This document discusses software reliability prediction and choosing a suitable model to forecast defects in a second release based on failure data from the first release. The authors analyze failure data from the first two releases using various models including Yamada's S-Shaped model and Goel-Okumoto Non-Homogeneous Poisson Process model. Based on the analysis, Yamada's S-Shaped model accurately predicted around 195 faults for the first release. This model is then used to estimate 255 faults for the second release. Based on the estimated defects and cost analysis, the authors recommend releasing after the 38th week.

1. Software Reliability Prediction
Shishir Kumar Saha Mirza Mohymen
Dept. of Software Engineering, Dept. of Software Engineering,
Blekinge Institute of Technology, Blekinge Institute of Technology,
Karlskrona, Sweden. Karlskrona, Sweden.
shsd10@student.bth.se mimo10@student.bth.se
ABSTRACT Model. Using SMERFS3 tools the first release data until 26 th
In this paper, we describe the procedure of analytical analysis weeks are used to estimate the total number of faults. From
to choose suitable software reliability growth model to forecast SMERFS3 the five models are selected and after calculation,
the number of defects in second release, base on the failure the Yamada’s S-Shaped Model’s result was closer to total
data of first release and a few failure data of second release. number of faults value of first release. The tool gives total no
We recommend an appropriate time for second release to put of faults 195 (approximately) by Yamada’s S-Shaped Model’s,
into operation, evaluating the study result of fault data. which is very close to 198 (actual number of total faults).
So for second release the Yamada’s S-Shaped Model is used to
Keywords calculate the total number of faults. After calculate the total
Software reliability prediction, Yamada’s S-Shaped Model, estimated faults the NHPPM are used for further calculation.
Goel-Okumoto Non-homogeneous Poisson Process Model Detection of defects depends on time interval and this model is
suitable for failure counts calculation and estimation [2]. Also
1. INTRODUCTION from data, it shows that the fault is not overlapping in different
Unpredicted errors or defects of software are not only time interval. So NHPP model is selected.
hampering the business value but also escalating the estimated
development time and cost. So, Software reliability growth 3. RELEASE DATA ANALYSIS
model is crucial to predict the future behavior of the software
[1]. 3.1 Goel-Okumoto Model
Goel-Okumoto (G-O) model is a quantitative software
In the report, we have presented our motivation, considering reliability appraisal model. It depends on Non-homogeneous
several alternatives & properties of model and nature of fault Poisson Process (NHPP) to predict the software release date.
data, to choose the reliability growth model. Later, we According to the G-O model, if a is the number of faults in the
calculated the number of predicted defects in second release software and b is the testing efficiency or the reliability growth
applying the reliability model on historical fault data and rate, then the mean value or cumulative faults and failure
recommended the time for second release to put into operation intensity at a given time t can be calculated using the following
considering the uncertainties of method or release date. formulas [3] –
Mean Value, (1)
2. RELIABILITY MODEL SELECTION
Failure Intensity, (2)
In the assignment, the 50 weeks fault data of first release and
the 18 weeks fault data of second release are provided. There Normalizing the likelihood function (1 & 2) we get the
are different categories of analytical models used for software following equation [3],
reliability measurement. Those are Times Between Failures
Models, Fault Seeding Models, Input Domain Based Models,
Failure Count Models.
Times Between Failures Models is based on time interval of ... (3)
failures. But according to assignment description and data,
time interval of failure is not given so this model is not chosen.
In Fault Seeding Models defect is seeded but here no seeding 3.2 Fault Detection Rate Calculation &
is occurred, so this category of models are not applicable here. Failure Data Processing
In Input Domain Based Models the input data is needed to In order to find out the predicted failure data of second release,
build test cases and observed the failure to measure the we need to calculate the value of a (estimated number of
reliability. But from the assignment there is no input domain faults) and b (reliability growth rate or constant quality of
and input data so the model is not suitable here. The Fault testing). We can get the value of reliability growth rate from
Count Models is based on failures counts in a specified time the provided first release fault data as the value of b is constant
interval. From the assignment it’s shown that the interval is for each release, using the equation (3). As the equation (3) is
one week so homogeneous and there are no overlapping faults. non-linear, we solved it numerically using Newton-Raphson
So Fault Count Models should have chosen. method. The value of a = 199.48 and b = 0.098076 [3] from
first release fault data. By the help of the value of reliability
Again we know that in Fault Count Models that have several growth rate b, we can calculate the predicted second release
sub models. As for example: Goel-Okumoto Non-homogeneous defects per week (19th week to 50th week), what is shown in
Poisson Process Model, Goel Generalized Non-homogeneous table 1.
Poisson Process Model, Yamada’s S-Shaped Model, Brook's For example, μ(18) = a*(1-exp(-0.098076*18)) [Here, μ(18) =
and Motley's Binomial Model, Brook's and Motley's Poisson 213]; a = 256.9515

2. Then, μ(19) = 256.9515*(1-exp(-0.098076*19)); μ(19) = But we would recommend 41th week or later for release since
217.1069; So, in 19th week the number of predicted defects are the operational cost become lower than test cost at 41th week.
(217.1069 – 213 = 4.1069)
According to the provided data, the test costs 2 units, defects
in test costs 1 unit and defects in operation costs 5 units per
week. So, table1 shows the total defects and corresponding
cost of second release up to 50th week.
Table1. Defects and Cost Estimation of Second Release
Value of
Defects
Week Defects Test Operational
in
s Detection Cost Cost
Release 2
μ(t)
1 3 3 5 15 Figure1. Cost Analysis
2 3 6 5 15
3 38 44 40 190
-- -- -- -- --
18 3 213 5 15
19 4.1069 217.1069 6.1069 20.5345
-- -- -- -- --
33 1.0401 246.8611 3.0401 5.2003
0.9429 247.8040 2.9429 4.7143 Figure2. Actual Failure and Predicted Failure
34
35 0.8548 248.6587 2.8548 4.2738 5. UNCERTAINTIES
0.7749 249.4336 2.7749 3.8745 The model used for predicting the reliability of fault data is not
36 architecture based reliability model. So, it is not possible to get
37 0.7025 250.1361 2.7025 3.5124 idea about the software architectural style whether it is
complex or simple. Also, we had no idea about the nature of
38 0.6368 250.7730 2.6368 3.1842
software e.g. size, requirements, usage profile, application’s
39 0.5773 251.3503 2.5773 2.8867 termination behavior, organizational structure, type of testing
tools and techniques, available & expert resources,
40 0.5234 251.8737 2.5234 2.6169 reproducibility of bugs, adequate time for re-testing, change
0.4745 252.3482 2.4745 2.3724 requests, product baseline, development life cycle, reliability
41 model used for first release, maximum available budget and
42 0.4301 252.7783 2.4301 2.1507 schedule. Those factors are very crucial to ensure for a release.
Release time may be effected by the factors and create more
43 0.3900 253.1683 2.3900 1.9498
defects than expected. Moreover, it is not possible to pledge,
44 0.3535 253.5218 2.3535 1.7676 the correction of older bugs would not lead to new bugs in
other units.
45 0.3205 253.8423 2.3205 1.6024
-- -- -- -- -- 6. CONCLUSION
Software reliability is very much important for successful
49 0.2165 254.8514 2.2165 1.0823
software. We used software reliability growth model (NHPP)
50 0.1962 255.0477 2.1962 0.9812 to predicate the faults; analyze the cost and effort for
estimating proper release date. Here the given data is faults
counts and it’s related to homogeneous time interval, so we
Calculating all steps according to the selected model, we found used NHPP model for manual calculation and Yamada’s S-
255 (app.) predictable defects in second release. The result is Shaped Model for precise outcome.
very alike with the calculated results of Yamada Model and
Goel – Okumoto Model. 7. REFERENCES
[1] Misra, P. 1983. Software Reliability Analysis. IBM
4. RECOMMENDATION ABOUT Systems Journal. Lang. Vol. 22, No. 3 (1983), 262-270.
SECOND RELEASE [2] Goel, A. L., Software Reliability Models: Assumptions,
According to the data analysis of table 1 and visual figure of Limitations, and Applicability, IEEE Transactions on
cost analysis, we can say that the test cost is quite steady after Software Engineering, 11(12), pp. 1411-1423, Dec. 1985.
38th week, because it decreases the cost value difference [3] Xie, M.; Hong, G.Y.; Wohlin, C., 1999, Software
between two consecutive weeks in later releases and no major reliability prediction incorporating information from a
spike or ups and downs is observed. So, we can put the second similar project. Journal of Systems and Software Volume:
release into operation in any week among 38th to 50th weeks. 49, Pages: 43-48.