## Estimating Concepts

The objectives of performing an estimate are twofold: to arrive at an expected value for the item be able to convey a figure of merit for that estimate. In this book we will focus on estimating deli' figure of merit we will use is the confidence interval that is calculable from the statistical data of 1 of the expected value of the estimate.

Most estimating fits into one of four models as illustrated in Figure 3-8:

■ Top-down value judgments from the business side of the project balance sheet conveyed ■

■ Similar-to judgments from either side of the project balance sheet, but most often from the

■ Bottom-up facts-driven estimates of actual work effort from the project side of the project I to the project sponsor

■ Parametric calculations from a cost-history model, developed by the project team, and cor sponsor

Naturally, it is rare that a project would depend only on one estimating technique; therefore, it is specific project team will use all the estimating methods available to it that fit the project context. them one by one.

### Top-Down Estimates

Top-down estimates could be made by anyone associated with the project, but most often top-d from the business and reflect a value judgment based on experience, marketing information, be consulting information, and other extra-project information. Top-down estimates rarely have con of the type needed by the project team to validate the estimate with the scope laid out on the WB

Working with top-down estimates requires the steps shown in Table 3-3. Project risks are greate methodology, and overall cost estimates are usually lowest. In its purest form, top-down estimat quantitative information that could be developed by the project team regarding the project cost. independent input to cost developed by the project team, the purpose of such an independent ir is to provide comparative data with the top-down estimate. Such a comparison serves to establi: of the risks of being able to execute the project for the top-down budget. Because risks are grea estimating, the risks developed in response to top-down budgets require careful identification, m estimation before the project begins. Risks are quantified and made visible on the project side o sheet.

A common application of the top-down methodology is in competitive bidding to win a project op

A common application of the top-down methodology is in competitive bidding to win a project op to the project sponsor. In this scenario, the top-down estimate usually comes from a marketing < what the market will bear, what the competition is bidding, and in effect "what it will take to win." is the figure offered to the customer as the price, then the project manager is left with the task ol performance and developing the risk management plan to contain performance cost within the o

Top-down offer to do business = Independently estimated cost of performance offered + Risk tc offer

From the steps in Table 3-3, we see that the project manager must allocate the top-down budge involves the following quantitative steps:

■ Develop the WBS from the scope statement, disregarding cost.

■ By judgment, experience, prototyping, or other means, determine or identify the deliverable deliverable that represents the smallest "standard unit of work." Give that deliverable a num and call it the "baseline" deliverable, B. This procedure normalizes all costs in the WBS to t deliverable.

■ Estimate the normalized cost of all other deliverables, D, as multiples, M, of the baseline de where M is a random variable with unknown distribution and "i" has values from 1 to n. "n" i: deliverables in the WBS.

■ Sum all deliverable weights and divide the sum into the available funds to determine an abi least costly deliverable.

(\$Top-down budget)/( Mi) = Allocated cost of baseline task B

■ A "sanity check" on the cost of B is now needed. Independently estimate the cost of B to de minus, between the allocated cost and the independent estimate. This offset, O, is a bias to deliverable in the WBS. The total bias in the WBS is given by:

■ Complete the allocation of all top-down budgets to the deliverables in the WBS according to

■ It is helpful at this point to simplify the disparate deliverables on the WBS to an average deli We know from the Central Limit Theorem that the average deliverable will be Normal distrib the Normal distribution will be helpful to the project manager:

Average deliverable cost = a d = (1/n) * [Di + (Mi * O)]

s 2 of average deliverable = (1/n) * [(Di + O) - a d]2, and s of average deliverable = v (1/n) * [(D,- + O) - a d]2

It is easier to calculate these figures than it probably appears from looking at the formulas. Table numerical example. In this example, a \$30,000 top-down budget is applied to a WBS of seven d estimated at 23% of the allocated cost. Immediately, it appears that there may be a \$6,900 risk ■ \$30,000). However, we see from the calculations employing the Normal distribution that the con down budget is only 24%, and with the \$6,900 risk included, the confidence increases to only 50 the level needed for many firms to do fixed price bidding, the risk increases significantly. Clearly reduced, then the scope will have to be downsized or the budget increased, or more time given t in order for this project to go forward.

Table 3-4: Top-Down Allocation to WBS

 WBS Element Weight, Mi Allocated Budget, Di Allocated Budget + (Mi * O) Distal a b c d 1 1.1.1 8 \$10,435 \$12,835 1.1.2 5 \$6,522 \$8,022 1.1.3 1 \$1,304 \$1,604 1.2.1 2 \$2,609 \$3,209 1.2.2 2.5 \$3,260 \$4,010 1.3.1 1.5 \$1,957 \$2,407 1.3.2 3 \$3,913 \$4,813 Totals: 23 \$30,000 \$36,900 Given: Top-down budget = \$30,000 Evaluated least costly baseline deliverable, B = \$1,304.35 Estimated independent cost of B = \$1,604.35 Calculated baseline offset, O, = \$300 = \$1,604.35 - \$1,304.35 D = (Mi * B) = \$30,000 Average deliverable, average d, with offset = \$36,900/7 = \$5,271 Variance, s 2 = 92,479,890/7 = 13,211,413 Standard deviation, s = \$3,635 Confidence calculations: Total standard deviation of WBS = v 7* s 2 = v 92,479,890 = \$9,616 24% confidence: WBS total = \$30,000 H 50% confidence: WBS total = \$36,900 68% confidence: WBS total = \$36,900 + \$9,616 = \$46,516 t'lFrom lookup on single-tail standard Normal table for probability of outcome = (\$36,900 -\$30,1 below the mean value. Assumes summation of WBS is approximately Normal with mean = \$36 \$9,616.

Once the risks are calculated, all the computed figures can be moved to the right side of the pre recap what we have so far. On the business side of the project balance sheet, we have the top-i project sponsors. This is a value judgment about the amount of investment that can be afforded desired. On the right side of the balance sheet, the project manager has the following variables:

■ The estimated "fixed" bias between the cost to perform and the available budget. In the exa

■ The average WBS for this project and the statistical standard deviation of the average WBS average WBS is \$36,900 (equal to the budget + bias) and the standard deviation is \$9,616.

As was done in the example, confidences are calculated and the overall confidence of the proje project sponsor until the project risks are within the risk tolerance of the business.

### Similar-To Estimates

"Similar-to" estimates have many of the features of the top-down estimate except that there is a with similar characteristics and a cost history to guide estimating. However, the starting point is th declares the new project "similar to" another completed project and provides the budget to the n on the cost history of the completed project. Of course, some adjustments are often needed to c of labor and material costs from an earlier time frame to the present, and there may be a need t difference. In most cases, the "similar-to" estimate is very much like a top-down estimate except history at the WBS deliverable level available to the project manager that can be used by the pro narrow the offsets. In this manner, the offsets are not uniformly proportional as they were in the rather they are adjusted for each deliverable to the extent that relevant cost history is available.

The quantitative methods applied to the WBS are not really any different from those we employe except for the individual treatment of the offsets. Table 3-5 provides an example. We assume cc the offset estimates (or provide the business with a more realistic figure to start with). If so, the c developed by the business as a "similar to" is generally much higher.

 WBS Element Allocated Budget from Cost History, Di Offset Allocated Budget + (Mi * O) a b c d 1 1.1.1 \$10,435 \$200 \$10,635 1.1.2 \$6,522 -\$100 \$6,422 1.1.3 \$1,304 \$300 \$1,604 1.2.1 \$2,608 \$50 \$2,658 1.2.2 \$3,261 -\$75 \$3,186 1.3.1 \$1,957 \$100 \$2,057 1.3.2 \$3,913 -\$200 \$3,713 Totals: \$30,000 \$275 \$30,275 Given: Top-down budget = \$30,000 Evaluated least costly baseline deliverable, B = \$1 ,304 D = (Mi * B) = \$30,000 Average deliverable, average d, with offset = \$30,275/7 = \$4,325 Variance, s 2 = (1/7) * (61,208,612) = 8,744,087 Standard deviation, s = \$2,957 Confidence calculations: Total standard deviation of WBS = v 61, 208,612 = \$7,823 46% confidence: WBS total = \$30,000 H 50% confidence: WBS total = \$30,275 68% confidence: WBS total = \$30,275 + \$7,823 = \$38,098

[*]From lookup on single-tail standard Normal table for probability of outcome = (\$30,275 - \$30, 0.09s below the mean value. Assumes summation of WBS is approximately Normal with mear \$2,957._

### Bottom-Up Estimating

So far we have seen that the project side of the balance sheet is usually a higher estimate than t business. Although there is no business rule or project management practice that makes this so happen more often than not. That trend toward a higher project estimate continues in bottom-up

Bottom-up estimating, in its purest form, is an independent estimate by the project management the WBS. The estimating team may actually be several teams working in parallel on the same e an arrangement is called the Delphi method. The Delphi method is an approach to bottom-up e. independent teams evaluate the same data, each team comes to an estimate, and then the pro a final estimate from the inputs from all teams.

The starting point for the estimating team(s) is the scope statement provided by the business. A is provided as information and guidance. Parametric data developed from cost history are assur practice, parametric data in some form are usually available, but we will discuss parametric data

Best practice in bottom-up estimating employs the "n-point" estimate rather than a single determ number of points is commonly taken to be three: most likely, most pessimistic, and most optimis "three-point estimates"). A distribution must be selected to go with the three-point estimate. The Triangular are the distributions of choice by project managers. The BETA and Triangular are us< and deliverables; the Normal is a consequence of the interaction of many BETA or Triangular di WBS. However, if there are deliverables with symmetrical optimistic and pessimistic values, then those cases.

Table 3-6 provides a numerical example of bottom-up estimating using the BETA distribution. Re distribution will give more pessimistic statistics than the BETA. Although individual deliverables ar somewhat wide swings in optimistic and pessimistic range, overall the confidence of hitting a low certainty is higher.

 WBS Element Most Likely Estimate Most Pessimistic Offset Most Optimistic Offset BETA Expecte Valu 1 1.1.1 \$11,000 \$3,000 -\$1,000 \$11,33 1.1.2 \$6,800 \$4,000 -\$700 \$7,35 1.1.3 \$1,500 \$800 -\$300 \$1,58 1.2.1 \$3,000 \$2,000 -\$500 \$3,25 1.2.2 \$3,100 \$1,800 -\$750 \$3,27 1.3.1 \$1,800 \$800 -\$300 \$1,88 1.3.2 \$3,700 \$1,900 -\$600 \$3,91 Totals: \$32,59 Business desires project outcome = \$30,000

Average deliverable from BETA = \$32,591/7 = \$4,656 Variance, s 2 = 1,653, 124/7 = 236,161

Standard deviation, s = \$486_

Confidence calculations:

Total standard deviation of WBS = v 1, 653,124 = \$1,286 50% confidence: WBS total = \$32,591 H

68% confidence: WBS total = \$32,591 + \$1,286 = \$33,877_

[*]Assumes approximately Normal distribution of WBS summation with mean = \$32,594 and s :

### Parametric Estimating

Parametric estimating is also called model estimating. Parametric estimating depends on cost h similarity between that project history available to the model and the project being estimated. Ps employed widely in many industries, and industry-specific models are well published and suppor many practitioners. [121 The software industry is a case in point with several models in wide use. industry that builds hardware, as well as the construction industry, environmental industry, pharr others have many good models in place. The general characteristics of some of these models s

 Estimating Application Model Identification Key Model Parameters and Calibration Factors Model < Construction PACES 2001 Covers new construction, renovation, and alteration Covers buildings, site work, area work Regression model based on cost history in military construction Input parameters (abridged list): size, building type, foundation type, exterior closure type, roofing type, number of floors, functional and utility space requirements Media/waste type: cleanup facilities and methods Specific (not ave specified accordii Project Life cyc Environmental RACER Handles natural attenuation, free product removal, passive water treatment, minor field installation, O&M, and phytoremediation Technical enhancements to over 20 technologies Ability to use either system costs or user-defined costs Professional labor template that creates task percentage template Program budgets remedia projects
 Hardware Price H® Key parameters: weight, size, and manufacturing complexity Input parameters: quantities of equipment to be developed, design inventory in existence, operating environment and hardware specifications, production schedules, manufacturing processes, labor attributes, financial accounting attributes Cost es Other p Six knowledge bases support the WBS elements: application, platform, optional description, acquisition category, standards, class Cost estimates are produced for development and production cost activities (18) and labor categories (14), as well as "other" categories (4) Product estimate and risk hardwar and acc NAFCOM (NASA Air Force Cost Model) Available to qualified government contractors and agencies WBS oriented Subsystem oriented within the WBS Labor rate inputs, overhead, and G&A costs Integration point inputs Test hardware and quantity Production rates Complexity factors Test throughput factors Integrates with some commercial estimating models Estimate develop evaluati unit, pro (DDT&E costs (waterfall methodology) Development environment: detached, embedded, organic Model complexity: basic, intermediate, detailed Parameters used to calibrate outcome (abridged list): estimated delivered source lines of code, product attributes, computer attributes, personnel attributes, project attributes (with breakdown of attributes, about 63 parameters altogether) Effort an hours or Other pa COCOMO II (object oriented) Development stages: applications composition, early design, post architecture (modified COCOMO 81) Parameters used to calibrate outcome (abridged list): estimated source lines of code, function points, COCOMO 81 parameters (with some modification), productivity rating (Stage 1) Effort an hours or Other pa
 Price S Nine categories for attributes: project magnitude, program application, productivity factor, design inventory, utilization, customer specification and reliability, development environment, difficulty, and development process Effort an hours or Other p SEER-SEM Three categories for attributes: size, knowledge base, input Input is further subdivided into 15 parameter types very similar to the other models discussed Effort an hours or Other p

Most parametric models are "regression models." We will discuss regression analysis in Chapte require data sets from past performance in order that a regression formula can be derived. The used to predict or forecast future performance. Thus, to employ parametric models they first mu history. Calibration requires some standardization of the definition of deliverable items and item . specific to the model or to the technology or process being modeled is a good device for obtainin complete history records. For instance, to use a software model, the definition of a line of code i attributes of complexity or difficulty require definitions. In publications, the page size and compos well as the type of original material that is to be received and published. Typically, more than ter obtain good calibration, but the requirements of cost history are model specific.

Once a calibrated model is in hand, to obtain estimates of deliverable costs the model is fed witl project being estimated. Model parameters are also set or adjusted to account for similarity or di project being estimated and the project history. Parameter data could be the estimated number to be written and their appropriate attributes, such as degree of difficulty or complexity. Usually, incorporated into the model. That is to say, if the methodology for developing software involves i development, prototyping, code and unit test, and system tests, then the model takes this metho Some models also allow for specification of risk factors as well as the severity of those risks.

Outcomes of the model are applied directly to the deliverables on the WBS. At this point, outcom bottom-up estimates. Ordinarily, these outcomes are expected values since the model will have risk factors and methodology to arrive at a statistically useful result. The model may or may not | information, such as the variance, standard deviation, or information about any distributions emp expected value is provided, then the project manager must decide whether to use some indepen develop statistics that can be used to develop confidence intervals. The model outcome may als dependencies accounted for in the result; as we saw in the discussion of covariance, dependent factors.

Table 3-8 provides a numerical example of parametric estimating practices in the WBS.

Table 3-8: Parametric Estimating

 WBS Element Deliverable Units Quantity Parametric Cost Model Expected Value M Stan Deviat 1 1.1.1 Software code Lines of code 5,000 \$25 \$125,000 \$25 1.1.2 Software test plans Pages 500 \$400 \$200,000 \$10 1.1.3 Software requirements Numbered items 800 \$100 \$80,000 \$12 1.2.1 Tested module Unit tests 2,000 \$100 \$200,000 \$3C 1.2.2 Integrated module Integration points 1,800 \$50 \$90,000 \$3 1.3.1 Training manuals Pages 800 \$400 \$320,000 \$4 1.3.2 Training delivery Students 900 \$500 \$450,000 \$5 Totals: \$1,465,000 Average deliverable from model = \$1,465,000/7 = \$209,286 Variance, s 2 = 1,822,250,000/7 = 260,321,429 Standard deviation, s = v 260.321 ,429 = \$16,134 Confidence calculations: Standard deviation of total expected value = v (1 ,822,250,000) = \$42,687 68% confidence: WBS total = \$1,465,000 + \$42,687 = \$1,507,687 ^Assumes approximately Normal distribution of WBS summation with mean = \$1 ,465,000 anc

t12lA current listing of some of the prominent sources of information about parametric estimating "Appendix E, Listing of WEB Sites for Professional Societies, Educational Institutions, and Suppl the Joint Industry/Government "Parametric Estimating Handbook," Second Edition, 1999, spons of Defense. Among the listings found in Appendix E are those for the American Society of Profe; International Society of Parametric Analysis, and the Society of Cost Estimating and Analysis.

Team LiB

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