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(IJCSIS) International Journal of Computer Science and Information Security,
Vol. 9, No. 7, July 2011
Recovery function of Components of Additive Model
of Biometric System Reliability in UML
Bihać, Bosnia and Hercegovina
Zoran Ćosić(Author) jacosic@gmail.com
director
Statheros d.o.o.
Kaštel Stari, Croatia Miroslav Bača (Author)
zoran.cosic@statheros.hr professor
Faculty of Organisational and Informational science
Varaždin, Croatia
Jasmin Ćosić (Author) miroslav.baca@foi.hr
IT Section of Police Administration
Ministry of Interior of Una-sana canton
number of successful tasks and the total number of tasks in the
time specified for the operation of the system:
Abstract- Approaches The development of biometric systems is
undoubtedly on the rise in the number and the application areas. n1 (t )
Modelling of system reliability and system data analysis after R(t )
failure and the time of re-establishing the operating regime is of n (t ) (1)
crucial importance for users of the system and also for producers
of certain components. This paper gives an overview of the
mathematical model of biometric system function recovery and its
where :R(t ) - assessment of reliability,
application through the UML model.
n1 (t ) - number of successful assignments in time t,
Keywords- Additive model, Biometric system, reliability, recovery n (t ) - total number of tasks performed in time t,
function, UML, component,
t - time specified for the operation of the
system.
I. INTRODUCTION
The value
R(t )
represents the estimated reliability due to the
Many models of reliability of biometric systems are applicable
only to specific parts or components of that same system. For fact that the number of tasks n(t) is final. Therefore, the actual
more complex considerations must be taken into account reliability R(t) is obtained when the number of tasks n(t) tends
models based on Markov processes that consider the reliability to infinity.
of the system as a whole, which includes components of the
system. In this paper the approach to restoring the functions of R(t ) lim R t
a biometric system that had failure at some of its components is n ( t )
(2)
elaborated. The basic model is an additive model which R(t) =1–F(t)=P(T>t) (3)
assumes a serial dependence between the components [1] (Xie
& Wohlin). Where the R ( t ) 1indicates the reliability function. Thus F ( t )
UML is also becoming standard in the process of system can be called non reliability function. Approximate form of the
design so the manufacture of component systems greatly function F ( t ), is shown in Figure 1. It is a continuous and
benefits from the UML view. The authors introduce the monotonically increasing function:
concept of UML modelling in the process of restoring function
analysis of biometric systems. The paper defines the conceptual F(0)=0
class diagram in UML, which provides a framework for F ( t ) →1, when t → ∞
analyzing the function recovery of biometric systems.
Density failure function is marked with F( t ), and from
II. ADDITIVE RELIABILITY MODEL probability theory we know that:
Reliability [2] as the probability [2] (number between 0 and 1
or 0% and 100%) can be represented as a ratio between the
1
R ( t ) is function of reliability
1 http://sites.google.com/site/ijcsis/
ISSN 1947-5500
(IJCSIS) International Journal of Computer Science and Information Security,
Vol. 9, No. 7, July 2011
dF (t ) G (t ) P ( > t) = 1 F1 (t ) (10)
f (t )
dt (4)
where F(t) is probability distribution function.
Failure intensity [3], [4], λ ( t ) represents the density of F1 (t ) is the probability density function of
conditional probability of failure at time t provided that until Refresh frequency
that moment there was no failure. random variable :
f (t ) dF1 (t ) dG (t )
(t ) f1 (t ) (11)
R (t ) (5) dt dt
Or according to the model of Xie and Wohlin: From here it follows that:
d (t )
(t ) ,t 0 t
dt (6) F1 (t ) f1 (t ) dt (12)
where µ(t) is mean value of the expected system failure. 0
It is also assumed that the intensity of the failure of the entire t
system is the sum of the intensity of failures of its components:
G (t ) 1 f1 (t ) dt (13)
(7)
0
So it follows that the expectations of failure of the system are
(6): B. Intensity of recovery function
(8) (t ) is the conditional probability density function2 of completion
of recovery of components (repair) within time t, provided that
recovery is not completed until the moment t.
III. BIOMETRIC SYSTEM RECOVERY FUNCTION Intensity recovery function is conditional probability density
Term recovery consider biometric system as a system that is function of the end of the recovery in time t, provided that recovery
maintained after a long period of use or recovered after failure of not complete until that moment t, we have:
is
particular components. Biometric system components, after the
failure, are maintained or exchanged and then continue to be part of
the system. When considering the reliability problems of generic G(t ) F1 (t ) f1 (t )
biometric system along with a random event that includes the
(t ) (14)
G (t ) G (t ) G (t )
appearance of failure within the system, it is necessary to consider
other random event and that is recovery the system after failure.
To this event corresponds a new random variable that indicates
t t
dG (t )
(t )dt G (t )
(15)
the time of recovery. As a characteristic of random variable 0 0
indicators similar to those being considered for the analysis of time t
without failure are used. ln G (t ) t0 (t )dt (16)
0
t
A. Distribution recovery function, refresh frequency ( t ) dt
0
G (t ) e (17)
is a random variable [3], [4] which marks the time of recovery
t
of the components in failure, then the probability of recovery is as a ( t ) dt
function of time: F1 (t)= 1- e 0 (18)
P ( < t ) F1 (t ) (9)
F 1 (t) probability distribution function of random variable .
The probability of non-recovery G(t) is defined as:
2 http://sites.google.com/site/ijcsis/
ISSN 1947-5500
(IJCSIS) International Journal of Computer Science and Information Security,
Vol. 9, No. 7, July 2011
Condition 1 represents a functional system and condition 2
represents a system that has been repaired after a failure.
C. Time recovery function The transition of system from condition 1 to 2 is represented
a. Mean recovery time with failure intensity function λ, the transition from condition 2
to condition 1 is defined with recovery intensity function µ.
Mean time of recovery M ( ) is the mathematical expectation of IV. RECOVERY FUNCTION OF BIOMETRIC SYSTEM IN UML
random variable whose probability density function is
f1 (t ) , A. Generalized biometric system
i.e.
Generalized biometric system model[7], [8], [9] is a schematic view
M ( ) tf1 (t ) dt (19) of Wyman biometric system model that depicts serial dependence
0
of a system components and can be summarized, in this exploitation
period of time, as shown on Figure 2.
M ( ) G (t )dt (20)
0
b. Recovery time variance
Recovery time variance
02 is characterized by deviation of Figure 2
duration of recovery from his mean recovery time. The system shown in Figure 2 works in time t0 without failure.
After the failure the system is recovered in time t1, after recovery
2 occurs time period of re-operation t2.
02 V E E ( ) 2 tG (t ) dt G (t )dt
2 Parameter which defines the conditions created by failure is
0 0 intensity of failure of particular component .
(21)
The intensity of the component failure can be expressed as:
c. Availability of system after recovery time
1
1
Probability [5], that the system after time t will be available for EL (23)
functioning is the expression (10). n n
Where is:
Where intensity recovery function µ can be defined as:
n- number of correct parts of the confidence interval (1 ) 0, 75
(22) - lower limit of confidence for the mean time between failures.
Recovery time of the system is the function of the recovery
MTTR –mean time to repair
intensity as described by the expression (22).
The process of transition from the state of failure to the state of
availability can be represented as in Figure 1: B. The conceptual class-diagram model of system
recovery
During the study [8] of the problem of reliability of generic
biometric system, object-relational approach of description of the
problem provides easier and clearer description of the sequence
analysis of events within the system during the verification of
Figure 1 failure.
Figure 3 shows the diagram of classes of the recovery of biometric
system model:
3 http://sites.google.com/site/ijcsis/
ISSN 1947-5500
(IJCSIS) International Journal of Computer Science and Information Security,
Vol. 9, No. 7, July 2011
REFERENCES
[1] An additive reliability model for the modular software failure data –
M.Xie, C.Wohlin - 2007
[2] Teorija pouzdanosti tehničkih sistema, Vojnoizdavački novinski centar,
Beograd 2005,
[3] Pouzdanost brodskih sustava – Ante Bukša, Ivica Šegulja – Pomorstvo -
2008
[4] Pouzdanost tehničkog sustava brodskog kompresora – Zoran Ćosić –
magistarski rad - 2007
[5] Eksploatacija i razvitak telekomunikacijskog sustava, Mr.sc Juraj Buzolić
, Split 2006
[6] Zasnivanje otvorene ontologije odabranih segmenata biometrijske
znanosti - Markus Schatten– Magistarski rad – FOI 2007
Figure 3 [7] Early reliability assessment of UML based software models – Vittorio
Cortellessa, Harshinder Singh, Bojan Cukic – WOSP’02 , July 24-26,
2002 Rome Italy
Class Biometric system is a set of components of that system [8] Modelling biometric systems in UML – Miroslav Bača, Markus
and is in relation to class Failure which contains data on the Schatten, Bernardo Golenja, JIOS 2007 FOI Varaždin
Component in failure, time of occurrence of failure and failure [9] Reliability, Availability and Maintainability in Biometric Applications–
intensity. © 2003-2007 Optimum Biometric Labs A WHITE PAPER Version r1.0,
Class Recovery is in relation to class Biometrical system Date of release: January 2, 2008, SWEDEN
because it contains information about the component, the time
AUTHORS PROFILE
of recovery of component and calculated recovery intensity of
component. Class Recovery is in relation to the class Zoran Ćosić, CEO at Statheros ltd, and business consultant in business process
standardization field. He received BEng degree at Faculty of nautical
Availability, which is a function of data on failure intensity and science , Split (HR) in 1990, MSc degree at Faculty of nautical science ,
the recovery intensity, with the class Mean time which contains Split (HR) in 2007 , actually he is a PhD candidate at Faculty of
data of recovery start time, duration and results of recovery, informational and Organisational science Varaždin Croatia. He is
a member of various professional societies and program
with the class Recovery intensity. Furthermore it is possible, at committee members. He is author or co-
the level of class diagrams to present and other factors of author more than 20 scientific and professional papers. His main
reliability and facilitate access to their prediction based on fields of interest are: Informational security, biometrics and privacy,
historical data (logs) of the system functioning. business process reingeenering,
Jasmin Ćosić has received his BE (Economics) degree from University of
V. CONCLUSION AND FURTHER RESEARCH Bihać, B&H in 1997. He completed his study in Information Technology
field (dipl.ing.Information Technlogy) in Mostar, University of Džemal
Information about the system failure must be considered in the Bijedić, B&H. Currently he is PhD candidate in Faculty of Organization
context of the whole biometric system and its performance in and Informatics in Varaždin, University of Zagreb, Croatia. He is
working in Ministry of the Interior of Una-sana canton, B&H. He is a
time. ICT Expert Witness, and is a member of Association of Informatics of
In accordance with the above information on the exploitation B&H, Member of IEEE and ACM. His areas of interests are Digital
of biometric systems must be part of a comprehensive analysis Forensic, Computer Crime, Information Security and DBM Systems. He
of the functioning and also information on recovery of the has presented and published over 20 conference proceedings and journal
articles in his research area
system and its functionality at any given time. The time to put
Miroslav Bača is currently an Associate professor, University of Zagreb,
the system into operation condition is often placed in clearly Faculty of Organization and Informatics. He is
defined time frames that are stipulated in contracts or SLA a member of various professional societies and program
addenda to the contract. The parameters monitoring processes committee members, and he is reviewer of several international
journals and conferences. He is also the head of the Biometrics centre in
associated with the reliability of the system are often Varaždin, Croatia. He is author or co-
complicated and laborious so UML approach to description of author more than 70 scientific and professional papers and two books.
problem simplifies the same. UML also imposes as general or His main research fields are computer forensics, biometrics and privacy
universal standard for descriptions of appearance. professor at Faculty of informational and Organisational science
Varaždin Croatia
Further work of the authors will be directed toward
specialization of model taking into consideration the other
models of reliability dependence and different system failure
probability distributions.
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ISSN 1947-5500
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