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

Sample solution

Dante Alighieri played a critical role in the literature world through his poem Divine Comedy that was written in the 14th century. The poem contains Inferno, Purgatorio, and Paradiso. The Inferno is a description of the nine circles of torment that are found on the earth. It depicts the realms of the people that have gone against the spiritual values and who, instead, have chosen bestial appetite, violence, or fraud and malice. The nine circles of hell are limbo, lust, gluttony, greed and wrath. Others are heresy, violence, fraud, and treachery. The purpose of this paper is to examine the Dante’s Inferno in the perspective of its portrayal of God’s image and the justification of hell. 

In this epic poem, God is portrayed as a super being guilty of multiple weaknesses including being egotistic, unjust, and hypocritical. Dante, in this poem, depicts God as being more human than divine by challenging God’s omnipotence. Additionally, the manner in which Dante describes Hell is in full contradiction to the morals of God as written in the Bible. When god arranges Hell to flatter Himself, He commits egotism, a sin that is common among human beings (Cheney, 2016). The weakness is depicted in Limbo and on the Gate of Hell where, for instance, God sends those who do not worship Him to Hell. This implies that failure to worship Him is a sin.

God is also depicted as lacking justice in His actions thus removing the godly image. The injustice is portrayed by the manner in which the sodomites and opportunists are treated. The opportunists are subjected to banner chasing in their lives after death followed by being stung by insects and maggots. They are known to having done neither good nor bad during their lifetimes and, therefore, justice could have demanded that they be granted a neutral punishment having lived a neutral life. The sodomites are also punished unfairly by God when Brunetto Lattini is condemned to hell despite being a good leader (Babor, T. F., McGovern, T., & Robaina, K. (2017). While he commited sodomy, God chooses to ignore all the other good deeds that Brunetto did.

Finally, God is also portrayed as being hypocritical in His actions, a sin that further diminishes His godliness and makes Him more human. A case in point is when God condemns the sin of egotism and goes ahead to commit it repeatedly. Proverbs 29:23 states that “arrogance will bring your downfall, but if you are humble, you will be respected.” When Slattery condemns Dante’s human state as being weak, doubtful, and limited, he is proving God’s hypocrisy because He is also human (Verdicchio, 2015). The actions of God in Hell as portrayed by Dante are inconsistent with the Biblical literature. Both Dante and God are prone to making mistakes, something common among human beings thus making God more human.

To wrap it up, Dante portrays God is more human since He commits the same sins that humans commit: egotism, hypocrisy, and injustice. Hell is justified as being a destination for victims of the mistakes committed by God. The Hell is presented as being a totally different place as compared to what is written about it in the Bible. As a result, reading through the text gives an image of God who is prone to the very mistakes common to humans thus ripping Him off His lofty status of divine and, instead, making Him a mere human. Whether or not Dante did it intentionally is subject to debate but one thing is clear in the poem: the misconstrued notion of God is revealed to future generations.

 

References

Babor, T. F., McGovern, T., & Robaina, K. (2017). Dante’s inferno: Seven deadly sins in scientific publishing and how to avoid them. Addiction Science: A Guide for the Perplexed, 267.

Cheney, L. D. G. (2016). Illustrations for Dante’s Inferno: A Comparative Study of Sandro Botticelli, Giovanni Stradano, and Federico Zuccaro. Cultural and Religious Studies4(8), 487.

Verdicchio, M. (2015). Irony and Desire in Dante’s” Inferno” 27. Italica, 285-297.