mid-point' column shows themid-point of the range of possible values for uncondi-tional expected impact.

For the `lay rate' section of Table 2, impacts arede®ned in terms of percentage decrease (for estimatingconvenience) to the nearest 10%. The `combined'uncertainty factor estimate involves an expecteddecrease of 5% in the nominal lay rate, de®ned by the`mid-point' column, and plus or minus 25% bounds,de®ned by the ip and io values.

The `days lost rate' section treats `weather' as everpresent in the context of an average month, but otherfactors have associated probabilities over the range 0to 1, estimated to one signi®cant ®gure. Impact esti-mates are also to one signi®cant ®gure in terms ofdays lost per month.

The `combined' uncertainty factor estimate providedin the ®nal row shows an expected impact `mid-point'of 7.12 days lost per month, and a corresponding opti-mistic estimate of 2 days lost per month, but 79 daysmight be lost if a buckle occurs together with equip-ment, supplies and weather `pessimistic' values. Thepipe laying process could ®nish the month well behindwhere it started in progress terms. The bounds hereare clearly not obtainable by adding pp� ip and po� iovalues.

The `cost rate' section is a simpli®ed version of the`lay rate' section.

2.1.3. Step 3: Recast the estimates of probability andimpact ranges

The next step is to recast the estimates in Table 2 tore¯ect more extreme values of probability and impactranges, and associated distribution assumptions. Thisstep can also convert units from those convenient forestimation to those needed for combinations, if necess-ary. Further, it can simplify the uncertainty factorstructure. Table 3 illustrates what is involved, buildingon Table 2. Apart from changes in units, 10% hasbeen added to each ( pp ÿ po) and (ip ÿ io) range ateither end. This approximates to assuming a uniformprobability distribution for both the Table 2 prob-ability and impact ranges and the extended Table 3ranges. Strictly, given 10 and 90 percentile ®gures inTable 2, ranges ought to be extended by 12.5% ateach end so that the extensions are 10% of theextended range. However, using 10% extensions is

Table 2

Crude, credible estimates of probabilities and impacts

Uncertainty Factors Event probability Impact Probability times impact

Pessimistic pp Optimistic po Pessimistic ip Optimistic io Pessimistic pp� ip Optimistic po� io Midpoint

Lay rate (impact scenarios: percentage decrease)

Personnel 1 1 10 ÿ20 10 ÿ20 ÿ5Other 1 1 20 0 20 0 10

Combined 30 ÿ20 5

Days lost rate (impact scenarios: days lost per month)

Weather 1 1 10 2 10 2 6

Supplies 0.3 0.1 3 1 0.9 0.1 0.5

Equipment 0.1 0.01 6 2 0.6 0.02 0.31

Buckles 0.01 0.001 60 20 0.6 0.02 0.31

Combined 79 2 7.12

Cost rate (impact scenarios: percentage increase)

Market 1 1 30 ÿ20 30 ÿ20 5

Combined 30 ÿ20 5


computationally more convenient and it emphasisesthe approximate nature of the whole approach. It alsohelps to avoid any illusion of spurious accuracy ando�ers one simple concession to optimism, whose e�ectis both limited and clear.

The `lay rate' section combines the `personnel' and`other' entries of Table 2 directly (using the combinedentries from Table 2 as its basis), on the grounds thatTable 2 revealed no serious concerns. It ®rst convertsthe 30% `pessimistic' impact estimate of Table 2 to a`very pessimistic' estimate of [30 + 0.1 (30 ÿ (ÿ20))]= 35%, adding 10% of the (ip ÿ io) range. It thenapplies this percentage decrease to the base lay rate toobtain a `very pessimistic' lay rate of [2 � (100 ÿ 35)/100) = 1.3 km per day, to move from units convenientfor estimation purposes to units required for analysis.Table 3 converts the io estimate of a 20% increase in asimilar way. Converting from percentage change®gures to km/day ®gures is convenient here for compu-tational reasons (it must be done somewhere).

The `days lost rate' section retains a breakdown ofindividual uncertainty factors directly, on the groundsthat Table 2 reveals some concerns. Event probabilityvalues less than 1 are converted to `very pessimistic ÿvery optimistic' ( pvp ÿ pvo) ranges in the same way asimpact ranges. In this case the `combined' entries mir-ror the `combined' entries of Table 2 on a `very pessi-mistic' and `very optimistic' basis.

The `cost rate' section is obtained in a similar wayto the `lay rate' section. The impact range in Table 2 isextended by 10% at either end and these extremevalues for percentage increase are applied to the basecost rate of £2.5m per month.

An obvious question is why do we need `very pessi-mistic' and `very optimistic' values as well as the `pessi-mistic' and `optimistic' values of Table 2? The answeris to make graphical presentation feasible in Step 5. Ifgraphical presentation is not required, and a simplespreadsheet model conversion from Table 2 to Table 3is not available, we could skip the `very pessimistic'and `very optimistic' conversions, but in practice thetime saved will be negligible. The term `minimalist'was chosen to imply minimal e�ort appropriate tocontext, ensuring that sophistication and generality todeal e�ectively with all contexts is preserved. Graphsare often useful, if not essential.

2.1.4. Step 4: Calculate expected values and ranges forcomposite parameters

The next step is to calculate the expected values andranges for the composite parameters of Table 1 usingthe range and mid-point values in Table 3.

The calculations are shown in Table 4 and workthrough the composite parameter relationships in the®rst section of Table 1 in reverse (bottom up) order.The `mid-point' columns use mid-point values fromT

able

3

Recast

estimates

Uncertainty

Factors

Eventprobability

Impact

Probabilitytimes

impact

Verypessimisticpvp

Veryoptimisticpvo

Verypessimistici vp

Veryoptimistici vo

Verypessimisticpvp�i vp

Veryoptimisticpvo�i vo

Midpoint

Layrate

(impact

scenarios:km/day)

combined

(direct)

11

1.3

2.5

1.9

Dayslost

rate

(impact

scenarios:dayslost

per

month)

Weather

11

11

111

16

Supplies

0.32

0.08

3.2

0.8

1.02

0.06

0.54

Equipment

0.11

06.4

1.6

0.70

00.35

Buckles

0.011

064

16

0.70

00.35

Combined

84.6

17.25

Cost

rate

(impact

scenarios:km/m

onth)

Combined

11

3.38

1.87

2.63


Table 3. The `very optimistic' columns use ivo valuesfrom Table 3. Because a `very pessimistic' or even a`pessimistic' calculation on the same basis wouldinvolve never ®nishing the pipeline, a `plausibly pessi-mistic' column uses ivp values except in the case of`days lost rate', when 20 days replaces the ivp value of84.6 days. The source of this 20 days ®gure might be asimple rule of thumb, like

3�mid-pointÿ ivo � �mid-point

rounded to one signi®cant ®gure. Later evaluationpasses might call for more e�ective but more time-con-suming approaches for estimating a plausibly pessi-mistic value.

The ®nal section of Table 4 summarises the results,rounding the `current estimate' based on the mid-pointand its `very optimistic' based lower limit to their near-est £m, and its `plausibly pessimistic' based upper limitto re¯ect an order of magnitude relationship with thelower limit.

2.1.5. Step 5: Present results graphically (optional)For key areas of concern, additional graphical rep-

resentation of assessments may be worthwhile, usingformats like Figs. 1 and 2 below.

Fig. 1 illustrates a Probability Impact Picture (PIP),which can be produced directly from Table 3. The esti-mator in our example context might produce Fig. 1because `days lost rate' is a key area of concern, theestimator anticipates discussion of assumptions in thisarea, and the person the estimator reports to likes aPIM format.

Fig. 1 can be a useful portrayal of Table 3 infor-mation in terms of con®rming estimation assumptions.It captures the key probability density function infor-mation of all the uncertainty factors in both eventprobability and impact dimensions.

Each Lj line plotted corresponds to an uncertaintyfactor which contributes to the `days lost rate'. If theLj lines are interpreted as diagonals of associatedboxes de®ning the set of possible combinations ofprobability and impact, the absence of these boxes can

be interpreted as a perfect correlation assumptionbetween event probability and impact for each uncer-tainty factor j, but nothing can be inferred about cor-relation between the j.

A horizontal Lj, like L1, implies some impact uncer-tainty but no event probability uncertainty. A verticalLj would imply the converse. A steep slope, like L2,implies more uncertainty about the event probabilitythan impact uncertainty. Slope measures necessarilyre¯ect the choice of units for impact, so they are rela-tive and must be interpreted with care. For example,L3 and L4 involve the same expected impact `mid-point', but order of magnitude di�erences with respectto event probability and impact, a relationship whichis not captured by Fig. 1 (although non-linear, iso-pro-duct mid-point values could be plotted).

Fig. 1 is a useful way to picture the implications ofthe `days lost rate' part of Table 3 for those who areused to using the PIM approach. However, in the con-text of the minimalist approach it is redundant as anoperational tool unless the use of computer graphicsinput make it an alternative way to specify the data inTables 2 and 3.

The authors hope that Fig. 1 in the context of theminimalist approach will help to end the use of con-ventional PIM approaches, illustrating the inherentand fatal ¯aws in these approaches from a somewhatdi�erent angle than that used earlier [3,9]. That is,those who use PIM approaches typically take (orshould take) longer to assess uncertainty in this frame-work than it would take in a Fig. 1 format for thoseused to this PIP format, and the minimalist approachcan put the information content of Fig. 1 speci®cationsto simple and much more e�ective use than a conven-tional PIM approach.

For evaluation purposes a CIP (Cumulative ImpactProbability) diagram like Fig. 2 is a more useful viewof the information in Table 3 than that portrayed byFig. 1. The estimator might produce Fig. 2 with orwithout Fig. 1. Fig. 2 shows the potential cumulativee�ect of each of the uncertainty factors contributing todays lost. For convenience the uncertainty factors are

Table 4

Results

Composite parameters Computation Results

Plausibly pessimistic Very optimistic Mid-point Plausibly pessimistic Very optimistic Mid-point

Productive days per month 30 ÿ 20 30 ÿ 1 30 ÿ 7.25 10 29 22.75

Progress rate (productive days� lay rate) 10� 1.3 29� 2.5 22.75� 1.9 13 72.5 43.23

Duration (months) (length� progress rate) 200/13 200/72.5 200/43.23 15.38 2.76 4.63

Cost (£m) (duration� cost rate) 15.38� 3.38 2.76� 1.87 4.63� 2.63 52.0 5.2 12.18

Current estimate of expected cost is £12m in the range 5 to 50


considered in order of decreasing event probabilityvalues.

In Fig. 2 the C1 curve depicts the potential impactof weather on days lost. It is plotted linearly betweenthe points: (ivo = 1, cumulative probability (CP) = 0),point à', and (ivp = 11, CP = 1), point `b', as for anyunconditional uniform probability density functiontransformation into a cumulative distribution form.

The C2 curve depicts the potential additional impactof supply failures on days lost in a manner which

assumes a degree of positive correlation with impactsfrom the weather. The idea is to incorporate a degreeof plausible pessimism re¯ecting Son of Sod's law.Sod's law is well known: ìf anything can go wrong itwill'. Son of Sod's law is a simple extension: ìf thingscan go wrong at the same time they will'.

C2 is plotted in three linear segments via four points,generalising the C1 curve procedure to accommodate aconditional uniform probability density function witha `minimalist Son of Sod' (MSS) form of correlation.

Fig. 1. Probability impact picture (PIP): days lost per month example.

Fig. 2. Layered cumulative distribution graph: MSS days lost per month example.


. First, pvp = 0.32 is used in the transformation 1 ÿ0.32 = 0.68 to plot point d2 on C1.

. Second, ivo = 0.8 is used to move from point d2horizontally to the right 0.8 days to plot point e2.

. Third, pvo = 0.08 is used in the transformation 1 ÿ0.08 = 0.92 along with ivp = 3.2 to move from apoint on C1 at CP = 0.92 horizontally to the right3.2 days to plot point f2.

. Fourth, ivp = 3.2 is used to move from point b tothe right 3.2 days to plot point g2.

. Fifth, points d2, e2, f2 and g2 are joined by linearsegments.

This implies the following correlation betweenweather and supply failure.

. If weather impact is in the range 0 to 7.8 days (the 0to 68 percentile values of weather occur, de®ned bypvp for the `supplies event'), the `supplies event' doesnot occur.

. If weather impact is in the range 10 to 11 days (the92 to 100 percentile values of weather occur, de®nedby the pvo value for `supplies event'), the `suppliesevent' occurs with impact ivp.

. If weather impact is in the range 7.8 to 10 (between68 and 92 percentile values of `weather'), the`supplies event' occurs with a magnitude rising fromivo to ivp in a linear manner.

A similar procedure is used for curves C3 and C4 as-sociated with equipment failures and `buckles', butwith f3g3 and f4g4 coinciding since pvo = 0 in eachcase.

Fig. 2 plots Ei values de®ned by `mid-point' valuesalong the median (0.5 CP) line. Given the uniformprobability density distribution assumption for theunconditional `weather' distribution, E1 lies on C1 andno new assumptions are involved. Given the con-ditional nature (`event prob' less than one) of theother three uncertainty factors, interpreting Table 3mid-point values as Ej is an additional assumption,and plotting them o� the Cj curves resists employingthe optimistic nature of these curves in the 0±68 per-centile range.

The `combined very optimistic' value = 1 is plottedas point `a', the `combined very pessimistic' value =84.6, is plotted as point f4. Fig. 2 also shows the `plau-sibly pessimistic' impact value (20), plotted on theimpact axis (CP = 0) as point h, to avoid a prescrip-tive probabilistic interpretation in CP terms. The plau-sibly pessimistic value should not be associated with aCP = 0.99 or 99% con®dence level in general becauseit is conditional upon the MSS correlation assumption,although that interpretation is invited by Fig. 2.

2.1.6. Step 6: Summarise resultsWhether or not the estimator produces Figs. 1 and

2, the thrust of a summary of analysis results might beas follows:

1. A £12m expected cost should be used as the basisfor bidding purposes at present.

2. This £12m expected value should be interpreted as aconservative estimate because it assumes a morecapable barge than may be necessary. Givenweather data and time to test alternative barges, itmay be possible to justify a lower expected costbased on a less capable barge. If this contract wereobtained it would certainly be worth doing this kindof analysis. If a bid is submitted without doing it,committing to a particular barge should be avoided,if possible, to preserve ¯exibility.

3. A cost outcome of the order of £50m is as plausibleas £5m. This range of uncertainty is inherent in the®xed price contract o�shore pipe laying business: noabnormal risks are involved. The organisation shouldbe able to live with this risk, or it should get out ofthe ®xed price o�shore pipe laying business. On thisparticular contract a £50m outcome could be associ-ated with no buckles but most other things goingvery badly, associating a `plausibly pessimistic'impact with f3 on Fig. 2, or a buckle and a moremodest number of other problems, for example.Further analysis will clarify these scenarios but it isnot going to make this possibility go away. Furtheranalysis of uncertainty should be primarily directedat re®ning expected value estimates for bidding pur-poses or for making choices (which barge to use,when to start, and so on) if the contract is obtained.Further analysis may reduce the plausible costrange as a spin-o�, but this should not be its pri-mary aim.

3. First pass interpretation and anticipation of furtherpasses

A key driver behind the shape of the minimalistapproach of the last section is the need for a simple®rst pass sizing of uncertainties which are usefullyquanti®ed.

Table 2 (or Table 3) should make it clear that `dayslost rate' is the major source of uncertainty. The 5%decrease implied by the mid-point value of the `layrate' distribution relative to the base value is import-ant, as is the 5% increase in the mid-point value of the`cost rate' distribution. However, re®ning the basis ofthese adjustments is a low priority relative to re®ningthe basis of the 7.12 (7.25) days lost per month adjust-ment, because of the size of that adjustment and its as-sociated variability. In any re®nement of the ®rst passof the last section, `days lost rate' is the place to start.


Within `days lost rate' uncertainty, Table 2 (orTable 3 or Fig. 2) should make it clear that `weather'is the dominant source of uncertainty in terms of the 6day increase in the mid-point value relative to the basevalue (Ej contribution). In Ej terms `weather' is anorder of magnitude more important than `supplies',the next most important uncertainty factor. To re®nethe E1 = 6 estimate there is no point in simply re®ningthe shape of the assumed distribution (with or withoutattempting to obtain data for direct use in re®ning theshape of the assumed distribution). Implicit in theTable 2 estimate is pipe laying taking place in an àver-age month', perhaps associated with the summer sea-son plus a modest proportion in shoulder seasons.This àverage month' should be roughly consistentwith the Table 4 duration mid-point of just 4.63months. However, the range of 2.76 months to 15.38months makes the àverage month' concept inherentlyunreliable because this range must involve `non-aver-age' winter months. To re®ne the E1 = 6 estimate it issensible to re®ne the àverage month' concept. The®rst step is to estimate an empirical `days lost' distri-bution for each month of the year, using readily avail-able wave height excedence data for the relevant seaarea, and the assumed barge's nominal wave heightcapability. The second step is to transform these distri-butions into corresponding `productive days' distri-butions. A Markov process model can then be used toderive a completion date distribution given anyassumed start date [10,11], with or without the other`days lost rate' uncertainty factors and the `lay rate'uncertainty of Table 2. Standard Monte Carlo simu-lation methods, discrete probability, or CIM (Con-trolled Internal and Memory) arithmetic [10,11] can beused.

An understanding of Markov processes should makeit clear that over the number of months necessary tolay the pipeline `weather', `supplies' and èquipment'uncertainty will cancel out on a `swings and round-abouts' basis to a signi®cant extent despite signi®cantdependence. This should reduce the residual variabilityassociated with these factors to the same order of mag-nitude as `lay rate' and `cost rate' uncertainty. How-ever, `buckles' involves an extreme event that has to beaveraged out over contracts, not months on a givencontract. A provision must be made for `buckles' ineach contract, but when one happens its cost is notlikely to be recovered on that contract, and it wouldendanger winning appropriate bids if attempts weremade to avoid making a loss if a `buckle' occurs.

It is important to ensure that risks like `buckles' areidenti®ed and expected value provisions are made atan appropriate organisational level. It is also import-ant to ensure that the risk they pose is an acceptableone. However, it should be clear that one `buckle'could happen, two or more are possible, and whether

the appropriate provision is 0.35 days lost per month,twice or half that ®gure, is a relatively minor issue. Inthe present context the ®rst pass would not suggestthat second pass attention should be given to bucklesas a priority relative to other `days lost' sources ofuncertainty or their dependence.

If the equivalent of C1 in Fig. 2 is available for eachrelevant month, it makes sense to model the C1 to C4

relationships illustrated by Fig. 2 plus the `lay rate'uncertainty via a standard Monte Carlo simulationprocess for each month, prior to running the Markovprocess. Further, it makes sense to then model, via asampling process, the `cost' = `duration' � `cost rate'relationship. This means layered cumulative represen-tations of the CIP form of Fig. 2 can be used to showa top level cumulative probability distribution for cost,including con®dence bands, and this can be decom-posed to provide built in sensitivity analysis for allcomponents of the overall uncertainty. A second passapproach might seek to do this as simply as possible.A tempting assumption to achieve this is assuming allthe Table 2 distributions other than `weather' stillapply, and independence is appropriate. However,independence on its own is not a reasonable defaultoption. For example, if the `lay rate' distribution has alow value in the ®rst month (because the barge is notworking properly) it is very likely to be low for thenext, and so on. The simplest acceptable default optionshort of perfect positive correlation is to assume inde-pendence for one run, a form of perfect positive corre-lation comparable to MSS for a second run, andinterpolate between the two for expected values at anoverall level of dependence which seems conservativebut appropriate. This will size the e�ect of dependenceat an overall level as well as the component uncer-tainty factors. The next simplest default option, whichthe authors strongly recommend, involves some levelof decomposition of this approach [3,10]. For example,the four uncertainty factors associated with `lost days'might be associated with one pair of bounds and in-terpolation, but the lay days distribution might be as-sociated with another level of dependence betweenperiods in the Markov process analysis, and the `dur-ation' and `cost rate' dependence interpolation assump-tion might be di�erent again.

In general, a second pass might re®ne the estimationof a small set of key uncertainty factors (just `weather'in our example), using a sampling process (MonteCarlo simulation) and some degree of decompositionof factors. This second pass might involve consider-ation of all the ®rst pass uncertainty factors in termsof both independence and strong or perfect positivecorrelation bounds with an interpolated intermediatelevel of dependence de®ning expected values, somelevel of decomposition generally being advisable forthis approach to dependence. Default correlation


assumptions of the kind used in Fig. 2 should su�ceas plausible correlation bounds in this context.

A third pass is likely to address and re®ne depen-dence assumptions and associated variability assump-tions in the context of particularly importantuncertainty factors, further passes adding to the re®ne-ment of the analysis as and where issues are identi®edas important relative to the attention paid to them tilldate.

The number of passes required to reach any givenlevel of understanding of uncertainty will be a functionof a number of issues, including the level of computersoftware support.

4. Scope for automation

The minimalist approach was deliberately designedfor simple manual processing and no supporting soft-ware requirements. A pertinent question is whethersoftware could provide useful support.

The Table 1 speci®cation input to a generic packagecould be used to present the user with Table 2 formats,and a request for the necessary information in Table 2format. The analysis could then proceed automaticallyto Fig. 2 formats with or without Fig. 1 portrayals (aspure outputs) in the same manner. The Fig. 2 formatdiagrams might be provided assuming independence aswell as a variant of MSS, with a request to use theseresults to select an appropriate intermediate depen-dence level. As discussed in the context of a secondpass approach, this `sizes' dependence as well as as-sociated parameter variability, and it could (andshould) be decomposed. Relatively simple hardwareand inexpensive commercially available software (like@Risk) could be used to make the input demands ofsuch analysis minimal, the outputs easy to interpretand rich, and the movement on to second and furtherpasses relatively straightforward.

In general, such application speci®c software shouldbe developed once it is clear what analysis is required,after signi®cant experience of the most appropriateforms of analysis for ®rst and subsequent passes hasbeen acquired. If such software and associated devel-opment experience is available, a key bene®t is analysison the ®rst pass at the level described here as secondor third pass, with no more e�ort or time required.

In our example context, a ®rm operating lay bargeson a regular basis would be well advised to develop acomputer software package, or a set of macros withina standard package, to automate the aspects of uncer-tainty evaluation which are common to all o�shorepipe laying operations, including drawing on the rel-evant background data as needed. Following theexample of BP [15], software could allow the selectionof a sea area and a wave height capability, and auto-

matically produce the equivalent of all relevant Fig. 2C1 diagrams for all relevant months using appropriateweather data. Given a start date and the Table 1 baseparameters, it could then run the Markov process cal-culations (with or without other `days lost' uncertaintyfactors), to derive completion date (duration) prob-ability distributions.

5. Managing and shaping expectations

The minimalist approach uses ranges primarily toobtain an estimate of expected impact in terms of costor time which is simple, plausible, and free of bias onthe low side. The estimator should be con®dent thatmore work on re®ning the analysis is at least as likelyto decrease the expected value estimate as to increaseit. A tendency for cost estimates to drift upwards asmore analysis is undertaken indicates a failure of ear-lier analysis. The minimalist approach has beendesigned to help manage the expectations of those theestimator reports to in terms of expected values. Pre-serving credibility should be an important concern.

The minimalist approach provides a lower bound onimpacts which is plausible and free of bias. However,in the current example, the approach does not providea directly comparable upper bound (in simpler con-texts it will [13]), and resorts to a very simple rule ofthumb in a ®rst pass to de®ne a plausible upperbound. The resulting ranges are wide. This shouldre¯ect the estimator's secondary interest in variabilityand associated downside risk at this stage, unlessmajor unbearable risks are involved. It should alsore¯ect a wish to manage the expectations of thosereported in terms of variability. Those reported toshould expect variability to decline as more analysis isundertaken.

In the example context, the extent to which the or-ganisation accepts the estimator's view that no abnor-mal risks are involved should have been tested by theplausible upper bound of £50m in Table 4. As notedearlier (Step 6), one implication of this plausible upperbound is that a pipe laying company in the business ofbidding for ®rm ®xed price contracts with a base costestimate of the order of £12m must be prepared for avery low probability extreme project to cost four timesthis amount. A 4.63 months expected duration andFig. 2 should suggest that a one season project is themost likely outcome (say probability = 0.90 to 0.99),but being unable to complete before winter weatherforces a second season as an outcome with a signi®-cant probability (say 0.01 to 0.1), and a third season isunlikely, but possible. The £50m upper bound couldbe viewed as a scenario associated with three moder-ately expensive seasons or two very expensive seasons,


without taking the time to clarify the complex pathsthat might lead to such outcomes at this stage.

Regarding this risk as `bearable' does not mean rea-lising it cannot be disastrous. It means either:

(a) accepting this level of risk is not a problem interms of swings and roundabouts which are accep-table; or(b) not accepting this risk would put the ®rm at aneven higher risk of going out of business, becausecompetitors would bid on the basis of acceptingsuch risks.

Firms working on the basis of (b) can balance therisk of going out of business on the basis of one pro-ject or a series of projects, but they cannot eliminatethe risk of going out of business. Being sure you willnever make a loss on any project is a sure way to goout of business. A ®rm operating in mode (b) shouldhave some idea what both probabilities are if a balanceis to be achieved consistently. The pipe laying contrac-tor may approach this issue operationally by preparingeach bid using the barge which is believed to be thehighest capability/cost rate option likely to win the bid(a conservative, lowest possible risk approach), andthen testing the attractiveness of successive lower capa-bility/cost rate options. Consideration of such optionswill focus attention on the question of what level ofrisk de®nes the limit of bearability for the contractor.This limit can then be assessed in relation to the needto take risk to stay in business, which may have mer-ger implications. In this sense the estimator can helpthe organisation to shape expectations.

6. Robustness of the minimalist approach

How might the estimator defend and explain theminimalist ®rst pass approach from all the substantivecriticisms others might put? The issue of interest hereis not robustness in terms of the sensitivity of speci®cparameter assumptions, but robustness in a more fun-damental process sense.

This section addresses robustness of the approach ina sequence chosen to facilitate further clari®cation ofthe rationale for the approach. The concern is morewith clarifying the rationale for the general form ofthe approach rather than with defending the details ofeach step, and the authors have no wish to defendexample parameter values or associated rules ofthumb.

6.1. The parameter structure

The example used to illustrate the approachemployed four basic parameters and four compositeparameters, which may seem excessively complex. In

many contexts it would be [13]. However, in the pre-sent example this detail o�ers a decomposition struc-ture for the estimation process which is extremelyuseful. The combinations which it makes formal andexplicit in Table 4 would have to be dealt with intui-tively and implicitly in Tables 1±3 if they were notbroken out in the ®rst section of Table 1. Saving timeby using a simpler structure is possible, but it wouldnot be a cost e�ective shortcut in the authors' view.

If eight parameters is better than six or seven, whatabout nine or ten? The answer here is less clear-cut.For example, `cost rate' might be decomposed into a`lay day cost rate' (associated with days when theweather is good and pipe laying takes place) and an`idle day cost rate' (associated with bad weather), the£2.5m being an average linked to about 7 idle daysand 23 lay days per month, consistent with Table 2.Uncertainty as to which rate applies might be explicitlynegatively correlated with weather uncertainty, redu-cing variability considerably. This might be useful.Certainly it would be useful to decompose in this wayif a subcontract de®ned the cost this way.

However, the spirit of the minimalist approach isnot to introduce complications which don't have aclear bene®t provided the simple assumptions are con-servative (biased on the pessimistic side). Deliberatebias on the conservative side is justi®ed on the groundsthat by and large people underestimate variability, soa failure to build an appropriate conservative bias willlead to inevitable optimistic bias. How far this conser-vatism needs to be taken can only be determinedempirically. When more projects come in under costand ahead of time than the original estimates suggestis statistically valid, a less conservative approach iswarranted. BP achieved this using the SCERTapproach [5], but they are unique in the authors' ex-perience. Few organisations have this `problem', and itis relatively easy to deal with if they do.

6.2. The uncertainty factor structure

It might be tempting to use a single uncertainty fac-tor for some or even all basic parameters which are tobe given a quantitative treatment. However, in the pre-sent example wide ranging experience suggests thatthis would produce a much lower estimate of potentialvariations, since estimators tend to underestimatevariability consistently. Accordingly, identi®ed contri-buting factors should yield wider ranges which are clo-ser to reality. Further, di�erent contributinguncertainty factors lend themselves to di�erent sourcesof expertise and data, di�erent responses includingdi�erent ownership, and a better understanding of thewhole via clear de®nition of the parts. It is di�cult tosee what would be gained by recombining any of theuncertainty factors associated with probabilistic treat-


ment in Table 1. The most attractive possible simpli®-cation would seem to be combining `supplies' and`equipment', but apart from di�erent sources of dataand expertise, it might be possible to transfer the`supplies' risk to the client if pipe supplies is the keycomponent.

Combining uncertainty factors which are not treatedprobabilistically saves minimal analysis e�ort, but it isworth considering in terms of interpretation e�ort. Acollection of non-quanti®ed `other' categories is therisk analyst's last refuge when risks occur which havenot been explicitly identi®ed. However, this should notmake it a `last refuge for scoundrels', and examplesnot worth separate identi®cation should be provided.

Pushing the argument the other way, there is adeclining bene®t as more sources of uncertainty areindividually identi®ed. There is no suggestion that theset of thirteen uncertainty factors in Table 1 is opti-mal, but ten is the order of magnitude (in a range ®veto ®fty) that might be expected to capture the opti-mum bene®t most of the time for a case involving thelevel of uncertainty illustrated by the example.

6.3. Treatment of low probability-high impact events

In our example context, suppose `catastrophic equip-ment failure' has a probability of occurring of about0.001 per month, with consequences comparable to a`buckle'. It might be tempting to identify and quantifythis uncertainty factor, but doing so would lead to avariant of Fig. 2 where the additional curve cannot bedistinguished from the CP = 1.0 bound and anexpected value impact observable on Table 3 of theorder of 0.35 days lost per month. The minimalistapproach will communicate the spurious nature ofsuch sophistication very clearly, to support the learn-ing process for inexperienced estimators. This is extre-mely important, because making mistakes is inevitable,but making the same mistakes over and over is not.Nevertheless, it may be very useful to identify `cata-strophic equipment failure' as an uncertainty factornot to be quanti®ed, or to be combined with other lowprobability-high impact factors like `buckles'.

Now suppose some other uncertainty factor has aprobability of occurring of about 0.01 per month,directly comparable to a `buckle', with consequencescomparable to a `buckle'. The expected value impact issmall (0.35 days per month, about a day and a halfover the project), but the additional downside risk issigni®cant, and clearly visible on the equivalent ofFig. 2. It is important not to overlook any genuine`buckle' equivalents, while studiously avoiding spurioussophistication.

There is no suggestion that the one `buckle' factorequivalent of Table 1 is optimal, but one factor is theorder of magnitude (in a range zero to ®ve) we might

expect to capture the optimum bene®t most of thetime for cases involving the level of uncertainty illus-trated by the example.

In our example context, the event `lay barge sinks'might have a probability of the order one tenth of thatof a `buckle', and implications a factor of 10 worse,giving an expected value of the same order as a`buckle' but with a much more catastrophic impli-cation when it happens. In expected value termsquanti®cation is of very modest importance, but recog-nising the risk exposure when bidding if insurance orcontractual measures are not in place is of great im-portance. The minimalist approach recognises the needto list such risks, but it clari®es the limited advantagesof attempting quanti®cation for present purposes.

6.4. Less than perfect positive correlation

Less than perfect positive correlation would a�ectthe expected value interpretation of mid-point valuesof Tables 2±4 and Fig. 2, and the Fig. 2 curves C2±C4

would develop `S' shapes.For example, in Table 2 the `supplies' event prob-

ability mid-point is (0.3 + 0.1)/2 = 0.2, and theimpact mid-point is (3 ÿ 1)/2 = 2. If these two distri-butions are combined assuming independence, theexpected impact of `supplies' should be (0.2� 2) = 0.4(and the product distribution will not be symmetric).However, the `supplies' mid-point expected impact is5, rising to 5.4 in Table 3.

There are several reasons for avoiding the sophisti-cation of less than perfect positive correlation for a®rst pass approach, although more re®ned assessmentslater may focus on statistical dependence structures.

1. It is important to emphasise that some form of per-fect positive correlation should be the default optionrather than independence, because perfect positivecorrelation is usually closer to the truth, and any®rst-order approximation should be inherently con-servative.

2. Successive attempts to estimate uncertainty tend touncover more and more uncertainty. This is part ofthe general tendency for people to underestimateuncertainty. It makes sense to counterbalance thiswith assumptions which err on the side of buildingin additional uncertainty. If this is done to a su�-cient level, successive attempts to estimate uncer-tainty ought to be able to reduce the perceiveduncertainty. Failure to achieve this clearly signalsfailure of earlier analysis, throwing obvious shadowsover current e�orts. The perfect positive correlationassumption is a key element in the overall strategyto control bias in the minimalist approach.

3. It is particularly important to have a ®rst passapproach which is biased on the pessimistic side if


one possible outcome of the ®rst pass is sub-sequently ignoring uncertainty or variability.

4. Perfect positive correlation is the simplest assump-tion to implement and to interpret, and a minimalistapproach should keep processes and interpretationsas simple as possible. This simplicity may be less im-portant than the ®rst two reasons, but it is still veryimportant.

5. Perfect positive correlation clearly proclaims itselfas an approximation which can be re®ned, avoidingany illusions of truth or unwarranted precision, andinviting re®nement where it matters.

6.5. The assumption of uniform probability densityfunctions

An assumption of uniform probability density func-tions involves a relatively crude speci®cation of uncer-tainty. Other forms of distribution would assign lowerprobabilities to extreme values and higher probabilitiesto central values, and allow a degree of asymmetry tobe incorporated.

Dropping the uniform probability distributionassumption is likely to a�ect expected value estimatesof both cost and duration because such distributionsare usually considered asymmetric. Typically, cost andduration distributions are perceived to be left skewed,implying a reduction in expected values compared withan assumption of a uniform distribution over the samerange of values. However, employing uniform distri-butions in a ®rst pass is useful for a number of reasonswhich are similar to the reasons for assuming perfectpositive correlation.

1. The ®rst pass is a ®rst order approximation whichshould be inherently conservative.

2. It is useful to build in enough uncertainty and bias inexpected values to overcome inherent tendencies tounder-estimate risk and make successive measurementof uncertainty diminish the perceived uncertainty.

3. Linearity in density and cumulative probabilityfunctions has the elegance of simplicity that works.It clari®es issues which smooth curves can hide.

4. A uniform distribution clearly proclaims itself as anapproximation which can be readily modi®ed iflater analysis warrants more sophisticated distri-bution shapes.

7. Conclusion

This paper describes a `minimalist' ®rst passapproach to estimation and evaluation of uncertaintywhich is aimed at achieving a cost e�ective approachto risk assessment. The `minimalist' approach de®nes

uncertainty ranges for probability and impact associ-ated with each source of uncertainty. Subsequent cal-culations preserve expected value and measures ofvariability, while explicitly managing associated opti-mistic bias.

The minimalist approach departs from the ®rst passuse of probability density histograms or convenientprobability distribution assumptions which the authorsand many others have used for years in similar con-texts. Readers used to ®rst pass approaches whichattempt considerable precision may feel uncomfortablewith the deliberate lack of precision incorporated inthe minimalist approach. However, more precise mod-elling is frequently accompanied by questionableunderlying assumptions like independence, and lack ofattention to uncertainty in original estimates. Theminimalist approach forces explicit consideration ofthese issues. It may be a step back in terms of taking asimple view of the ``big picture'', but it should facili-tate more precise modelling of uncertainty where itmatters, and con®dence that precision is not spurious.To quote one of this paper's referees, `simple, timely,transparent models are often of more value in practicethan sophisticated ``accurate'' methods'.

The paper makes use of a particular example contextto illustrate the approach, but the focus is importantgeneric assessment issues. Nevertheless, context speci®cissues cannot be avoided, and there is considerablescope for addressing the relevance of the speci®c tech-niques and the philosophy behind the minimalistapproach in other contexts. For example, the processoutlined could be used as the basis for more detailedpasses for risk management purposes later than thebidding stage in a project life cycle.

An important process issue is the level of detail ordecomposition of contextual factors to employ. Whilesome discussion of this problem has been presentedhere, there is scope for further work on this issue. Theminimalist approach is entirely ¯exible in this respect.Much simpler composite parameter and uncertaintyfactor structures than those employed in this papercould be used for projects which warrant less e�ortdevoted to formal risk management. In the limit asingle parameter could be associated directly withuncertainty, like total cost, but insight and consequentunderstanding of uncertainty management issues maybe lost.

The main purpose of this paper is to generate a dia-logue about the developing `uncertainty management'paradigm which underlies the seven objectives outlinedin the introduction, and to expose the philosophybehind it to constructive criticism. The authors hopesome of the uncertainty assessment ideas outlined herewill stimulate others to put them to the test in practi-cal applications and contribute to the evolution of theparadigm as a whole.


References

[1] Simon P, Hillson D, Newland K, editors. Project risk analysis

and management guide (PRAM). UK: Association for Project

Management, 1997.

[2] Chapman CB. Project risk analysis and management Ð PRAM

the generic process. International Journal of Project

Management 1997;15:273±81.

[3] Chapman CB, Ward SC. Project risk management: processes,

techniques and insights. Chichester, UK: John Wiley, 1997.

[4] MoD (PE) Ð DPP(PM), Risk Management in Defence

Procurement. Available from Ministry of Defence Procurement

Executive, Directorate of Procurement Policy (Project

Management), Whitehall, London, 1991.

[5] Chapman CB. Large engineering project risk analysis. IEEE

Transactions on Engineering Management 1979;EM-76:78±86.

[6] Institution of Civil Engineers and the Faculty and Institute of

Actuaries, RAMP: Risk Analysis and Management for Projects.

Thomas Telford, London, 1998.

[7] Knight F. Risk, uncertainty and pro®t. Boston: Houghton

Mi�n, 1921.

[8] Rai�a H. Decision analysis: introductory lectures on choices

under uncertainty. Reading, MA: Addison-Wesley, 1968.

[9] Ward SC. Assessing and managing important risks.

International Journal of Project Management 1999;17:331±6.

[10] Cooper DF, Chapman CB. Risk analysis for large projects:

models, methods and cases. Chichester, UK: John Wiley, 1987.

[11] Chapman CB, Cooper DF. Risk engineering: basic controlled

interval and memory models. Journal of the Operational

Research Society 1983;43:647±64.

[12] Ward SC, Chapman CB. Developing competitive bids: a frame-

work for information processing. Journal of the Operational

Research Society 1988;39:123±34.

[13] Chapman CB, Ward SC, Bennell JA. Incorporating uncertainty

in competitive bidding. International Journal of Project

Management, forthcoming.

[14] Moder JJ, Philips CR. Project Management with CPM and

PERT. New York: Van Nostrand, 1970.

[15] Clark P, Chapman CB. The development of computer software

for risk analysis: a decision support system case study.

European Journal of Operations Research 1987;29:252±61.

Chris Chapman is Professor of Man-

agement Science at the School of

Management, University of South-

ampton, UK. For about 25 years his

consulting and research have centred

on the management of risk. Most of

his consulting has been concerned

with large energy projects in the UK,

USA and Canada, but other concerns

have included computer hardware and

software systems, aircraft production,

warship building, ®nancial asset and

commodity broking portfolio manage-

ment. He was founding chairman of the APM Speci®c Interest

Group (SIG) on Project Risk Management, and is a past president

of the Operational Research Society. He holds a BSc in Industrial

Engineering (Toronto), an MSc in Operational Research (Birming-

ham) and a PhD in Economics and Econometrics (Southampton).

Stephen Ward is a Senior Lecturer in

Management Science, at the School of

Management, University of South-

ampton, UK. He was responsible for

setting up the School's MBA pro-

gramme and is now Director of the

School's Masters programme in Risk

Management. His research and con-

sulting interests include project and

contract risk management, strategic

investment appraisal and managerial

decision processes. He holds a BSc in

Mathematics and Physics (Notting-

ham), an MSc in Management Science

(Imperial College, London), and a PhD in Operational Research

(Southampton).


estimation and evaluation of uncertainty: a minimalist first pass approach

Documents