Determination of Software Release Instant of Three-Tier Client Server Software System

Yogesh Singh & Pradeep Kumar
International Journal of Software Engineering (IJSE), Volume (1): Issue (3) 51
Determination of Software Release Instant of Three-Tier Client
Server Software System
Yogesh Singh ys66@rediffmail.com
Professor & COE University School of Information Technology
Guru Gobind Singh Indraprastha University, Kashmere Gate,
Delhi - 110403, India
Pradeep Kumar pksharma26@rediffmail.com
Associate Professor, Department of Information Technology
ABES Engineering College affiliated to UPTU Lucknow,
Ghaziabad - 201009, India
Abstract
Quality of any software system mainly depends on how much time testing take
place, what kind of testing methodologies are used, the complexity of software
and the amount of efforts put by software developers subject to the cost and time
constraint. More time developers spend on testing more errors can be removed
leading to better reliable software. On the contrary, if testing time is too short, the
software cost could be reduced, but in that case the customers may take a higher
risk of buying unreliable software. However, this will increase the cost during
operational phase since it is more expensive to fix an error during operational
phase than during testing phase. Therefore it is essentially important to decide
when to stop testing and release the software to customers based on cost and
reliability assessment. In this paper we present a mechanism of when to stop
testing process and release the software to end-user by developing software cost
model with risk factor. Based on the proposed method we specifically address
the issues of how to decide that now we should stop testing and release the
software that is based on three-tier client server architecture which would
facilitates software developers to ensure on-time delivery of a software product
matching the criteria of attaining a predefined level of reliability and minimizing
the cost. A numerical example has been cited to illustrate the experimental
results showing significant improvements over the conventional statistical models
based on NHPP.
Keywords: Software Reliability Growth Model (SRGM), Optimal Release Policy, Three-tier Client server
System
1. INTRODUCTION
Several software cost models and optimal release policies have been studied for modeling
software reliability growth trends with different predictive capabilities at different phases of testing.
Software Reliability Growth Models (SRGMs) have been known as most widely used
mathematical tools for measuring, assessing, and predicting software reliability quantitatively. The
project managers and practitioners of software development have a great challenge of how to
develop a reliable software system economically that can be used for reliability assessment in a

realistic environment. As one of the major issues is to decide when to stop testing and release the
software to customer timely at low price with high degree of reliability.
SRGMs associated with software reliability measurement structure enhance both developer and
customer understanding of software quality and the factors affecting it. The factors include time
for how long a program has been executing, software product characteristics, development
process characteristics including resources, and operational environment in which the software is
used. Since early 1970s, software reliability modeling has been in practice to model past failure
data to predict future behavior. This approach employs either the observed number of failures
discovered per time period or observed time between failures of software. Software reliability
models therefore fall into two basic classes, depending upon types of data the model uses:
failures per time period and time between failures. Basically one of the well-known and most
important applications of SRGMs is to determine the software release instant [1, 2, 3, 7, 8, 9, 10,
11, 12, 14, 17]. In our study we investigate that how software faults detection process can be
employed to develop software reliability models to predict the behavior of failure occurrences and
the fault content of a software product that can be used in the determination of software release
instant.
Rest of the paper is organized as follows: In section 2, we discuss in detail the motivational work
done in the field of software reliability growth modeling and release policy. Section 3 describes
the mathematical formulation of software risk cost model and in section 4, numerical example is
provided to examine the optimal testing policies for proposed model. The concluding remarks and
directions for future work are discussed in section 5.
2. RELATED WORK
Many researchers and practitioners have addressed the problem of software release instant over
the years particularly Okumoto and Goel (1980) discussed a cost model addressing linear
development cost during testing and operational phase. Yamada (1983) developed S-shaped
reliability growth model for software error detection. Yamada and Osaki (1986) presented an
optimal software release policy for a non-homogeneous software error detection rate model.
Othera and Yamada (1990) discussed optimum software release time problem with fault-
detection during operation by introducing two evaluation criteria for the problem, first software
reliability and second mean time between failures. Yamada (1991) discussed software reliability
measurement and assessment of various software reliability growth models and data analysis.
KK Aggarwal and Y Singh (1993) presented a method for determination of software release
instant using a non-homogeneous error detection rate model based on the fact that some faults
can be regenerated during the process of correction. Pham (1996) developed a cost model with
an imperfect debugging and random life cycle besides a penalty cost to determine optimal
release policies for a software system. Kimura et al. (1999) discussed optimal software release
policy with consideration of an operational warranty period during which developer has to pay the
cost for fixing any detected errors. Pham and Zhang (1998) developed a generalized cost model
including fault removal cost, warranty cost and software risk cost due to software failures. They
also developed a GUI tool to determine the optimal software release time. Pham and Zhang
(1999) reviewed optimum release policy literature and concluded that quality of software system
depends on how much time testing takes and what kind of testing methodologies are used.
Hoang Pham (2003) categorically studied software reliability modeling based on
nonhomogeneous Poisson process (NHPP) with environmental factors and cost factors. Chin
Huang (2005) reviewed software reliability growth modeling with generalized logistic testing-effort
function and concluded that generalized logistic testing-effort function can be used to describe
actual consumption of resources during the software development process. Kuei-Chen Chiu et al.
(2007) proposed in their study that perspective of learning effects can influence the process of
learning effect that comes from inspecting the testing /debugging codes. Chu and Huang (2008)

further enhanced the predictive capabilities of testing effort dependent software reliability models
by introducing multiple change-points into Weibull-type testing-effort functions.
2.1 Software Reliability Growth Model for Three-Tier Client Server System
In a distributed computing environment to improve the process of reliability estimation and
prediction of software products we discuss and describe a three-tier client server architecture
based system for error detection process during testing phase. However reliability can be
enhanced through various means such as improving the process of designing, effectiveness of
testing, manual & automated inspections, familiarization with developers, users & product, and
improving the management processes & decisions [1, 2]. The rate of reliability growth depends on
the factors related to how rapidly defects are identified, how fast corrective action take place &
how soon the impact of the changes is implemented in the operational phase. Nevertheless all
preventive measures need to be taken during fault detection in order to correct and freeze them.
To formulate our methodology we consider a conventional client server architecture where
presentation logic and application logic are split off into separate components resulting into three-
tier system shown in figure1.
FIGURE 1: A Three-Tier Client Server Architecture View of the proposed model
The presentation layer of proposed model contains forms providing user interface, display data,
collect user inputs and sends the requests to next layer. Application layer provides the support
services to receive the requests for data from user tier, evaluates against business rules, and
pass on them to data tier. Data layer includes data access logic and to store the data at backend.
In modern computing system particularly for web based applications where various modules of
software are executed on different machine under different network architecture and operating
conditions we apply software cost model with risk factor to make a realistic reliability prediction
and assessment.
2.2 Terminology
NHPP: nonhomogeneous Poisson process represents the number of failures experienced up to
time t i.e., {N (t), t ≥ 0}. The NHPP based model provides an analytical framework for describing
the software failure phenomenon during testing phase.
Testing-effort: resource expenditures spent on software testing, e.g., test cases, man-power,
CPU time etc.
Fault: an incorrect logic, incorrect instruction, or inadequate instruction that upon execution will
cause a failure.
Error: a cause of a failure, which is unacceptable departure from nominal program operation.
Software error: an error made by a programmer or designer, such as a typographical error or an
incorrect numerical value or an omission, etc.
Operational profile: the set of operations that the software can execute, given the probabilities of
their occurrence.
2.3 Acronyms
MLE maximum likelihood estimation
MVF mean value function
Front End sending request Back End
Client Application Server Database Server
Sending reply
Level 1
Presentation
Layer
Presentation
Logic
Level 2
Business
Layer
Application
Logic
Level 3
Data Layer
Data Access
Logic
Database

SRGM software reliability growth model
SSE sum of squared errors
2.4 Notations used
m(t) mean value function in NHPP model
a Total number of software errors to be detected
bi error correction rate during initial testing phase of i
th
layer of model for i=1,2,3
ri error generation factor due to correction of errors in initial testing phase of i
th
layer of the
model
ti time spent in initial testing phase at i
th
layer of model for i=1,2,3
t total time spent in all three phases of testing
λ(t) Fault detection rate per unit time
T Software release time
C1 Software test cost per unit time
C2 Cost of removing each error per unit time during testing
C3 Cost of risk due to software failure
E(T) Expected total cost of a software system by time T
N(T) Number of errors to be detected by time T
µy Expected time to remove an error during testing phase which is E(Y)
Y Time to remove an error during testing phase
R(x|t) conditional software reliability
2.5 Assumptions
The proposed software cost model is developed based on the following assumptions under
different circumstances as follows:
1. Initially there is a set-up cost of the software development process.
2. Cost to perform testing is proportional to testing time.
3. Cost to remove errors during testing phase is proportional to total time of removing all
errors detected by the end of testing phase.
4. Time to remove each error during testing follows a truncated exponential distribution.
5. There is a risk cost related to the reliability at each release time point.
2.6 A nonhomogeneous Poisson process model
The counting process {N(t), t ≥ 0} is known as NHPP with an intensity function λ(t), t ≥ 0 and N(t)
has a Poisson distribution with a mean value function m(t) given by:
Pr {N(t) =k} = [m(t)]
k
exp {-m(t)} / k! , where k = 0,1,2,…n. and (1)
m(t) = E[N(t)] is the mean value function.
The Pr {N(t)} denotes the probability of event N(t), the mean value function m(t) represents expected
cumulative number of faults detected during testing time interval (0,t] and intensity function λ(t) representing
fault detection rate per fault. Using Goel-Okumoto NHPP reliability model the mean value function m(T) can
be written as follows:
m(T) = a ( 1 – exp{-bT}) , where a>0 and b>0
(2)
3. SOFTWARE COST MODEL WITH RISK FACTOR
Here we describe mathematically a software cost model with risk factor for three-tier client server
system consisting of three type of faults where some faults are easier to detect then others based
on the amount of efforts required to detect causes of failure in order to fix and remove it. These
faults are associated with presentation layer, business layer and database layer during testing
phase addressing risk level and time to remove errors. The optimal release policy that minimizes
the expected total software cost is obtained without loss of generality, by using mean value
function m (T) given as follows:

3
m(T) = a ∑ (1 – exp{-bi Ti}) *(1- ri ) (3)
i=1
Where t = t1 + t2 + t3 , a > 0, and 0 < b3 < b2 < b1 < 1, 0 < ri < 1
For three types of fault at each layer the error detection rate function dm(T) / dT can be written
as: 3
λ(T) = a ∑ bi exp{-biTi} *(1- ri ) (4)
i=1
The probability of a software failure which does not occur in (T, T+x], given that last failure
occurred in T >=0 (x>=0) is defined as:
R(x | T) = exp[-{m(T+x) – m(T)}] (5)
By substituting the values from eqn. (3) we get
3 3
R(x | T) = exp(–) a ∑ (1 – exp{-bi (Ti +x)})*(1- ri ) – a ∑ {1 – exp(-biTi )}*(1- ri ) (6)
i=1 i=1
Also it is observed that R(x | T) and λ(T) are strictly decreasing function of T, i.e.,
3
R(x | 0) = exp(–) a ∑ (1 – exp{-bix})*(1- ri ) (7)
i=1
3
λ(0) = a∑ bi(1- ri ) and λ(∞) =0 (8)
i=1
Therefore the total expected software system cost, E(T) can be defined as: (i) cost to perform
testing; (ii) cost incurred in removing errors during the testing phase; and (iii) a risk cost due to
software failure.
The cost to perform testing can be defined as
E1(T) = C1T (9)
The expected total time to remove all N(T) can be expressed using Zhang [8] as:
N(T)
E2(T) = E ∑ Yi = E[N(T)]* E[Yi] = m(T)µy (10)
i=1
where µy = [1 – (λT0 +1)*exp{-λT0} ] / [λ(1 - exp{-λT0}]
Also the expected cost to remove all errors detected by time T can be written as:
N(T)
E2(T) = C2 E[∑ Yi ] = C2m(T)µy (11)
i=1
The risk cost due to software failure after releasing software is E3 (T) = C3 [1- R(x |T)], where C3
is cost due to software failure. Assuming T is to be release time of the software, total cost
incurred during SDLC, the expected total software cost can be expressed using Zhang 1998 [8]
as follows:
E(T) = C1(T) + C2 m(T) µy + C3[1 – R(x|T)] (12)
By substituting the values from eqn. (6), (7) and (8) we get
3
E(T) = C1(T) + C2 a ∑ [{1 – exp(-biTi )} *(1- ri )] * [1 – (λT0 +1)*exp{-λT0}] / [λ(1 - exp{-λT0}]
i=1
3 3
+ C3 1 – exp (–) a ∑ (1 – exp {-bi (Ti +x)})*(1- ri ) – a ∑ {1 – exp(-biTi )}*(1- ri )
i=1 i=1
(13)

3.2 Optimal Release Policy
Here we discuss the behavior of the software cost model given in eq. (12) and determine optimal
release time T* that minimizes the expected software cost of the system subject to attaining a
desired reliability level, R0 the optimization problem can be characterized as follows:
Minimizing E(T) given as in eq.(12) subject to {R(x | T) ≥ R0 }
Differentiating eq.(12) with respect to T and equating them to zero we get the optimal testing time
T* as follows:
3
d E(T) = C1 + C2 a∑ [bi exp{-biTi}]* [(1- ri )] * [1 – (λT0 +1) *exp{-λT0}] / [λ(1 - exp{-λT0}]
dT
i=1
3 3
+ C3 exp (–) a∑ (1 – exp {-bi (Ti +x)})*(1- ri ) – a ∑ (1 – exp{-biTi})*(1- ri )
i =1 i =1
3
* a ∑ bi exp {-bi Ti} *(1- ri ) exp{-bix} –1 = 0
i=1
(14)
T* = T1 can be represented as:
C1 = - {C2 A + C3 B} (15)
3
Where A = a∑ [bi exp{-biTi}]* [(1- ri )] * [1 – (λT0 +1) *exp{-λT0}] / [λ(1 - exp{-λT0} ]
i=1
3 3
B = exp (–) a∑ (1 – exp {-bi (Ti +x)})*(1- ri ) – a ∑ (1 – exp{-biTi})*(1- ri )
i =1 i =1
3
* a ∑ bi exp {-bi Ti} *(1- ri ) exp{-bix} –1
i =1
The second derivative with respect to T of equation (12) yields:
3
d
2
E(T) = C2 a∑ [ (-)b
2
i exp{-biTi}]* [(1- ri )] * [1 – (λT0 +1) *exp{-λT0}] / [λ(1 - exp{-λT0}]
dT
2 i=1
3 3
+ C3 exp (–) a ∑ (1 – exp {-bi (Ti +x)}) *(1- ri ) – a∑ (1 – exp {-biTi}) *(1- ri )
i=1 i=1
3 3
* a ∑ bi exp {-bi Ti} *(1- ri ) exp{-bix} –1 a∑ bi exp{-biTi}*(1- ri ) exp{-bix} –1– bi
i=1
i=1
(16)
Let: 3
h(T) = a∑ bi *(1- ri ) * (exp {-bi Ti} ) and h(T) ≥ 0 ∀ T (17)
i=1
3 3
g(T) = C3 exp (–) a ∑ (1 – exp {-bi (Ti +x)}) *(1- ri ) – a∑ (1 – exp {-biTi}) *(1- ri )
i=1 i=1
3 3
* ∑ exp{-bi x} – 1
2
– ∑ bi exp{-bix} –1
i=1 i=1
(18)
3
v(T) = - C2 ∑ bi [1 – (λT0 +1) *exp{-λT0}] / [λ(1 - exp{-λT0}
i=1
(19)
We can rewrite eq. (14) by using eq.(15) to eq. (17) as below:
d
2
E(T) = h(T) v(T) + g(T) (20)
dT
2
Using eq. (17) we can see that d
2
E(T) ≥ 0 | T =T1

dT
2
Where h(T), g(T), v(T), bi, Ti , x, ri all are positive values defined in equations (12) to equations
(20) and the objective function E(T) can be strictly decreasing, increasing or both in T depending
upon the solutions obtained from these equations respectively. Therefore E(T) yields the
minimum value at T* = T1 for the following policies:
Optimum Release Policy 1:
T* = T1 when λ(0) ≥ λ(T1)
T* = 0 when λ(0) < λ(T1)
Now let TR denote the optimal testing time satisfying the condition {R(x|T) ≥ R0} we can minimize
E(T) as follows:
(a) If λ(0) ≥ λ(T1) and R(x|0) < R0 then T* = max (T1, TR)
(b) If λ(0) > λ(T1) and R(x|0) ≥ R0 then T* = T1
(c) If λ(0) ≤ λ(T1) and R(x|0) < R0 then T* = TR
(d) If λ(0) ≤ λ(T1) and R(x|0) ≥ R0 then T* = 0
4. NUMERICAL EXAMPLE
In this section we present a numerical example to illustrate the determination of optimal release
policies of proposed model. Testing data has been collected from Misra [5] summarizing the
number of failures per one-hour interval of execution time. We have applied this data to proposed
model for fitting the data using MATLAB version 7.0.1 under Windows XP environment, assuming
that testing staff are working for 10 hrs per day and five days a week.
Model Name Mean Value Function m (T) SSE
Goel-Okumoto [14] m(T) = a (1 – exp{-bT}) 766.1
Yamada-Ohba [15] m(T) = a 1 – (1 + bT) exp{-bT} 592.1
Proposed Model
3
m(T) =a ∑ (1 – exp{-bi Ti}) *(1- ri )
i=1
241.7
TABLE 1: Comparison of the models
The criteria used for determining the goodness of fit is the Sum of Square Error (SSE). This
statistic measures the deviation of the responses from the fitted values of the responses. A value
closer to 0 indicates that the model has a smaller random error component and the fit will be
more useful for prediction. The model that produces the smallest SSE has the better performance
and can be expressed as follows:
SSE = Sum { i =1 to 25} [yi – fi]
2
(21)
where yi is the observed value and fi is the predicted value from the fit. From Table 1 we observe
that the proposed methodology fit the data to a greater extent than the other two models.
Therefore we apply the proposed model to fit the data and in the determination of software
release instant.
4.1 The impact of cost coefficients on the expected total cost
The impact of cost coefficients C1, C2, and C3 on expected total cost has been evaluated under
different conditions. We increase the values of C1, C2, C3 and keep the values of other
parameters unchanged without lack of generality. The parameters of present model are estimated
by using maximum likelihood estimation (MLE) method and other related parameters are as
follows: Expected total potential error = 143.21, b1=0.8736, b2=0.6094, b3=0.1942, r1=0.7536,
r2=0.5104, r3=0.0272 and mean value function m (T) = 0.4248.

Case I:
C1=$50/day, C2=$100/day, C3=$150/day, µy =0.1 and x=0.05
Case II:
Case III:
4.2 Observations
• From the results for three different cases mentioned above we observed that increasing the
cost factor C1 and C3 results in increasing total expected cost initially very high but then
decreases gradually, which has a significant impact on optimal release policies of software
product. In other words if developers don’t spend sufficient amount of time for testing before
release then it is going to be more risky and unreliable for the customer for obvious reason
because to remove an error after delivery require more effort and involve more risk which
results in a longer testing time.
• We also observe that even if we consider cost factor C2 as constant in all three cases,
increase in cost factor C1 still increases cost factor C3 but then expected time to remove error
µy becomes double, which is quite encouraging reasonably. We summarize the result of total
expected cost of software, expected number of errors to be detected by time T with reliability
objective keeping more than 90%.
• Based on the calculations for case I, we find the total expected cost E1 (T*)=$382.70 and
reliability of the software application at the end of testing on 4
th
day is 0.9127 that is more
than 90%. After changing the cost parameters, we get total expected cost E2 (T*)=$661.39 for
the reliability assessment at 0.9018 (> 90%) marginally low as in case II.
• Finally in case III, we achieve the reliability level of 0.9239 (> 92%) at the cost of
E3(T*)=$509.28 after improving the software continuously in operational phase and which is
very satisfactory. The summary of results shown in Table 2 and figure 2 to figure 5 show the
variation of the total expected testing cost, the reliability achieved at the end of testing phase
and the expected number of errors detected at release instant.
• Furthermore the validity of proposed assessment method heavily depends upon the
representation of software reliability failure data available through various sources is highly
fluctuating and not being updated frequently by the community of researchers which is out of
the scope of this paper and need to be addressed separately in near future.

•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
TABLE 2: Summary of Total Expected Cost E (T), R (x |T) and m (T)
TABLE 2: Summary of total expected cost E(T), R(x|T) and m(T)
Expected cost vs Testing time
0
1000
2000
3000
4000
0 10 20 30
Time (in days)
Cost(US$)
E(T)
E1(T)
E2(T)
FIGURE 2: Release Instant and Total Expected Cost for Different Cost Factors
Release
time T
Expected
total cost
E1 (T)
Case I
Expected
total cost
E2 (T)
Case II
Expected
total cost
E3 (T)
Case III
Expected no.
of errors to be
detected m(T)
Conditional
Reliability
R (x|T)
1 587.24 718.26 1155.50 58.38 0.9002
2 457.21 661.39* 818.59 36.35 0.9018
3 399.48 694.61 644.09 24.22 0.9112
4 382.70* 774.97 557.67 17.11 0.9127
5 388.88 880.73 519.61 12.67 0.9185
6 408.44 1000.84 509.28* 9.70 0.9239
7 436.25 1129.52 515.77 7.62 0.9327
8 469.44 1263.65 533.09 6.08 0.9421
9 506.35 1401.46 557.81 4.90 0.9510
10 545.98 1541.87 587.84 3.98 0.9589
11 587.63 1684.21 621.84 3.25 0.9657
12 630.87 1828.03 658.90 2.66 0.9715
13 675.36 1973.00 698.37 2.18 0.9764
14 720.85 2118.90 739.76 1.79 0.9805
15 767.16 2265.54 782.70 1.47 0.9839
16 814.12 2412.79 826.91 1.21 0.9867
17 861.62 2560.53 872.15 1.00 0.9890
18 909.57 2708.67 918.23 0.82 0.9910
19 957.88 2857.13 965.01 0.68 0.9925
20 1006.49 3005.87 1012.36 0.56 0.9939

Expected total cost vs Testing time
0
200
400
600
800
1000
1200
1400
0 10 20 30
Time (days)
E(T)inUS$
E(T)
FIGURE 3: Expected Cost During Testing Phase
FIGURE 4: Expected Cost with Reliability Achieved During Testing Phase
Expected cost & Reliability
0
20
40
60
80
1 5 9 13 17 21 25
Time (days)
m(T)
0
500
1000
1500
Release Time m(T)
R(x|T) E(T)
FIGURE 5: Cost and Reliability with Mean Value Function m (T) and Release Instant
Expected cost vs Testing time
0
1000
2000
3000
4000
0 10 20 30
Time (in days)
Cost(US$)
m(T)
R(x|T)
E(T)
E1(T)
E2(T)

5. CONCLUSION & FUTURE WORK
Practically project managers need to know when testing the software can be stopped so that they
can deliver the product to customers attaining the requirement of software quality and minimize
the related testing costs. In this paper we have formulated a release policy for software reliability
growth model under three-tier client server architecture reflecting the cost of postponing software
release based on testing efforts. With the help of proposed cost model and designed release
policies it can be determined that whether more testing is required or the software has been
tested sufficiently to allow its release to the customer for operational use. The results revealed
that proposed model not only has a goodness-of-fit but also offers a good explanation of the
process of software reliability growth. However a study of comparative analysis to evaluate the
effectiveness of the proposed model and other existing software failure models would supplement
the present technique by applying more failure data sets of various standard real life projects.
In near future the proposed model can be extended by considering the change-point problem and
by introducing extended warranty period. The change-point problem results when some factors of
testing process are changed which subsequently can cause the software failure intensity function
to decrease or increase. Whereas by extending warranty period the penalty cost may be reduced
up to a certain level provided the maintenance cost during operational phase is paid by the
customer partially.
Acknowledgement
Authors would like to thank the editor and referees for their useful suggestions and valuable
comments.
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