Proceedings of the 2000 Winter Simulation Conference
J. A. Joines, R. R. Barton, K. Kang, and P. A. Fishwick, eds.
VERIFICATION, VALIDATION, AND ACCREDITATION OF SIMULATION MODELS
Robert G. Sargent
Simulation Research Group
Department of Electrical Engineering and Computer Science
College of Engineering and Computer Science
Syracuse University
Syracuse, NY 13244, U.S.A.
ABSTRACT
that purpose. If the purpose of a model is to answer a
variety of questions, the validity of the model needs to be
determined with respect to each question. Numerous sets of
experimental conditions are usually required to define the
domain of a model’s intended applicability. A model may
be valid for one set of experimental conditions and invalid in
another. A model is considered valid for a set of experimental
conditions if its accuracy is within its acceptable range,
which is the amount of accuracy required for the model’s
intended purpose. This usually requires that the model’s
output variables of interest (i.e., the model variables used in
answering the questions that the model is being developed
to answer) be identified and that their required amount of
accuracy be specified. The amount of accuracy required
should be specified prior to starting the development of the
model or very early in the model development process. If
the variables of interest are random variables, then properties
and functions of the random variables such as means and
variances are usually what is of primary interest and are what
is used in determining model validity. Several versions of a
model are usually developed prior to obtaining a satisfactory
valid model. The determination of whether a model is valid
or not, i.e., model verification and validation, is usually a
process and is part of the total model development process.
It is often too costly and time consuming to determine
that a model is absolutely valid over the complete domain
of its intended applicability. Instead, tests and evaluations
are conducted until sufficient confidence is obtained that a
model can be considered valid for its intended application
(Sargent 1982, 1984 and Shannon 1975). Figure 1 contains
the relationships of cost (a similar relationship holds for
the amount of time) of performing model validation and
the value of a model to the user as a function of model
confidence. The cost of model validation is usually quite significant, especially when extremely high model confidence
is required.
The remainder of this paper is organized as follows:
Section 2 discusses the basic approaches used in decid-
This paper discusses verification, validation, and
accreditation of simulation models. The different approaches to deciding model validity are presented; how model
verification and validation relate to the model development
process are discussed; various validation techniques are
defined; conceptual model validity, model verification, operational validity, and data validity are described; ways to
document results are given; a recommended procedure is
presented; and accreditation is briefly discussed.
1
INTRODUCTION
Simulation models are increasingly being used in problem
solving and in decision making. The developers and users
of these models, the decision makers using information derived from the results of the models, and people affected by
decisions based on such models are all rightly concerned
with whether a model and its results are “correct.” This concern is addressed through model verification and validation.
Model verification is often defined as “ensuring that the
computer program of the computerized model and its implementation are correct,” and is the definition adopted here.
Model validation is usually defined to mean “substantiation
that a computerized model within its domain of applicability possesses a satisfactory range of accuracy consistent
with the intended application of the model” (Schlesinger et
al. 1979) and is the definition used here. A model sometimes
becomes accredited through model accreditation. Model accreditation determines if a model satisfies a specified model
accreditation criteria according to a specified process. A
related topic is model credibility. Model credibility is concerned with developing in (potential) users the confidence
they require to use a model and the information derived
from that model.
A model should be developed for a specific purpose
(or application) and its validity determined with respect to
50
Sargent
Value
Cost
Cost
evaluation is extremely costly and time consuming for what
is obtained. This author’s view is that if a third party is
to be used, it should be during the model development
process. If a model has already been developed, this author
believes that a third party should usually only evaluate the
verification and validation that has already been performed.
The last approach for determining whether a model is
valid is to use a scoring model (see, e.g., Balci (1989), Gass
(1993), and Gass and Joel (1987)). Scores (or weights) are
determined subjectively when conducting various aspects
of the validation process and then combined to determine
category scores and an overall score for the simulation
model. A simulation model is considered valid if its overall
and category scores are greater than some passing score(s).
This approach is infrequently used in practice.
This author does not believe in the use of a scoring model
for determining validity because (1) the subjectiveness of
this approach tends to be hidden and thus appears to be
objective, (2) the passing scores must be decided in some
(usually subjective) way, (3) a model may receive a passing
score and yet have a defect that needs correction, and (4)
the score(s) may cause overconfidence in a model or be
used to argue that one model is better than another.
We now discuss how model verification and validation
relate to the model development process. There are two
common ways to view this relationship. One way uses
some type of detailed model development process, and the
other uses some type of simple model development process.
Banks, Gerstein, and Searles (1988) reviewed work using
both of these ways and concluded that the simple way more
clearly illuminates model validation and verification. This
author recommends the use of a simple way (see, e.g.,
Sargent (1981) and Sargent (1982)), which is presented
next.
Consider the simplified version of the modeling process
in Figure 2. The problem entity is the system (real or proposed), idea, situation, policy, or phenomena to be modeled;
the conceptual model is the mathematical/logical/verbal representation (mimic) of the problem entity developed for a
particular study; and the computerized model is the conceptual model implemented on a computer. The conceptual model is developed through an analysis and modeling phase, the computerized model is developed through
a computer programming and implementation phase, and
inferences about the problem entity are obtained by conducting computer experiments on the computerized model
in the experimentation phase.
We now relate model validation and verification to this
simplified version of the modeling process (see Figure 2).
Conceptual model validity is defined as determining that the
theories and assumptions underlying the conceptual model
are correct and that the model representation of the problem
entity is “reasonable” for the intended purpose of the model.
Computerized model verification is defined as ensuring that
Value
of
Model
to
User
Model Confidence 100%
Figure 1: Model Confidence
0%
ing model validity; Section 3 defines validation techniques;
Sections 4, 5, 6, and 7 contain descriptions of data validity,
conceptual model validity, model verification, and operational validity, respectively; Section 8 describes ways of
documenting results; Section 9 gives a recommended validation procedure; Section 10 contains a brief description
of accreditation; and Section 11 has the summary.
2
VALIDATION PROCESS
Three basic approaches are used in deciding whether a
simulation model is valid or invalid. Each of the approaches
requires the model development team to conduct verification
and validation as part of the model development process,
which is discussed below. The most common approach is
for the development team to make the decision as to whether
the model is valid. This is a subjective decision based on
the results of the various tests and evaluations conducted
as part of the model development process.
Another approach, often called “independent verification and validation” (IV&V), uses a third party to decide
whether the model is valid. The third party is independent
of both the model development team and the model sponsor/user(s). (A third party is also usually used for model
accreditation.) There are two common ways that IV&V is
conducted. One way is to conduct IV&V concurrently with
model development. The other way is to conduct IV&V
after the model has been completely developed by the model
development team. IV&V is often used when a large cost is
associated with the problem the simulation model is being
used for and/or to help in model credibility.
In the concurrent way of conducting IV&V, the model development team receives input regarding verification
and validation from the IV&V team as the model is being
developed. Thus, the development of a model should not
progress beyond each stage of development if the model is
not satisfying the verification and validation requirements. If
the IV&V is conducted after the model has been completely
developed, the evaluation performed can range from simply
evaluating the verification and validation conducted by the
model development team to a complete verification and
validation effort. Wood (1986) describes experiences over
this range of evaluation by a third party on energy models.
One conclusion that Wood makes is that a complete IV&V
51
Sargent
Comparison to Other Models: Various results (e.g.,
outputs) of the simulation model being validated are compared to results of other (valid) models. For example, (1)
simple cases of a simulation model may be compared to
known results of analytic models, and (2) the simulation
model may be compared to other simulation models that
have been validated.
Degenerate Tests: The degeneracy of the model’s behavior is tested by appropriate selection of values of the
input and internal parameters. For example, does the average number in the queue of a single server continue to
increase with respect to time when the arrival rate is larger
than the service rate?
Event Validity: The “events” of occurrences of the
simulation model are compared to those of the real system
to determine if they are similar. An example of events is
deaths in a fire department simulation.
Extreme Condition Tests: The model structure and
output should be plausible for any extreme and unlikely
combination of levels of factors in the system; e.g., if inprocess inventories are zero, production output should be
zero.
Face Validity: “Face validity” is asking people knowledgeable about the system whether the model and/or its
behavior are reasonable. This technique can be used in
determining if the logic in the conceptual model is correct
and if a model’s input-output relationships are reasonable.
Fixed Values: Fixed values (e.g., constants) are used for
various model input and internal variables and parameters.
This should allow the checking of model results against
(easily) calculated values.
Historical Data Validation: If historical data exist (or
if data are collected on a system for building or testing the
model), part of the data is used to build the model and
the remaining data are used to determine (test) whether the
model behaves as the system does. (This testing is conducted
by driving the simulation model with either samples from
distributions or traces (Balci and Sargent 1982a, 1982b,
1984b).)
Historical Methods: The three historical methods of
validation are rationalism, empiricism, and positive economics. Rationalism assumes that everyone knows whether
the underlying assumptions of a model are true. Logic
deductions are used from these assumptions to develop the
correct (valid) model. Empiricism requires every assumption and outcome to be empirically validated. Positive
economics requires only that the model be able to predict
the future and is not concerned with a model’s assumptions
or structure (causal relationships or mechanism).
Internal Validity: Several replications (runs) of a
stochastic model are made to determine the amount of (internal) stochastic variability in the model. A high amount
of variability (lack of consistency) may cause the model’s
results to be questionable and, if typical of the problem
Problem
Entity
Conceptual
Model
Validity
Analysis
and
Modeling
Operational
Validity
Experimentation
Data
Validity
Computerized
Model
Computer Programming
and Implementation
Conceptual
Model
Computerized
Model
Verification
Figure 2: Simplified Version of the Modeling
Process
the computer programming and implementation of the conceptual model is correct. Operational validity is defined
as determining that the model’s output behavior has sufficient accuracy for the model’s intended purpose over the
domain of the model’s intended applicability. Data validity
is defined as ensuring that the data necessary for model
building, model evaluation and testing, and conducting the
model experiments to solve the problem are adequate and
correct.
Several versions of a model are usually developed in
the modeling process prior to obtaining a satisfactory valid
model. During each model iteration, model validation and
verification are performed (Sargent 1984). A variety of
(validation) techniques are used, which are described below.
No algorithm or procedure exists to select which techniques
to use. Some attributes that affect which techniques to use
are discussed in Sargent (1984).
3
VALIDATION TECHNIQUES
This section describes various validation techniques (and
tests) used in model verification and validation. Most of
the techniques described here are found in the literature, although some may be described slightly differently. They can
be used either subjectively or objectively. By “objectively,”
we mean using some type of statistical test or mathematical
procedure, e.g., hypothesis tests and confidence intervals.
A combination of techniques is generally used. These techniques are used for validating and verifying the submodels
and overall model.
Animation: The model’s operational behavior is displayed graphically as the model moves through time. For
example, the movements of parts through a factory during
a simulation are shown graphically.
52
Sargent
To build a conceptual model we must have sufficient
data on the problem entity to develop theories that can
be used to build the model, to develop the mathematical
and logical relationships in the model that will allow it
to adequately represent the problem entity for its intended
purpose, and to test the model’s underlying assumptions. In
addition, behavioral data are needed on the problem entity
to be used in the operational validity step of comparing
the problem entity’s behavior with the model’s behavior.
(Usually, this data are system input/output data.) If behavior
data are not available, high model confidence usually cannot
be obtained, because sufficient operational validity cannot
be achieved.
The concern with data is that appropriate, accurate,
and sufficient data are available, and if any data transformations are made, such as disaggregation, they are correctly
performed. Unfortunately, there is not much that can be
done to ensure that the data are correct. The best that can
be done is to develop good procedures for collecting and
maintaining data, test the collected data using techniques
such as internal consistency checks, and screen for outliers
and determine if they are correct. If the amount of data is
large, a data base should be developed and maintained.
entity, may question the appropriateness of the policy or
system being investigated.
Multistage Validation: Naylor and Finger (1967) proposed combining the three historical methods of rationalism,
empiricism, and positive economics into a multistage process of validation. This validation method consists of (1)
developing the model’s assumptions on theory, observations,
general knowledge, and function, (2) validating the model’s
assumptions where possible by empirically testing them,
and (3) comparing (testing) the input-output relationships
of the model to the real system.
Operational Graphics: Values of various performance
measures, e.g., number in queue and percentage of servers
busy, are shown graphically as the model moves through
time; i.e., the dynamic behaviors of performance indicators
are visually displayed as the simulation model moves through
time.
Parameter Variability–Sensitivity Analysis:
This
technique consists of changing the values of the input and
internal parameters of a model to determine the effect upon
the model’s behavior and its output. The same relationships
should occur in the model as in the real system. Those
parameters that are sensitive, i.e., cause significant changes
in the model’s behavior or output, should be made sufficiently accurate prior to using the model. (This may require
iterations in model development.)
Predictive Validation: The model is used to predict
(forecast) the system behavior, and then comparisons are
made between the system’s behavior and the model’s forecast
to determine if they are the same. The system data may come
from an operational system or from experiments performed
on the system. e.g., field tests.
Traces: The behaviors of different types of specific
entities in the model are traced (followed) through the
model to determine if the model’s logic is correct and if
the necessary accuracy is obtained.
Turing Tests:
People who are knowledgeable
about the operations of a system are asked if they
can discriminate between system and model outputs.
(Schruben (1980) contains statistical tests for use with Turing
tests.)
4
5
CONCEPTUAL MODEL VALIDATION
Conceptual model validity is determining that (1) the
theories and assumptions underlying the conceptual
model are correct, and (2) the model representation of the
problem entity and the model’s structure, logic, and mathematical and causal relationships are “reasonable” for the
intended purpose of the model. The theories and assumptions underlying the model should be tested using mathematical analysis and statistical methods on problem entity
data. Examples of theories and assumptions are linearity,
independence, stationary, and Poisson arrivals. Examples
of applicable statistical methods are fitting distributions to
data, estimating parameter values from the data, and plotting
the data to determine if they are stationary. In addition,
all theories used should be reviewed to ensure they were
applied correctly; for example, if a Markov chain is used,
does the system have the Markov property, and are the states
and transition probabilities correct?
Next, each submodel and the overall model must be
evaluated to determine if they are reasonable and correct
for the intended purpose of the model. This should include
determining if the appropriate detail and aggregate relationships have been used for the model’s intended purpose,
and if the appropriate structure, logic, and mathematical and
causal relationships have been used. The primary validation
techniques used for these evaluations are face validation and
traces. Face validation has experts on the problem entity
evaluate the conceptual model to determine if it is correct and
reasonable for its purpose. This usually requires examining
DATA VALIDITY
Even though data validity is often not considered to be
part of model validation, we discuss it because it is usually
difficult, time consuming, and costly to obtain sufficient,
accurate, and appropriate data, and is frequently the reason
that attempts to validate a model fail. Data are needed
for three purposes: for building the conceptual model, for
validating the model, and for performing experiments with
the validated model. In model validation we are concerned
only with the first two types of data.
53
Sargent
the flowchart or graphical model, or the set of model equations. The use of traces is the tracking of entities through
each submodel and the overall model to determine if the
logic is correct and if the necessary accuracy is maintained.
If errors are found in the conceptual model, it must be
revised and conceptual model validation performed again.
6
results are obtained. If there are a large number of variables, one might aggregate some of the variables to reduce
the number of tests needed or use certain types of design
of experiments (Kleijnen 1987).
It is necessary to be aware while checking the correctness of the computer program and its implementation that
errors may be caused by the data, the conceptual model,
the computer program, or the computer implementation.
For a detailed discussion on model verification, see
Whitner and Balci (1989).
MODEL VERIFICATION
Computerized model verification ensures that the computer
programming and implementation of the conceptual model
are correct. The major factor affecting verification is whether
a simulation language or a higher level programming language such as FORTRAN, C, or C++ is used. The use of
a special-purpose simulation language generally will result
in having fewer errors than if a general-purpose simulation
language is used, and using a general purpose simulation
language will generally result in having fewer errors than if
a general purpose higher level language is used. (The use of
a simulation language also usually reduces the programming
time required and the flexibility.)
When a simulation language is used, verification is primarily concerned with ensuring that an error free simulation
language has been used, that the simulation language has
been properly implemented on the computer, that a tested
(for correctness) pseudo random number generator has been
properly implemented, and that the model has been programmed correctly in the simulation language. The primary
techniques used to determine that the model has been programmed correctly are structured walk-throughs and traces.
If a higher level language has been used, then the
computer program should have been designed, developed,
and implemented using techniques found in software engineering. (These include such techniques as object-oriented
design, structured programming, and program modularity.)
In this case verification is primarily concerned with determining that the simulation functions (such as the time-flow
mechanism, pseudo random number generator, and random variate generators) and the computer model have been
programmed and implemented correctly.
There are two basic approaches for testing simulation software: static testing and dynamic testing (Fairley
1976). In static testing the computer program is analyzed
to determine if it is correct by using such techniques as
structured walk-throughs, correctness proofs, and examining the structure properties of the program. In dynamic
testing the computer program is executed under different
conditions and the values obtained (including those generated during the execution) are used to determine if the
computer program and its implementations are correct. The
techniques commonly used in dynamic testing are traces,
investigations of input-output relations using different validation techniques, internal consistency checks, and reprogramming critical components to determine if the same
7
OPERATIONAL VALIDITY
Operational validity is concerned with determining that the
model’s output behavior has the accuracy required for the
model’s intended purpose over the domain of its intended
applicability. This is where most of the validation testing
and evaluation takes place. The computerized model is used
in operational validity, and thus any deficiencies found may
be due to an inadequate conceptual model, an improperly
programmed or implemented conceptual model (e.g., due
to programming errors or insufficient numerical accuracy),
or due to invalid data.
All of the validation techniques discussed in Section 3
are applicable to operational validity. Which techniques and
whether to use them objectively or subjectively must be decided by the model development team and other interested
parties. The major attribute affecting operational validity
is whether the problem entity (or system) is observable,
where observable means it is possible to collect data on
the operational behavior of the program entity. Table 1
gives a classification of the validation approaches for operational validity. “Comparison” means comparing/testing
the model and system input-out behaviors, and “explore
model behavior” means to examine the output behavior
of the model using appropriate validation techniques and
usually includes parameter variability-sensitivity analysis.
Various sets of experimental conditions from the domain of
the model’s intended applicability should be used for both
comparison and exploring model behavior.
Table 1: Operational Validity Classification
OBSERVABLE
SYSTEM
SUBJECTIVE
APPROACH
• COMPARISON USING
GRAPHICAL DISPLAYS
• EXPLORE MODEL
BEHAVIOR
OBJECTIVE
APPROACH
• COMPARISON
USING
STATISTICAL
TESTS AND
PROCEDURES
NON-OBSERVABLE
SYSTEM
• EXPLORE
MODEL BEHAVIOR
• COMPARISON TO
OTHER MODELS
• COMPARISON
TO OTHER
MODELS USING
STATISTICAL
TESTS AND
PROCEDURES
To obtain a high degree of confidence in a model and
its results, comparisons of the model’s and system’s input-
54
Sargent
output behaviors for several different sets of experimental
conditions are usually required. There are three basic comparison approaches used: (1) graphs of the model and system
behavior data, (2) confidence intervals, and (3) hypothesis
tests. Graphs are the most commonly used approach, and
confidence intervals are next.
7.1 Graphical Comparison of Data
The behavior data of the model and the system are graphed
for various sets of experimental conditions to determine
if the model’s output behavior has sufficient accuracy for
its intended purpose. Three types of graphs are used:
histograms, box (and whisker) plots, and behavior graphs
using scatter plots. (See Sargent (1996a) for a thorough
discussion on the use of these for model validation.) An
example of a box plot is given in Figure 3, and examples
of behavior graphs are shown in Figures 4 and 5. A variety
of graphs using different types of (1) measures such as the
mean, variance, maximum, distribution, and time series of
a variable, and (2) relationships between (a) two measures
of a single variable (see Figure 4) and (b) measures of two
variables (see Figure 5) are required. It is important that
appropriate measures and relationships be used in validating
a model and that they be determined with respect to the
model’s intended purpose. See Anderson and Sargent (1974)
for an example of a set of graphs used in the validation of
a simulation model.
120
System
Figure 4: Reaction Time
Model
100
80
60
40
Figure 3: Box Plot
These graphs can be used in model validation in different
ways. First, the model development team can use the graphs
in the model development process to make a subjective
judgment on whether a model possesses sufficient accuracy
for its intended purpose. Second, they can be used in the face
validity technique where experts are asked to make subjective
judgments on whether a model possesses sufficient accuracy
for its intended purpose. Third, the graphs can be used is
in Turing tests. Another way they can be used is in IV&V.
We note that independence of data is not required (as is
required for most formal statistical approaches) in the use
of these graphs. See Sargent (1996a) for details.
Figure 5: Disk Access
7.2 Confidence Intervals
Confidence intervals (c.i.), simultaneous confidence intervals (s.c.i.), and joint confidence regions (j.c.r.) can be
obtained for the differences between the means, variances,
55
Sargent
H1 :
and distributions of different model and system output variables for each set of experimental conditions. These c.i.,
s.c.i., and j.c.r. can be used as the model range of accuracy
for model validation.
To construct the model range of accuracy, a statistical
procedure containing a statistical technique and a method
of data collection must be developed for each set of experimental conditions and for each variable of interest. The
statistical techniques used can be divided into two groups:
(1) univariate statistical techniques and (2) multivariate statistical techniques. The univariate techniques can be used
to develop c.i., and with the use of the Bonferroni inequality
(Law and Kelton 1991), s.c.i. The multivariate techniques
can be used to develop s.c.i. and j.c.r. Both parametric and
nonparametric techniques can be used.
The method of data collection must satisfy the underlying assumptions of the statistical technique being used. The
standard statistical techniques and data collection methods
used in simulation output analysis (Banks, Carson, and Nelson 1996, Law and Kelton 1991) can be used for developing
the model range of accuracy, e.g., the methods of replication
and (nonoverlapping) batch means.
It is usually desirable to construct the model range of
accuracy with the lengths of the c.i. and s.c.i. and the sizes
of the j.c.r. as small as possible. The shorter the lengths or
the smaller the sizes, the more useful and meaningful the
model range of accuracy will usually be. The lengths and
the sizes (1) are affected by the values of confidence levels,
variances of the model and system output variables, and
sample sizes, and (2) can be made smaller by decreasing the
confidence levels or increasing the sample sizes. A tradeoff
needs to be made among the sample sizes, confidence levels,
and estimates of the length or sizes of the model range of
accuracy, i.e., c.i., s.c.i., or j.c.r. Tradeoff curves can be
constructed to aid in the tradeoff analysis.
Details on the use of c.i., s.c.i., and j.c.r. for operational
validity, including a general methodology, are contained in
Balci and Sargent (1984b). A brief discussion on the use
of c.i. for model validation is also contained in Law and
Kelton (1991).
Model is invalid for the acceptable range of accuracy under the set of experimental conditions.
Two types of errors are possible in testing hypotheses.
The first, or type I error, is rejecting the validity of a valid
model and the second, or type II error, is accepting the
validity of an invalid model. The probability of a type error
I, α, is called model builder’s risk, and the probability of
the type II error, β, is called model user’s risk (Balci and
Sargent 1981). In model validation, the model user’s risk
is extremely important and must be kept small. Thus both
type I and type II errors must be carefully considered when
using hypothesis testing for model validation.
The amount of agreement between a model and a system
can be measured by a validity measure, λ, which is chosen
such that the model accuracy or the amount of agreement
between the model and the system decreases as the value
of the validity measure increases. The acceptable range of
accuracy can be used to determine an acceptable validity
range, 0 ≤ λ ≤ λ∗ .
The probability of acceptance of a model being valid,
Pa , can be examined as a function of the validity measure by
using an Operating Characteristic Curve (Johnson 1994).
Figure 6 contains three different operating characteristic
curves to illustrate how the sample size of observations
affect Pa as a function of λ. As can be seen, an inaccurate
model has a high probability of being accepted if a small
sample size of observations is used, and an accurate model
has a low probability of being accepted if a large sample
size of observations is used.
7.3 Hypothesis Tests
Figure 6: Operating Characteristic Curves
Hypothesis tests can be used in the comparison of means,
variances, distributions, and time series of the output variables of a model and a system for each set of experimental
conditions to determine if the model’s output behavior has
an acceptable range of accuracy. An acceptable range of
accuracy is the amount of accuracy that is required of a
model to be valid for its intended purpose.
The first step in hypothesis testing is to state the hypotheses to be tested:
H0 :
The location and shape of the operating characteristic
curves are a function of the statistical technique being used,
the value of α chosen for λ = 0, i.e., α ∗ , and the sample
size of observations. Once the operating characteristic
curves are constructed, the intervals for the model user’s
risk β(λ) and the model builders risk α can be determined
for a given λ∗ as follows:
α ∗ ≤ model builder’s risk α ≤ (1 − β ∗ )
0 ≤ model user’s risk β(λ) ≤ β ∗ .
Model is valid for the acceptable range of accuracy under the set of experimental conditions.
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Sargent
Thus there is a direct relationship among the builder’s risk,
model user’s risk, acceptable validity range, and the sample
size of observations. A tradeoff among these must be made
in using hypothesis tests in model validation.
Details of the methodology for using hypothesis tests in
comparing the model’s and system’s output data for model
validations are given in Balci and Sargent (1981). Examples
of the application of this methodology in the testing of
output means for model validation are given in Balci and
Sargent (1982a, 1982b, 1983). Also, see Banks et al. (1996).
8
6.
7.
8.
In at least the last model iteration, make comparisons, if possible, between the model and system
behavior (output) data for several sets of experimental conditions.
Develop validation documentation for inclusion in
the simulation model documentation.
If the model is to be used over a period of time, develop a schedule for periodic review of the model’s
validity.
Models occasionally are developed to be used more than
once. A procedure for reviewing the validity of these models
over their life cycles needs to be developed, as specified by
step 8. No general procedure can be given, as each situation
is different. For example, if no data were available on the
system when a model was initially developed and validated,
then revalidation of the model should take place prior to
each usage of the model if new data or system understanding
has occurred since its last validation.
DOCUMENTATION
Documentation on model verification and validation is usually critical in convincing users of the “correctness” of a
model and its results, and should be included in the simulation model documentation. (For a general discussion on
documentation of computer-based models, see Gass (1984).)
Both detailed and summary documentation are desired. The
detailed documentation should include specifics on the tests,
evaluations made, data, results, etc. The summary documentation should contain a separate evaluation table for data
validity, conceptual model validity, computer model verification, operational validity, and an overall summary. See
Table 2 for an example of an evaluation table of conceptual
model validity. (See Sargent (1994, 1996b) for examples
of two of the other evaluation tables.) The columns of the
table are self-explanatory except for the last column, which
refers to the confidence the evaluators have in the results
or conclusions, and this is often expressed as low, medium,
or high.
The DoD has moved to accrediting simulation models. They
define accreditation in DoDD 5000.59 as “the official certification that a model or simulation is acceptable for use for
a specific application.” The evaluation for accreditation is
usually conducted by a third (independent) party, is subjective, and often includes not only verification and validation
but items such as documentation and how user friendly the
simulation is. The acronym VV&A is used for Verification,
Validation, and Accreditation.
9
11 SUMMARY
10 ACCREDITATION
RECOMMENDED PROCEDURE
Model verification and validation are critical in the development of a simulation model. Unfortunately, there is no
set of specific tests that can easily be applied to determine
the “correctness” of the model. Furthermore, no algorithm
exists to determine what techniques or procedures to use.
Every new simulation project presents a new and unique
challenge.
There is considerable literature on verification and validation. Articles given in the limited bibliography can
be used as a starting point for furthering your knowledge on model verification and validation. For a fairly
recent bibliography, see the following UHL on the web:
<http://manta.cs.vt.edu/biblio/>.
This author recommends that, as a minimum, the following
steps be performed in model validation:
1.
2.
3.
4.
5.
Have an agreement made prior to developing the
model between (a) the model development team
and (b) the model sponsors and (if possible) the
users, specifying the basic validation approach and
a minimum set of specific validation techniques to
be used in the validation process.
Specify the amount of accuracy required of the
model’s output variables of interest for the model’s intended application prior to starting the development of the model or very early in the model
development process.
Test, wherever possible, the assumptions and theories underlying the model.
In each model iteration, perform at least face validity on the conceptual model.
In each model iteration, at least explore the model’s
behavior using the computerized model.
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57
Sargent
Table 2: Evaluation Table for Conceptual Model Validity
Category/Item
• Theories
• Assumptions
• Model
representation
Technique(s)
Used
• Face validity
• Historical
• Accepted
approach
• Derived from
empirical data
• Theoretical
derivation
Justification for
Technique Used
Reference to
Supporting Report
Result/
Conclusion
Confidence
In Result
Strengths
Weaknesses
Overall evaluation for
Computer Model Verification
Overall
Conclusion
Justification for
Conclusion
Confidence
In Conclusion
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AUTHOR BIOGRAPHY
ROBERT G. SARGENT is a Research Professor and Professor Emeritus at Syracuse University. He received his
education at The University of Michigan. Dr. Sargent
has served his profession in numerous ways and has been
awarded the TIMS (now INFORMS) College on Simulation
Distinguished Service Award for longstanding exceptional
service to the simulation community. His current research
interests include the methodology areas of both modeling and discrete event simulation, model validation, and
performance evaluation. Professor Sargent has published
extensively and is listed in Who’s Who in America. His
email and web addresses are <
[email protected]> and
<www.cis.syr.edu/srg/ rsargent/>.
59