STATISTICAL QUALITY CONTROL APPROACHES TO NETWORK INTRUSION DETECTION

International Journal of Network Security & Its Applications (IJNSA), Vol.3, No.6, November 2011
DOI : 10.5121/ijnsa.2011.3608 115
STATISTICAL QUALITY CONTROL
APPROACHES TO NETWORK INTRUSION
DETECTION
Rohitha Goonatilake1
, Rafic Bachnak1
, and Susantha Herath2
1
Department of Engineering, Mathematics, and Physics
Texas A&M International University, TX 78041, USA
E-mails: harag@tamiu.edu and rbachnak@tamiu.edu
2
Department of Information Systems, St. Cloud State University, MN 56301, USA
E-mail: sherath@stcloudstate.edu
ABSTRACT
In the study of network intrusion, much attention has been drawn to on-time detection of intrusion to
safeguard public and private interest and to capture the law-breakers. Even though various methods
have been found in literature, some situations warrant us to determine intrusions of network in real-time
to prevent further undue harm to the computer network as and when they occur. This approach helps
detect the intrusion and has a greater potential to apprehend the law-breaker. The purpose of this article
is to formulate a method to this effect that is based on the statistical quality control techniques widely
used in the manufacturing and production processes.
KEYWORDS
Anomalies, control charts, false alarm, intrusion, network system, and quality control
1. INTRODUCTION
The rapid growth of Internet use in public and private enterprises has increased cyber-crimes.
Conventional mechanisms for secured networks include firewalls, virtual private networks, and
authentication tools. These provide a protective layer, but are vulnerable to more sophisticated
attacks. However, completely preventing intrusions and attacks on systems is impossible.
Hence, intrusion detection is considered to be the next step in providing defense to systemsas
the prevention is given much greater attention accordingly. The objective of current research is
to explore advances for the benefits tothe general public. This is essential as the consequences
can be enormous as vulnerabilities could be exploited to obtain authority, to disrupt service, to
inject additional damages into the system, or to deny service to the legitimate users [1]. Online
intrusion detection provides the architecture that uses the comparison of outputs from diverse
applications to provide a significant and novel approach to preventing intrusion attacks.
In order to detect intrusions and have a secured network, Network Intrusion Detection Systems
(NIDS) have been introduced. Network security architectures, such as NIDS and firewalls, will
attempt to detect break-ins by monitoring the incoming and outgoing trafficof the network.
According to the Computer Crime Research Center survey, new threats are on the rise [6].
There has also been an increase in reported cases of cybercrimes in recent years, with one
major difference being that the motives for breaches have multifaceted. Apart from viruses and
worms, a varied number of unauthorized activities play a role in disturbing both computer and
breaching network security. Another aspect of risks to any network activity distinguishes

116
between risks occurring internally and externally to the organization. Internal sources can be
people inside a firm working against policies and taking over privileges to access confidential
files, etc. External sources include threats and attacks from outside the organization’s access to
the information for monitory and private uses. Quiet internal attacks can result in substantial
financial losses to an organization [9].
2. PRELIMINARIES
Major attacks include denial of service, sniffing, spoofing, SYN (synchronized) flooding,
viruses, and worms. Denial of service attacks try to prevent legitimate users from accessing the
network by sending huge numbers of data packets to the network. Since the Internet has limited
resources, it is hard to cope with heavy traffic, thereby, denying access to legitimate users [4].
In SYN flooding, the attacker sends SYN packets to the server using fake IP addresses, but
does not acknowledge the server’s messages. If a legitimate user sends a message, it does not
get acknowledgement from the server since the server’s resources have been used up by the
attacker. Yahoo, Amazon, e-Bay, and other popular websites have been exposed to denial of
service attacks [2 & 9]. Worms and viruses are the programs when injected, spread through
emails and Internet packets and begin toreplicate themselves and send copies to other nodes in
the network. For example, the SQL Slammer worm replicated once every eight seconds; within
ten minutes, it had spread to almost all parts of the world. It created chaos, hampered credit
card transactions, interrupted airline reservations, and did many other related activities of
disruption [4]. An IDS detects intrusions and misuses by collecting and analyzing the
information from different variety of network sources. The IDS compares the signatures of the
received packets with the known signatures in the database. If the same signature is found, it
treats it as an attack and filters it. For unknown signatures, the data is sent to the anomaly
detection unit. This unit builds models of normal data. It checks for patterns that deviate from
normal behavior to be suspected as a possible intrusion. One of the many advantages of
anomaly detection is that it does not require a database of signatures. On the basis of network
protection, an IDS is classified into either a host-based intrusion detection systems (HIDS) or
network-based intrusion detection systems (NIDS). IDS tools use data from a single host in
HIDS [5].
A situation can warrantee us to determine intrusions of the network in real-time to prevent
further harm to the computer network as they occur. This possibility will help detect the
intrusion and has a greater potential to apprehend the law breaker.There are other applications,
as well. For example, mobile communication networkstransmit a large amount of data that can
be used in identifying the place of an emergency that requires immediate attention and it can be
disrupted from intrusions. Accordingly, the abilityto quickly identify anomalous data in real-
time is paramount important[8]. Another approach in this effortis multivariate statistical
analysis of audit trails for host-based intrusion detection [11]. The performance of this test is
not as good as that of the Chi-square test that detects only mean shifts [14]. However, the
results show that the multivariate statistical techniques based on the Chi-square test statistic
achieved the 0% false alarm rate and the 100% detection rate [12].
3. TECHNIQUE AND IMPLEMENTATION
Among all statistical techniques, control charts appear to be the most widely used to maintain
the quality of products in manufacturing processes. Samples of the packetsare collected
successively in order for this technique to work. A set of commands in a network system

117
consists of strings used to specify the goals for each of the virtual performer agents running on
the individual computers and are sent using the UDP protocol. Anomalous traffic in the
network system is generally identified as a potential intrusion. Traffic analysis does not deal
with the payload of a measure (not available for analysis) but with other characteristics such as
source, destination, routing, length, duration, and frequency of the communication [13]. Traffic
may be encrypted to analyze the packet payload. Traffic behavior in the network is
characterized by statistical measures to capture the behavior. Means and standard deviations of
anomalies are referred to in the corresponding measures of the distribution of data so
obtained.It is assumed that the anomalies that belong to each sampleare independent and
identically distributed with mean, ,µ and standard deviation, .s
In order to construct control charts, reliable historical data is not available. As mean,ߤ, and
standard deviation,ߪ, would not be known, the three-standard-deviation-rule cannotbe
employed. Since the statistic,‫,ݏ‬ is not an unbiased estimator of ߪ,transforming the same to an
unbiased estimator requires some work.Let K,, 21 XX denote the measures of the
communications successively obtained from the network system. Items are collected
periodically in some fixed size, .n The average of the ith
sample is denoted by .iX That is,
,21
1
n
XXX
X n+++
=
L
,221
2
n
XXX
X nnn +++
= ++ L
,32212
3
n
XXX
X nnn +++
= ++ L
and so on. It is appropriate to estimate µ by ,X the
average of these sample averages. Let is denote the sample standard deviation of the
ith
collection. That is, letting ∑=
+−
−
−
=
n
i
kink
k
n
XX
s
1
2
)1(
1
)(
for ki ,,2,1 K= so that
./)( 21 kssss k+++= L It follows that )(/ ncs is an unbiased estimator of ,σ where





 −
Γ−






Γ
=
2
1
1
2
2
)(
n
n
n
nc and )(⋅Γ is the gamma function [6]. Now, the corresponding upper
and lower control limits for X are:
andthe upper and lower control limits for s are:
, respectively.
The lower and upper control limits for X and s play a significant role in the determination of
whether the intrusion detection system will work normally as expected. The control charts for
variability of the measures can also be plotted. If the distribution of breaking strength is
normally distributed with mean equals ߤ and standard deviation equals ߪ, we can construct a
control chart for the variance or standard deviation. If ‫ݏ‬ଶ
is the sample variance, then ݊ ‫ݏ‬ଶ
/ߪଶ

118
has a ߯ଶ
−distribution with (݊ − 1) degrees of freedom. Unfortunately, the mean, ,µ and
standard deviation, ߪ, would not be available. So, the LCL and ULC derived abovefor ‫ݏ‬are
used.
An IDSplays an important role in network security process and provides a peace of mind for
those who continue to work on innovative and advancement of cyber applications. This
technique requiresperforming a set of calculations using the data obtained from the network
system periodically. This would include intrusion modeling, detection, prevention and
advancements in IDS; a comparison of these techniques will be made with other IDS tools.
Several intrusion detection systems have recently enjoyed the limelight as they improve the
efficiency of intrusion detection [1, 2,& 3]. It has proved to be efficient in diagnosing misuses
and other anomalies which were not detected otherwise.
As an illustration, let us assume that a sample of fivecommunications is collected from the
network successively. As such, the value of .9399851.0)5( =c Let us assume that the
successive thirtysamples of five network communications collected have yielded the means and
standard variations as listed in Table 1.
Table 1: Means (ܺ) and standard variations (‫)ݏ‬ collected for thirty samples of fixed size
Sample 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
ܺ 13.01 12.97 13.12 12.99 13.03 13.02 13.10 13.14 13.09 13.20 14.88 13.03 13.00 13.04 12.99
‫ݏ‬ 1.12 1.14 1.08 1.11 1.09 1.08 1.15 1.25 1.16 1.13 1.16 1.17 1.23 1.11 1.10
Sample 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
ܺ 12.98 13.05 13.02 13.03 13.04 13.11 11.65 12.98 14.10 13.02 13.04 13.09 13.00 13.03 11.03
‫ݏ‬ 1.13 1.12 1.08 1.07 1.10 1.11 1.03 1.11 0.97 0.99 1.13 1.11 1.02 1.01 1.12
The necessary calculations of the control limits for X and ‫ݏ‬ provide whether there would be
anomalies or suspicious activities in the network system. These estimations can be computed
periodically to ensure new X and ‫ݏ‬ are within these limits. For data listed in Table 1, the lower
and upper control limits (LCLs & UCLs) for X and s are ( )650.14,405.11 and
( ).310.2,101.0− Since ,0≥s these estimates are corrected to be read as ( )650.14,405.11
and ( )310.2,0000.0 for X and ,s respectively. The calculations are continued beyond the
thirtieth samples in order to secure the system is in complete control. Network systems will be
investigated if at any time the values of X and s go outside the limits of the intervals. From
Figure 1, two instances are seen where the values of ܺ went outside the control limits of ܺ;at
the same time, the values of ‫ݏ‬ stayed within the control limits of ‫ݏ‬due to larger variation seen in
the data set. This now provides that an anomaly has occurred.

119
Figure 1: Control charts for ܺ and ‫ݏ‬
The effectiveness of this technique depends on frequency of updates and nature of monitoring
by collecting samples of fixed size necessary to plot control charts for X and ‫ݏ‬ as provided in
Figure 1.
4. SAMPLING INSPECTION
Among many methods employed for sampling inspection to meet the demands of network
provider and the user, the single sample plan is considered a commonly used technique [10].
Given a sample of ܰ packages, only ݊ of them will be tested for anomalies. Among ݊items, if
݀ or fewer anomalies are found,the sample will be accepted and rejected otherwise. The user
insisted that the fraction of anomalies is no more than ‫݌‬௧ called “sample tolerance fraction
anomaly” in each accepted sample. There can be a situation that this value can only be achieved
when the complete sampling that involves higher cost of inspection is done. The user position
needs to be modified depending on meeting the fraction. The probability of user’s risk of
accepting a samplethat has fraction ‫݌‬௧of anomalies, ܲ஼is given by
ܲ஼ = ෍
ቀ
ܰ௣௧
‫ݔ‬
ቁ ቀ
ܰ − ܰ௣௧
݊ − ‫ݔ‬
ቁ
ቀ
ܰ
݊
ቁ
ௗ
௫ୀ଴
.
It is assumed that ݊ items are to be tested from among the collection of ܰ communications that
contain ܰ௣௧ anomalies. It appears that ‫ݔ‬ anomalies in the sample so that 0 ≤ ‫ݔ‬ ≤ ܰ. Forܰ is
sufficiently large compared to ݊, we obtain,
ܲ஼ ≈ ∑ ቀ
݊
‫ݔ‬
ቁ ‫݌‬௧
௫(1 − ‫݌‬௧)௡ି௫ௗ
௫ୀ଴ .
Suppose that we want to estimate some possible values of ݊ and ݀. For ܲ஼ = 0.06, ‫݌‬௧ = 0.02,
we will have the smallest possible choice of ݊ by setting ݀ = 0. If ܰ is large, we have the
equation, ቀ
݊
0
ቁ (0.02)଴
(0.98)௡
= 0.06, thus giving ݊ ≈ 140.
Revision to this number may be required due to the cost of testing such a large number of
anomalies. There are instances that the network provider has given additional thought to their
own risk. The Copula model provides a framework to quantify the risk associated with online

120
business transactions as a result of a security breach [7]. They now insist on a probability of
invoking this risk, ܲோ,of rejecting the sample if the mean fraction of anomaly is‫.݌‬The network
provider is willing to adjust ‫݌‬௧ and ܲ஼on the demand by the userwho is now willing to propose‫݌‬
to the network provider. This can now be regarded as the choice forthe random sampledrawn
from the process (conceptually infinity) producing a mean fraction of anomalies, ‫.݌‬Assuming
the statistical process corresponds to ݊independent Bernoulli trails of an event with probability
‫݌‬ is:
ܲோ = ∑ ቀ
݊
‫ݔ‬
ቁ ‫̅݌‬௫௡
௫ୀௗାଵ (1 − ‫̅݌‬)௡ି௫
,
= 1 − ෍ ቀ
݊
‫ݔ‬
ቁ ‫̅݌‬௫
ௗ
௫ୀ଴
(1 − ‫̅݌‬)௡ି௫
.
The network provider’s risk, ܲோ, can also be defined as the probability that the sample will be
rejected if the fraction ‫݌‬ of anomalies of this sample is ‫݌‬ = ‫.݌‬Accordingly, we now have two
equations to be solved for ݊ assuming ܰ is sufficiently large.
෍ ቀ
݊
‫ݔ‬
ቁ
ௗ
௫ୀ଴
‫݌‬௧
௫
(1 − ‫݌‬௧)௡ି௫
= ܲ஼, and
෍ ቀ
݊
‫ݔ‬
ቁ ‫̅݌‬௫
ௗ
௫ୀ଴
(1 − ‫̅݌‬)௡ି௫
= 1 − ܲோ.
Obviously, we need to have ‫̅݌‬ < ‫݌‬௧ since it is presumed that 1 − ܲோ > ܲ஼given ‫ݔ‬ and ݊‫݌‬are
small relative to ݊,whilst‫݌‬ (either‫݌‬or ‫݌‬௧) is very small to calculate ݊and ‫݌‬ using Poisson
probability approximation to the binomial probability. The values should be modified thereafter
to meet the interest of the network provider and the user in the single sampling plan. The
sequential testing (sampling) of hypotheses results in statistical cost-cutting measuresis
introduced to reduce the number of samples required to arrive at a specific precision in the
quality control process. The idea is naturally analogous to testing hypothesis. After each sample
is collected the network provider decides to continue the process before the user decides to
reject the null hypothesis or the alternative hypothesis(appropriately defined).
5. OPERATING CHARACTERISTIC CURVE
The risk associated with a sampling inspection plan can be investigated from the operating
characteristic curve (OCC) showing the probability of acceptance of the sample for different
quality levels. The OCC of a single sampling plan is a curve obtained from the probability of
accepting the sample when it contains a fraction,‫,݌‬ of anomalies as it varies. For large ܰ,the
OCC is obtained by plotting the graph of ܲ(‫)݌‬ = ∑ ቀ
݊
‫ݔ‬
ቁ ‫݌‬௫(1 − ‫)݌‬௡ି௫ௗ
௫ୀ଴ as a function of ‫.݌‬

121
Figure 2: Operating characteristics curve, ܲ(‫)݌‬ as a function of ‫݌‬ (forܰ is large, ܰ = 300,
and ݀ = 8)
The network user may now demand at least worry-free ongoing network activities.
Accordingly, the user insists that no matter what fractions of anomalies in the samples before,
the average fraction of anomalies per sample finally accepted should not exceed the user’s
average ongoing quality limitations. An alternative is always available for the network
provider. Instead of specifying the maximum allowable probability of rejecting a sample, if the
process is under a control,the network providerprefers to minimize the average number of
inspections subject to other requirements of the user. Let ܹ denote the number of packetsto be
inspected before an acceptable sample is turned over to the user. If ݀ or fewer anomalies are
found, the value of ܹ will be ݊; the probability, ܲ‫ݎ‬ሼܹ = ݊ሽ, is:
ܲ‫ݎ‬ሼܹ = ݊ሽ = ෍
ቀ
ܰ௣
‫ݔ‬
ቁ ቀ
ܰ − ܰ௣
ܰ − ‫ݔ‬
ቁ
ቀ
ܰ
݊
ቁ
ௗ
௫ୀ଴
,
whereܰ௣ is the actual number of anomalies. If more than ݀anomalieswere found, then ܰ
packets must be inspected, the probability of this event, ܲ‫ݎ‬ሼܹ = ݊ሽ, is equal to 1 − ܲ(‫.)݌‬
Let ܻ be the number of items expectedfor inspection prior to accepting the samplethat is
returned over to the user. Consequently the expected number of inspections is,
‫)ܻ(ܧ‬ = ݊ܲ(‫)݌‬ + ܰሾ1 − ܲ(‫)݌‬ሿ = ݊ + (ܰ − ݊)ሾ1 − ܲ(‫)݌‬ሿ.
If ܲ(‫)݌‬ = 0.5,then‫)ܻ(ܧ‬ =
ேା௡
ଶ
. That is, the expectation equals to the average of two sample
sizes in this case. However, there can be a method that can be formulated to meet the
expectation of the network provider. These methods and ideas are applicable in acceptance
sampling implementation, with the exception that the inspection is still carried out by the
network provider. They can neglect the user’s point of view, and have their own choice of
values for ݊ and ݀ to safeguard user’s risk and minimum inspectionrequired for theongoing
0
0.2
0.4
0.6
0.8
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
P(p)
p
Operating Characteristic Curve

122
quality limitations. Discussion of other plans such as double sampling and sequential sampling
can be carried out as detailed in the literature [15, 16, & 17].
6. FALSE ALARM RATE AND SPECIFICITY
In probability models, there are two kinds of properties worth considering. One is that the
probability of calculating changes when none have occurred(the power of the model), and the
other is the probability of calculating changes incorrectly occurred, (false alarm rate or more
precisely, the false positive probability), respectively. The latter is the probability that the
values are not falling between the lower control and upper control limits. For ܺcontrol charts of
normally distributed random variables, the probability that the values are not falling between
the lower control and upper control limits, provided the system remains in statistical control,
can be calculated using the standard normal random variable, ܼ, as follows.
False alarm probability = ߙ = ܲr൛ܺ < LCLൟ + ܲ‫ݎ‬൛ܺ > UCLൟ
= ܲ‫ݎ‬ ቊܼ < −
3
√݊ܿ(݊)
ቋ + ܲ‫ݎ‬ ቊܼ > +
3
√݊ܿ(݊)
ቋ
= ܲ‫ݎ‬ሼܼ < −1.42730ሽ + ܲ‫ݎ‬ሼܼ > +1.42730ሽ ≈ 2 × 0.0764 = 0.1528.
The specificity for ܺ control charts is (1- False alarm probability)≈ 1 − 0.1528 = 0.8472,
thus enabling to conclude that almost all sample means should be between the LCL and ULC if
the system remains to be in control. False alarm events occur infrequently, at the rate of
approximately 1.5 per 10 successive samples. This rate can be further improved by choosing
larger sample sizes. Of course, this depends on the distribution of the data providing a high
level of specificity. If the threshold is set on this value, then false alarms would be generated
within the obtained interval [13]. Natural expectationsare thatfewer false alarms can
compromise the method that tolerates greater possible malicious traffics. The existing methods
may not ensure the inclusion or exclusion of unnecessary quality controls. However, choosing a
novel approach for evaluating information security controls can help decision-makers to select
the most effective techniques in the resource-constrained being the focus. The proposed
approach quantifies the desirability of each information security control taking into account
benefits and restrictions associated with the technique [18].
7. CONCLUSIONS
Learningabout online attacks, correcting the situations, and generalizingthe techniques are part
of the online testing to positively identify attacks, eliminating false positives, and rule-base
similarity reasoning to avoid further vulnerabilities. The policy issues need to be periodically
reviewed or revisedto safeguard both public and private interest in this regard. This also
evaluates the ability to detect outliers in a data set and to describe how it can be used as an
indicator of an emergency response management system. Generally, outliers are removed to
calculate modified set of control limits for X and s as the process is being continued. This
article provided an introduction to the use of statistical quality control methods for intrusion
detection assuming the availability and accuracy of sufficient data at the necessary level of
breadth and intensitywhilst a risk and cost comparison isyet to be undertaken.
In this article, an initial attempt also has been made to the study of emerging attacks, detection
and prevention techniques, intrusion detection systems, and how they have advanced in recent

123
times using quality control techniques. Naturally, the next steps would be to extend these
techniques to more sophisticated ones based on moving-average, exponentially weighted
moving-average, and cumulative sum control charts. It is hoped that the recent approaches and
comparative studies willcomplement the preliminary results of this topic and the extensions
proposed by the work of this paper.
ACKNOWLEDGEMENTS
The authors would like to thank the reviewers for their suggestions that greatlyimproved this
manuscript.
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Authors:
Rohitha Goonatilake received a Ph.D. in applied mathematics from Kent State
University, Kent, Ohio in 1997 and is currently working as an associate professor of
mathematics in the Department of Engineering, Mathematics, and Physics at Texas
A&M International University. He was a Co-PI for two grants funded by the Texas
Higher Education Coordinating Board for the Engineering Summer Programs held
in 2010 and 2011 to provide enrichment for area middle and high school students to
enter into careers in engineering. He is a member of American Mathematical
Society, Mathematical Association of America, Institute of Mathematical Statistics, and The Honor
Society of Phi Kappa Phi.
Rafic Bachnak is Professor and Chair of the Department of Engineering,
Mathematics, and Physics at Texas A&M International University (TAMIU). He
received his B.S., M.S., and Ph.D. degrees in Electrical from Ohio University in
1983, 1984, and 1989, respectively. Prior to joining TAMIU in 2007, Dr. Bachnak
was on the faculty of Texas A&M University-Corpus Christi, Northwestern State
University, and Franklin University. His experience includes several fellowships
with NASA and the US Navy Laboratories and employment with Koch Industries.
Dr. Bachnak is a registered Professional Engineer in the State of Texas, a senior member of IEEE and
ISA, and a member of ASEE. During the 2009-2010 academic year, he was a Fulbright Scholar at Notre
Dame University, Lebanon.
Susantha Herath is a Professor and Chair of the Information Systems Department at
St. Cloud State University, Minnesota. Before moving to St. Cloud, Dr. Herath
worked as an Associate Professor of Computer Science at Aizu University, Japan
and as an Assistant Professor of Computer Science at Southwest Texas State
University, San Marcos, TX. Also, he worked as a visiting researcher at George
Mason University, Fairfax, VA, and Electrotechnical Laboratory, Japan. He received
his Ph.D. in Computer Engineering from Keio University, M.S. in Industrial
Engineering Management from the University of Electrocommunications, Japan and B.S. in Business
Administration from the Sri JayawardenapuraUniversity, Sri Lanka. His current research interests are in
Information Assurance and Security. He taught numerous courses related to security and has published
many papers. Dr. Herath is a Senior Member of the IEEE.

STATISTICAL QUALITY CONTROL APPROACHES TO NETWORK INTRUSION DETECTION

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STATISTICAL QUALITY CONTROL APPROACHES TO NETWORK INTRUSION DETECTION