Confidence Interval . Each time you take a sample from a population of values you can calculate

a mean and a standard deviation. Even if all the samples are the same size and taken using the

same random procedures, it is unlikely that every sample will have the same mean and standard

deviation. However, if you could collect all possible samples from the normally distributed

population and calculate the mean value for all the sample means, the result would be equal to

the population mean. In statistical terminology, the mean of the sampling distribution is equal to

the population mean.

You can combine the sample mean and sample standard deviation with an understanding of the

shape of distribution of sample means to develop a confidence interval — a probability

statement about an interval which is likely to contain the true population mean.

For example: Suppose that you are preparing a solicitation for an indefinite-quantity

transmission overhaul contract to support a fleet of 300 light utility trucks. You believe that you

can develop an accurate estimate of the number of transmissions that will require a major

overhaul during the contract period, if you can determine the date of the last major overhaul for

each vehicle transmission and estimate the period between overhauls. You select a simple

random sample (without replacement) of 25 vehicle maintenance records from the 300 fleet

vehicle maintenance records. Analyzing the sample, you find that the mean time between

overhauls is 38 months and the sample standard deviation (S) is 4 months. Based on this

analysis, your point estimate of the average transmission life for all vehicles in the fleet (the

population mean) is 38 months. But you want to establish reasonable estimates of the minimum

and maximum number of repairs that will be required during the contract period. You want to be

able to state that you are 90% confident that the average fleet transmission life is within a

defined range (e.g., between 36 and 40 months).

To make this type of statement, you need to establish a confidence interval. You can establish a

confidence interval using the sample mean, the standard error of the mean, and an understanding

of the normal probability distribution and the t distribution.

Standard Error of the Mean . If the population is normally distributed, the standard error of the

mean is equal to the population standard deviation divided by the square root of sample size.

Since we normally do not know the population standard deviation, we normally use the sample

standard deviation to estimate the population standard deviation.

Though the population mean and the population standard deviation are not normally known,

we assume that cost or pricing information is normally distributed. This is a critical

assumption because it allows us to construct confidence intervals (negotiation ranges) around

point estimates (Government objectives).

Calculate the Standard Error of the Mean for the Transmission Example.

Remember that: S = 4 months

n = 25 vehicle maintenance records

Normal Probability Distribution . The normal probability distribution is the most commonly

used continuous distribution. Because of its unique properties, it applies to many situations in

which it is necessary to make inferences about a population by taking samples. It is a close

approximation of the distribution of such things as human characteristics (e.g., height, weight,

and intelligence) and the output of manufacturing processes (e.g., fabrication and assembly). The

normal probability distribution provides the probability of a continuous random variable, and has

the following characteristics:

• It is a symmetrical (i.e., the mean, median, and mode are all equal) distribution and half

of the possible outcomes are on each side of the mean.

• The total area under the normal curve is equal to 1.00. In other words, there is a 100

percent probability that the possible observations drawn from the population will be

covered by the normal curve.

• It is an asymptotic distribution (the tails approach the horizontal axis but never touch it).

• It is represented by a smooth, unimodal, bell-shaped curve, usually called a “normal

probability density function” or “normal curve.”

• It can be defined by two characteristics-the mean and the standard deviation. (See the

figure below.)

NORMAL CURVE

Conditions for Using the Normal Distribution . You can use the normal curve to construct

confidence intervals around a sample mean when you know the population mean and standard

deviation.

t Distribution . In contract pricing, the conditions for using the normal curve are rarely met. As a

result, you will normally need to use a variation of the normal distribution called the ” tdistribution .”

The t distribution has the following characteristics:

• It is symmetrical, like the normal distribution, but it is a flatter distribution (higher in the

tails).

• Whereas a normal distribution is defined by the mean and the standard deviation, the t

distribution is defined by degrees of freedom.

• There is a different t distribution for each sample size.

• As the sample size increases, the shape of the t distribution approaches the shape of the

normal distribution.

t Distribution

Relationship Between Confidence Level and Significance Level .

Confidence Level. The term confidence level refers to the confidence that you have that a

particular interval includes the population mean. In general terms, a confidence interval for a

population mean when the population standard deviation is unknown and n < 30 can be

constructed as follows:

Where:

t = t Table value based on sample size and the significance level

S = Standard error of the mean

Significance Level. ) The significance level is equal to 1.00 minus the confidence level. For

example if the confidence level is 95 percent, the significance level is 5 percent; if the

confidence level is 90 percent, the significance level is 10 percent. The significance level is,

then, the area outside the interval which is likely to contain the population mean.

The figure below depicts a 90 percent confidence interval. Note that the significance level is 10

percent — a 5 percent risk that the population mean is greater than the confidence interval plus a

5 percent risk that the mean is less than the confidence interval.

90 Percent Confidence Interval

Setting the Significance Level . When you set the significance level, you must determine the

amount of risk you are willing to accept that the confidence interval does not include the true

population mean. As the amount risk that you are willing to accept decreases, the confidence

interval will increase. In other words, to be more sure that the true population mean in included

is the interval, you must widen the interval.

Your tolerance for risk may vary from situation to situation, but for most pricing decisions, a

significance level of .10 is appropriate.

Steps for Determining the Appropriate t Value for Confidence Interval Construction . After

you have taken a random sample, calculated the sample mean and the standard error of the mean,

you need only a value of t to construct a confidence interval. To obtain the appropriate t value,

use the following steps:

Step 1. Determine your desired significance level. As stated above, for most contract pricing

situations, you will find a significance level of .10 appropriate. That will provide a confidence

level of .90 (1.00 – .10 = .90).

Step 2. Determine the degrees of freedom. Degrees of freedom (df) are the sample size minus

one (n – 1).

Step 3. Determine the t value from the t Table . Find the t value at the intersection of the df

row and the .10 column.

Constructing a Confidence Interval for the Transmission Overhaul Example . Recall the

transmission overhaul example, where you wanted to estimate the useful life of transmissions of

a fleet of 300 light utility trucks. We took a random sample of size n = 25 and calculated the

following:

Where:

= 38 months

S = 4 months

= .8 months

Assume that you want to construct a 90% confidence interval for the population mean (the actual

average useful life of the transmissions). You have all the values that you need to substitute into

the formula for confidence interval except the t value. To determine the t value for a confidence

interval, use the following steps:

Determine the appropriate t value:

Step 1. Determine the significance level. Use the significance level of .10.

Step 2. Determine the degrees of freedom.

Step 3. Determine the t value from the t Table . Find the t value at the intersection of the df =

24 row and the .10 column. The following table is an excerpt of the t Table:

Partial t Table

df t

23 1.714

24 1.711

25 1.708

26 1.706

Reading from the table, the appropriate t value is 1.711.

Use the t Value and Other Data to Construct Confidence Interval:

The confidence interval for the true population mean (the actual average useful life of the

transmissions) would be:

38 1.711 (.8)

38 1.37 (rounded from 1.3688)

Confidence interval for the population mean ( ): 36.63 < < 39.37

That is, you would be 90 percent confident that the average useful life of the transmissions is

between 36.63 and 39.37 months.

3.5 Using Stratified Sampling

Stratified Sampling Applications in Contract Pricing . You should consider using sampling

when you have a large amount of data and limited time to conduct your analysis. While there are

many different methods of sampling, stratified sampling is usually the most efficient and

effective method of sampling for cost/price analysis. Using stratified sampling allows you to

concentrate your efforts on the items with the greatest potential for cost/price reduction while

using random sampling procedures to identify any general pattern of overpricing of smaller value

items.

The most common contract pricing use of stratified sampling is analysis of detailed material cost

proposals. Often hundreds, even thousands, of material items are purchased to support

production of items and systems to meet Government requirements. To analyze the quantity

requirements and unit prices for each item would be extremely time consuming and expensive.

Effective review is essential, because often more than 50 percent of the contract price is in

material items. The overall environment is custom made for the use of stratified sampling.

Steps in Stratified Sampling . In stratified sampling, the components of the proposed cost (e.g., a

bill of materials) to be analyzed are divided into two or more groups or strata for analysis. One

group or stratum is typically identified for 100 percent review and the remaining strata are

analyzed on a sample basis. Use the following steps to develop a negotiation position based on

stratified sampling:

Step 1. Identify a stratum of items that merit 100 percent analysis. Normally, these are highvalue items that merit the cost of 100 percent analysis. However, this stratum may also include

items identified as high-risk for other reasons (e.g., a contractor history of overpricing).

Step 2. Group the remaining items into one or more stratum for analysis. The number of

additional strata necessary for analysis will depend on several factors:

• If the remaining items are relatively similar in price and other characteristics (e.g.,

industry, type of source, type of product), only one additional stratum may be required.

• If the remaining items are substantially different in price or other characteristics, more

than one stratum may be required. For example, you might create one stratum for items

with a total cost of $5,001 to $20,000 and another stratum for all items with a total cost of

$5,000 or less.

• If you use a sampling procedure that increases the probability of selecting larger dollar

items (such as the dollar unit sampling procedure available in E-Z-Quant), the need for

more than one stratum may be reduced.

Step 3. Determine the number of items to be sampled in each stratum. You must analyze all

items in the strata requiring 100 percent analysis. For all other strata, you must determine how

many items you will sample. You should consider several factors in determining sample size.

The primary ones are variability, desired confidence, and the total count of items in the stratum.

Use statistical tables or computer programs to determine the proper sample size for each stratum.

Step 4. Select items for analysis. In the strata requiring random sampling, each item in the

stratum must have an equal chance of being selected and each item must only be selected once

for analysis. Assign each item in the population a sequential number (e.g., 1, 2, 3; or 1001, 1002,

1003). Use a table of random numbers or computer generated random numbers to identify the

item numbers to be included in the sample.

Step 5. Analyze all items identified for analysis, summing recommended costs or prices for

the 100 percent analysis stratum and developing a decrement factor for any stratum being

randomly sampled. In the stratum requiring 100 percent analysis, you can apply any

recommended price reductions directly to the items involved. In any stratum where you use

random sampling, you must apply any recommended price reductions to all items in the stratum.

• Analyze the proposed cost or price of each sampled item.

• Develop a “should pay” cost or price for the item. You must do this for every item in the

sample, regardless of difficulty, to provide statistical integrity to the results. If you cannot

develop a position on a sampled item because offeror data for the item is plagued by

excessive misrepresentations or errors, you might have to discontinue your analysis and

return the proposal to the offeror for correction and update.

• Determine the average percentage by which should pay prices for the sampled items

differ from proposed prices. This percentage is the decrement factor .

(There are a number of techniques for determining the “average” percentage which will produce

different results. For example, you could (1) determine the percentage by which each should pay

price differs from each proposed price, (2) sum the percentages, and (3) divide by the total

number of items in the sample. This technique gives equal weight to all sampled items in

establishing the decrement factor. Or you could (1) total proposed prices for all sampled items,

(2) total the dollar differences between should pay and proposed prices, and (3) divide the latter

total by the former total. This technique gives more weight to the higher priced sampled items in

establishing the decrement factor.)

• Calculate the confidence interval for the decrement factor.

Step 6. Apply the decrement factor to the total proposed cost of all items in the stratum .

The resulting dollar figure is your prenegotiation position for the stratum. Similarly, use

confidence intervals to develop the negotiation range.

Step 7. Sum the prenegotiation positions for all strata to establish your overall position on

the cost category .

Stratified Sampling Example . Assume you must analyze a cost estimate that includes 1,000

material line items with a total cost of $2,494,500. You calculate that you must analyze a simple

random sample of 50 line items.

Step 1. Identify a stratum of items that merit 100 percent analysis. You want to identify

items that merit 100 percent analysis because of their relatively high cost. To do this, you prepare

a list of the 1,000 line items organized from highest extended cost to lowest extended. The top

six items on this list look like this:

Item 1: $675,000

Item 2: $546,500

Item 3: $274,200

Item 4: $156,800

Item 5: $101,300

Item 6: $ 26,705

Note that the top five items $1,753,800 (about 70 percent of the total material cost). You will

commonly find that a few items account for a large portion of proposed material cost. Also note

that there is a major drop from $101,300 to $26,705. This is also common. Normally, you should

look for such break points in planning for analysis. By analyzing Items 1 to 5, you will consider

70 percent of proposed contract cost. You can use random sampling procedures to identify

pricing trends in the remaining 30 percent.

Step 2. Group the remaining items into one or more stratum for analysis. A single random

sampling stratum is normally adequate unless there is a very broad range of prices requiring

analysis. This typically only occurs with multimillion dollar proposals. Here, the extended prices

for the items identified for random sampling range from $5.00 to $26,705. While this is a wide

range, the dollars involved seem to indicate that a single random sampling strata will be

adequate.

Step 3. Determine the number of items to be sampled in each stratum. Based on the dollars

and the time available, you determine to sample a total of 20 items from the remaining 995 on

the bill of materials.

Step 4. Select items for analysis.

• One way that you could select items for analysis would be putting 1,000 sheets of paper,

one for each line item, into a large vat, mix them thoroughly, and select 20 slips of paper

from the vat. If the slips of paper were thoroughly mixed, you would identify a simple

random sample.

• A less cumbersome method would be to use a random number table (such as the example

below) or a computer program to pick a simple random sample. A random number is one

in which the digits 0 through 9 appear in no particular pattern and each digit has an equal

probability (1/10) of occurring.

• The number of digits in each random number should be greater than or equal to the

number of digits we have assigned to any element in the population.

• To sample a population of 995 items, numbered 1 to 995, random numbers must have at

least three digits. Since you are dealing with three digit numbers, you only need to use the

first three digits of any random number that includes four or more digits.

• Using a random number table below:

o You could start at any point in the table. However, it is customary to select a start

point at random. Assume that you start at Row 2, Column 3. The first number is

365; hence the first line item in our sample would be the item identified as 365.

o Proceed sequentially until all 20 sample line items have been selected. The second

number is 265, the third 570, etc. When you get to the end of the table you would

go to Row 1, Column 4.

Random Number Table

6698450

8230671

3307349

4557294

4867520

5256666

7629754

7388907

3756022

2261081

1606742

4487241

4593304

7532438

4443063

6027106

1379873

3651245

2651096

5709649

7859673

4932550

2645070

4214053

1091250

2403835

8733169

8443898

4715519

3189230

5402375

7360106

2464369

3796196

8020931

4186082

8672562

5767320

6320447

6648860

6976195

1120094

7471111

7569916

1317932

3440584

6472532

2676982

1662752

7408077

5564193

6419575

5382237

1407827

2090333

3264983

1574530

6645401

6934253

1063302

5189339

6771677

3827223

8270134

8911616

6576524

2313736

6406297

3716016

8524653

7385363

8443370

3848937

7393468

6976185

7079107

1717118

2462752

1746847

4831573

8266361

1395104

7209557

7664148

2887476

2226093

1633582

4641095

3428616

5135877

5304620

6426810

1674986

1586219

4385234

5890046

7170044

7446749

1766538

2857463

2933809

6157406

1628707

1288533

7587864

2353445

3195410

8064010

7834674

6893288

2105629

4804056

7202428

2026354

6997446

5255558

2467063

4375027

5523693

2960020

7504068

4812842

7563765

4779259

4227992

2096146

7348618

8520402

3200243

2436229

5557861

3204198

8731495

2250677

6889909

6881881

8676962

3478729

2012393

3094506

5298851

3833765

8285177

4262484

7835932

4099476

1857184

2439038

6628536

5754865

7643316

5672442

5152933

2493145

2270414

6916635

6543891

8106527

2860934

1853083

5267758

5399702

3169397

8863730

8565980

3900542

3480353

2810982

7469248

8863103

8075579

1717450

1489100

3585772

5584309

7473486

3877732

1949660

4791406

3935202

5243559

6599457

6377260

5318753

7169566

Step 5. Analyze all items identified for analysis summing recommended costs or prices for

the 100 percent analysis stratum and developing a decrement factor for any stratum being

randomly sampled.

Results of 100 Percent Analysis. Use of the 100 percent analysis is straight forward. In this

example, the offeror proposed a total of $1,753,800 for 5 line items of material. An analysis of

these items found that the unit cost estimates were based on smaller quantities than required for

the contract. When the full requirement was used, the total cost for those five items decreased to

$1,648,600. Since the analysis considered all items in the stratum, you simply need to use the

findings in objective development.

Random Sample Results. The random sample included 20 items with an estimated cost of

$75,000. Analysis finds that the cost of the sampled items should be only 98 percent of the

amount proposed. However, the confidence interval indicates that costs may range from 96 to

100 percent of the costs proposed.

Step 6. Apply the decrement factor to the total proposed cost of all items in the stratum.

Results of 100 Percent Analysis. There is no need to apply a decrement factor to these items

because the recommended cost of $1,648,600 resulted from analysis of all items in this stratum.

Random Sample Results. The assumption is that the sample is representative of the entire

population. If the sample is overpriced, the entire population of is similarly overpriced. As a

result the recommended cost objective would be $725,886, or 98 percent of the proposed

$740,700. However, the confidence interval would be $711,072 ( 96 percent of $740,700) to

$740,700 (100 percent of $740,700).

Step 7. Sum the prenegotiation positions for all strata to establish your overall position on

the cost category.

Point Estimate. The total point estimate results from the 100 percent and random sample

analyses would be $2,374,486 ($1,648,600 + $725,886).

Confidence Interval: The confidence interval would run from $2,359,672 ($1,648,600 +

$711,072) to $2,389,300 ($1,648,600 + $740,700). Note that the position on the stratum subject

to 100 percent analysis would not change.

3.6 Identifying Issues and Concerns

Questions to Consider in Analysis . As you perform price or cost analysis, consider the issues

and concerns identified in this section, whenever you use statistical analysis.

• Are the statistics representative of the current contracting situation?

Whenever historical information is used to make an estimate of future contract performance

costs, assure that the history is representative of the circumstances that the contractor will face

during contract performance.

• Have you considered the confidence interval in developing a range of reasonable

costs?

Whenever sampling procedures are used, different samples will normally result in different

estimates concerning contractor costs. Assure that you consider the confidence interval in

making your projections of future costs. Remember that there is a range of reasonable costs and

the confidence interval will assist you in better defining that range.

• Is the confidence interval so large as to render the point estimate meaningless as a

negotiation tool?

If the confidence interval is very large (relative to the point estimate), you should consider

increasing the sample size or other means to reduce the risk involved.

• Is your analysis, including any sample analysis, based on current, accurate, and

complete information?

A perfect analysis of information that is not current accurate and complete will likely not provide

the best possible estimates of future contract costs.

• Do the items with questioned pricing have anything in common?

If items with questioned pricing are related, consider collecting them into a separate stratum for

analysis. For example, you might find that a large number of pricing questions are related to

quotes from a single subcontractor. Consider removing all items provided by that subcontractor

from existing strata for separate analysis

• 4.0 – Chapter Introduction

• 4.1 – Identifying Situations For Use

• 4.2 – Identifying And Using Rules Of Thumb

• 4.3 – Developing And Using Estimating Factors

• 4.4 – Developing And Using Estimating Equations

• 4.5 – Identifying Issues And Concerns

4.0 – Chapter Introduction

In this chapter, you will learn to use cost estimating relationships to estimate and analyze

estimates of contract cost/price.

Cost Estimating Relationship Definition. As the name implies, a cost estimating relationship

(CER) is a technique used to estimate a particular cost or price by using an established

relationship with an independent variable. If you can identify an independent variable (driver)

that demonstrates a measurable relationship with contract cost or price, you can develop a CER.

That CER may be mathematically simple in nature (e.g., a simple ratio) or it may involve a

complex equation.

The goal is to create a statistically valid cost estimating relationship using historical data. The

parametric CER can then be used to estimate the cost of the new program by entering its specific

characteristics into the parametric model. CERs established early in a programs life cycle should

be continually revisited to make sure they are current and the input range still applies to the new

program. In addition, parametric CERs should be well documented, because serious estimating

errors could occur if the CER is improperly used.

It is important to make sure that the program attributes being estimated fall within (or, at least,

not far outside) the CER dataset. For example, if a new software program was expected to

contain 1 million software lines of code and the data points for a software CER were based on

programs with lines of code ranging from 10,000 to 250,000, it would be inappropriate to use the

CER to estimate the new program.

Among the several advantages to using cost estimating relationships are :

• Versatility: If the data are available, parametric relationships can be derived at any level,

whether system or subsystem component. And as the design changes, CERs can be

quickly modified and used to answer what-if questions about design alternatives.

• Sensitivity: Simply varying input parameters and recording the resulting changes in cost

can produce a sensitivity analysis.

• Statistical output: Parametric relationships derived from statistical analysis generally

have both objective measures of validity (statistical significance of each estimated

coefficient and of the model as a whole) and a calculated standard error that can be used

in risk analysis. This information can be used to provide a confidence level for the

estimate, based on the CERs predictive capability.

• Objectivity: CERs rely on historical data that provide objective results. This increases the

estimates defensibility.

Disadvantages of CERs include :

• Database requirements: The underlying database must be consistent and reliable. It may

be time consuming to normalize the data or to ensure that the data were normalized

correctly, especially if someone outside the estimators team developed the CER. Without

understanding how the data were normalized, the analyst has to accept the database on

faith-sometimes called the black-box syndrome, in which the analyst simply plugs in

numbers and unquestioningly accepts the results. Using a CER in this manner can

increase the estimates risk.

• Currency: CERs must represent the state of the art; that is, they must be updated to

capture the most current cost, technical, and program data. Existing CERs must be

validated that the current data still result in the established CER.

• Relevance: Using data outside the CER range may cause errors, because the CER loses

its predictive ability for data outside the development range.

• Complexity: Complicated CERs (such as nonlinear CERs) may make it difficult for

others to readily understand the relationship between cost and its independent variables.

Steps for Developing a CER . Strictly speaking, a CER is not a quantitative technique. It is a

framework for using appropriate quantitative techniques to quantify a relationship between an

independent variable and contract cost or price.

Developing a CER is a 6-step process. Follow the six steps whenever you develop a CER.

Whenever you evaluate a CER developed by someone else, determine whether the developer

followed the six steps properly.

Step 1. Define the dependent variable (e.g., cost dollars, hours, and so forth.) Define what

the CER will estimate. Will the CER be used to estimate price, cost dollars, labor hours, material

cost, or some other measure of cost? Will the CER be used to estimate total product cost or

estimate the cost of one or more components? The better the definition of the dependent variable,

the easier it will be to gather comparable data for CER development.

Step 2. Select independent variables to be tested for developing estimates of the dependent

variable. In selecting potential independent variables for CER development:

• Draw on personal experience, the experience of others, and published sources of

information. When developing a CER for a new state-of-the-art item, consult experts

experienced with the appropriate technology and production methods.

• Consider the following factors:

o Variables should be quantitatively measurable. Parameters such as maintainability

are difficult to use in estimating because they are difficult to measure

quantitatively.

o Data availability is also important. If you cannot obtain historical data, it will be

impossible to analyze and use the variable as a predictive tool. For example, an

independent variable such as physical dimensions or parts count would be of little

value during the conceptual phase of system development when the values of the

independent variables are not known. Be especially wary of any CER based on 2

or 3 data observations.

o If there is a choice between developing a CER based on performance or physical

characteristics, performance characteristics are generally the better choice,

because performance characteristics are usually known before design

characteristics.

Step 3. Collect data concerning the relationship between the dependent and independent

variables. Collecting data is usually the most difficult and time-consuming element of CER

development. It is essential that all data be checked and double checked to ensure that all

observations are relevant, comparable, and relatively free of unusual costs.

Step 4. Explore the relationship between the dependent and independent variables. During this

step, you must determine the strength of the relationship between the independent and dependent

variables. This phase of CER development can involve a variety of analytical techniques from

simple graphic analysis to complex mathematical analysis. Simple ratio analysis, moving

averages, and linear regression are some of the more commonly used quantitative techniques

used in analysis.

Step 5. Select the relationship that best predicts the dependent variable. After exploring a

variety of relationships, you must select the one that can best be used in predicting the dependent

variable. Normally, this will be the relationship that best predicts the values of the dependent

variable. A high correlation (relationship) between a potential independent variable and the

dependent variable often indicates that the independent variable will be a good predictive tool.

However, you must assure that the value of the independent variable is available in order for you

to make timely estimates. If it is not, you may need to consider other alternatives.

Step 6. Document your findings. CER documentation is essential to permit others involved in

the estimating process to trace the steps involved in developing the relationship. Documentation

should involve the independent variables tested, the data gathered, sources of data, time period of

the data, and any adjustments made to the data.

4.1 – Identifying Situations For Use

Situations for Use . You can use a cost estimating relationship (CER) in any situation where you

quantify one of the following:

• A relationship between one or more product characteristics and contract cost or

price. A product-to-cost relationship uses product physical or performance

characteristics to estimate cost or product price. The characteristic or characteristics

selected for CER development are usually not the only ones driving cost, but the

movement of cost has been found to be related to changes in these characteristics. The

following table identifies several product characteristic that have been used in CER

development:

Product Independent Variable

Building

Construction

Floor space, roof surface area, wall surface

Gears Net weight, gross weight, horsepower,

number of driving axles, loaded cruising

speed

Trucks Empty weight, gross weight, horsepower,

number of driving axles, loaded cruising

speed

Passenger Car Curb weight, wheel base, passenger space,

horsepower

Turbine Engine Dry weight, maximum thrust, cruise thrust,

specific fuel consumption, by-pass ratio,

inlet temperature

Reciprocating

Engine

Dry weight, piston displacement,

compression ratio, horsepower

Sheet Metal Net weight, percent of scrap, number of

holes drilled, number of rivets placed,

inches of welding, volume of envelope

Aircraft Empty weight, speed, useful load, wing

area, power, landing speed

Diesel Locomotive Horsepower, weight, cruising speed,

maximum load on standard grade at

standard speed

• A relationship between one or more elements of contract cost and another element

of contract cost or price. A cost-to-cost relationship uses one or more elements of

contract cost to estimate cost or product price. If you can establish a relationship between

different elements of cost (e.g., between senior engineering labor hours and engineering

technician hours), you can use a CER to reduce your estimating or analysis effort while

increasing accuracy. If you can establish a relationship between an element of cost and

total price (e.g., between direct labor cost and total price), you can use that information to

supplement price analysis, without requiring extensive cost information.

Sample Solution