Estimation and Analysis of MYSQL Database Server Reliability using Beta and Generalized Gamma Distribution

Estimation and Analysis of MYSQL Database Server Reliability using Beta and Generalized Gamma Distribution

Sanjeev Kumar Jha Ph.D. Research Scholar,

School of Computer Science and IT Singhania University Rajasthan

Shivlok Singh Ph.D. Research Scholar,

School of Computer Science and IT Singhania University Rajasthan

Dr. Amod Tiwari Dean, ,PSIT Kanpur,India

Abstract: Arrival failure times for different major sub versions of MySQL5 open source data base server are analyzed and compared. In this research 3-step approach consists of bug-gathering, bug-filtering, and bug-analysis is followed. After collecting failure data for this project, time to failures for each of these products is calculated. On this time to failure data entire analysis is performed.

Apart from reliability measurement, each of these sub versions are analyzed on the basis of bug frequency and hazard function and then compared. It is projected that the future release of this project under the same operational environment to follow similar reliability patterns. The results exhibit that Generalized Gamma and Beta distributions are powerful analytical tools to be used in reliability modeling of such open source products.

Keywords: Open source software (OSS) Mysql; Software reliability model; Software architecture; Reliability growth model; Generalized Gamma Distribution; Beta Distribution; Goodness of Fit Test.;

1. INTRODUCTION

   The Mysql database [3] has become the world's most popular open source database because of its high performance, high reliability and ease of use. It is database of choice for a new generation of applications. The purpose of this study is to develop reliability models suitable for main sub versions of Mysql5 series. There are different editions of Mysql used for specific purposes. Commercial customers have the flexibility of

   choosing from multiple editions to meet specific business and technical requirements:

   • Mysql Standard Edition

   • Mysql Enterprise Edition

   • Mysql Cluster Carrier Grade Edition

   In this research mainly 5.0, 5.1 and 5.5 sub versions of Mysql5 are considered. All the failure records are extracted from online bug repositories and after preprocessing it is stored in Mysql database. Initially it is analyzed on the basis of bug severity and bug frequency and is shown graphically. Later on it is analyzed by considering major sub versions of Mysql5 individually. Finally the entire result is compared from all possible dimensions and result is shown.

   Due to worldwide usage of Mysql as an open source database its reliability becomes a major concern which is defined as the probability of failure free operation of a computer program in a specified environment for a specified period of time [4],[5]. Here in this research for software reliability concern growth modeling [6], [7] approach is used. Software reliability growth models generally fall into two major classes: time between failures and fault count models. The main input parameter to the time between failures models is the intervals of successful operations. As the failures occur and fixed, it is expected that these intervals to increase. The pattern of these intervals is reflected by different statistical distributions. By using these distributions reliability models are constructed and then data is analyzed

   in detail.

   In case of fault count the input parameter of study is the number of faults in a specified period of time rather than the times between failures. Normally the failure rate, defined as the number of failures per hour, is used as the parameter of a Probability Distribution Function (PDF). Like the first class, as the fault counts drop, the reliability is expected to increase [8], [9].

   This study is concerned with Time to failure data of latest versions of three Mysql5 versions Mysql5.0, 5.1 and 5.5.Additionally, this product of open source software is widely used on all operating systems for web as well as windows application.

   The following table reflects on the number of years that these products have been in operation.

   TABLE: 1. RELEASE DATES OF THE Mysql5
   Mysql Version	Release Date
   Mysql5.0	04-10-2005
   Mysql5.1	02-11-2008
   Mysql5.5	01-12-2009

   On the basis of goodness of fit test applied on Time to failure data of above products Generalized Gamma and Beta Distributions are identified as best distribution for reliability model construction. [11], [18].

   These distributions are widely used in lifetime data analysis because of its flexibility in modeling different phases of bathtub reliability.

   The rest of the paper is organized as follows. Section 2 provides some definitions and background information.

   Section 3 concentrates on Research Methodology Used for reliability modeling process. Section 4 concludes the paper with a summary.

2. BACKGROUND

   Normally White box and black-box models are used for predication of software reliability. The white-box models

   are used to estimate reliability at design phase of software product .Thus for White box models Relationship of software components and their correlation are focus for software reliability measurement [19],[20].

   In Black-Box approach, the entire software system is considered as a single entity. These models are used to measure and predict software quality in the later phases of software development, such as testing or operation phase.

   Black Box models rely on the testing data collected over an observed time period. This study is concentrated on the black-box reliability approach to measure and compare the reliability of the selected products.

   To represent failure behavior of a software product different life data distributions are used. On the basis of goodness fit test applied in selected samples best distribution is identified [21]. On the basis of PDF, which is relative concentration of data samples at different points of measurement scale, such that the area under the graph is unity reliability is estimated.

   CDF is another function which is derived from PDF and is given by F(t)=P[T<=t]

   t

   F(t)= f(t)dt

   Mathematically reliability is defined as R (t)= P[T>=t]

   t

   R(t)=1-CDF =1- f(t)dt

   Apart from this hazard function that is failure rate of a product is also used for reliability analysis which is defined as ratio of pdf and reliability.

   Thus

   f (t)

   H(t)=

   R(t)

   Problem Identification

   After a detail study of research papers, articles and books related to reliability and other statistical analysis, it has been found that in maximum of researches either a single goodness of fit test is applied or a particular distribution is selected randomly. Apart from this only Reliability that is R

   1. is used for reliability analysis. Very little importance is given to Goodness of fit test and other aspects of reliability due to which sometimes researchers got unexpected results.

      The main problems in all these researches are:

      • Random selection of distributions without any test.[22]

      • Complete analysis on the basis of R(t) by excluding H(t) and failure frequency?

        It is very difficult to analyze reliability by calculating only reliability estimate of a software product. Final conclusion is given on the basis of following calculations:

      • Weekly Failure Count of Mysql 5 as well as its sub versions.

      • Graphical view of Failure Count with respect to Severity.

      • Probability density function i.e. probability of occurrence of failure.

      • Weekly Reliability Estimates.

      • Hazard function which is ratio of pdf and reliability.

      • Average Estimates of probability of failure, reliability estimates and Hazard function.

3. RESEARCH METHODOLOGY USED

In this study for reliability analysis failure data of Mysql5 versions 5.0, 5.1 and 5.5 are extracted from online bug repository www.bugs.mysql.com.

Data is collected for Mysql5, which is latest available stable version of Mysql. This version of Mysql came into existence in year 2005. Failure data are collected from October 2005 to February 2011. Data are extracted directly from the web site. Bugs reported might be duplicates, provide incomplete information, or may not represent real defects. Therefore, during the bug preprocessing such noises are removed from the bugs gathered in the first step. Finally, in the third step, the preprocessed data is stored in Mysql database. Initially data was in csv (comma separated value) format. Total of 6399 records were extracted from repository and after preprocessing finally 2171 records were stored in Mysql Table. During preprocessing following records were deleted:

Versions other than Mysql5: Because here only Mysql5 with major subversions are considered, thus versions other than Mysql5 are not considered.

Some of the Sub Versions of Mysql5 have fewer records: Sample size less than 30, so difficult to fit distribution. All those records were deleted.

The records whose status was Need Info: These types of records may or may not be considered as failure records.

The records having severity other than S1 to S5 were deleted.

Some of the records were irrelevant means there open date were less than that of the release date. All those records were deleted.

Some of the records were without any versions, all those records were deleted.

Main fields of the table are as given below:

Table2: TABLE STRUCTURE
Field	Data Type	Purpose

Bug_Id Int Identification Number (Primary Key)

Opendate Date Date of submission of the bug

Figure 2:Monthly Bug Frequency

FAILURE COUNT

Bug_Severity Varchar and can be any of the following:

S5: Performance S4:Feature Request

S3:Normal-Severity(Non Critical) S2: Serious

S1:Critical

MONTH

FAILURE COUNT

Abstract of the Failure count of sample under study is graphically shown in Figure 1.

Figure 1:Version wise Abstract of Mysql

MONTH

FAILURE COUNT

MONTH

Before applying goodness of fit test on data collected for each of the major sub versions of Mysql5 series bug frequency corresponding to time to failure in month is plotted and shown in Figure 2. From Figure 1 it is clear that in all three cases maximum of the bugs has S3 and S4 bug severity. Further from Figure2 no idea regarding distribution to be fitted can be drawn, thus Goodness of fit Test is applied for all the samples and best distribution is identified. By using these distributions models are constructed and using these models different measures are estimated and analyzed in detail.

Mysql 5.0

From collected failure data, on the basis of version, records related to Mysql 5.0 version is extracted and stored in a separate table. By using appropriate Sql query Time to Failure in terms of week is calculated and stored. This data is used for further analysis.

Goodness of Fit Test [21]

Goodness of Fit Test is applied for extracted time to failure data for Mysql5.0.

For goodness of fit test all major life data distributions are tested by using

• Kolmogorov Smirnov Test

• Anderson Darling Test and

• Chi Square Test

  All above tests are applied on 1%, 2%, 5%, 10% and 20% level of significance. On the basis of these tests best distribution which is accepted on the basis of these tests and at maximum number of level of significance is selected for reliability model construction.

  On the basis of goodness fit test result following is the list of distributions which are suitable for time to failure data of Mysql 5.0 sample.

• Gen. Gamma Distribution(4 Parameters)

  H (t) =

  f (t)

  R(t)

  (4)

• Gen. Extreme Value Distribution.

Among these two distributions on the basis of their test statistic ranking and detail result of goodness of fit test Gen. Gamma distribution with 4 parameters is identified as best distribution to be fitted. Gen. Gamma distribution (4 Parameters) is accepted by Kolmogorov-Smirnov test at 1%, 2%, 5% and 10% level of significance. It is accepted by Anderson-Darling test at 1%, 2% and 5% level of significance and by Chi-Squared test it is accepted at 1% level of significance. On the basis of this distribution reliability model is constructed and all other measures are estimated and shown graphically.

Model Construction and Reliability Estimation (C3), (C4) using Gen. Gamma Distribution

Generalized Gamma distribution with 4 parameters is one of the life data distributions which are widely used in life data analysis. This distribution is used in many researches regarding reliability Analysis.

Its pdf is given by

By using above equations value of pdf, cdf, reliability and hazard function (failure rate) is estimated. Weekly value of these estimates after every 4 weeks is shown in Table 3 and its graphical representation is shown in Figure 6.2.

f (t)

k(t

k

)k (

(

1)

exp(

)

((t

) / )k )

Table3: Value of Pdf , Reliability, and Hazard Function: Mysql 5.0
TTFWEE K	PDF	RELIABIL TY	HAZARD FUNCTIO N
4	0.00243353	0.99220381	0.002452654
8	0.00278207	0.9817052	0.00283392
12	0.00300492	0.97010626	0.003097516
16	0.00317271	0.95773774	0.003312708
20	0.00330881	0.94476638	0.003502254
24	0.0034241	0.93129481	0.003676706
28	0.00352455	0.91739328	0.003841919
32	0.00361385	0.90311322	0.004001546
36	0.00369442	0.88849409	0.004158071
40	0.00376796	0.87356721	0.004313304
44	0.0038357	0.85835813	0.004468644
48	0.00389855	0.84288814	0.004625226
52	0.00395722	0.82717531	0.004784016
56	0.00401226	0.81123522	0.004945868
60	0.00406411	0.79508147	0.005111566
64	0.00411311	0.77872612	0.00528185
24	0.0034241	0.93129481	0.003676706
28	0.00352455	0.1739328	0.003841919
32	0.00361385	0.90311322	0.004001546
36	0.00369442	0.88849409	0.004158071
40	0.00376796	0.87356721	0.004313304
44	0.0038357	0.85835813	0.004468644
48	0.00389855	0.84288814	0.004625226
52	0.00395722	0.82717531	0.004784016
56	0.00401226	0.81123522	0.004945868
60	0.00406411	0.79508147	0.005111566
64	0.00411311	0.77872612	0.00528185
68	0.00415955	0.76217998	0.005457434
72	0.00420363	0.74545287	0.005639028
76	0.00424553	0.72855384	0.005827344

(1)

Its CDF is given by

F (t)

((t

)/)k )( ) ()

(2)

where k=continuous shape parameter, =continuous shape parameter , =continuous scale parameter and =continuous location parameter(k,,>0).

Here to construct reliability model parameters are estimated

. Parameters are estimated by using method of Maximum Likelihood . These parameters are estimated with the help of Easy Fit 5.5 and is given by K=6.3702, =0.1862, =243.69 and =0.20005.

Thus we have

Reliability Model R (t) =1-F (t)

k ( )

= 1-

((t )/) )

()

1. and Hazard function

   which is defined as failure rate is given by

   Figure 3: Graphical Representation of Reliability Measures Mysql5.0[Weekly after every 4 Weeks]

   Goodness of Fit Test is applied for collected sample data. For goodness of fit test all major life data distributions are tested by using

   • Kolmogorov Smirnov Test

     Probability Density Function

   • Anderson Darling Test and

     0.005

     0.004

     0.003

     0.002

     0.001

     0

     0 100 200 300

     WEEK

   • Chi Square Test

     PDF

     All above tests are applied on 1%, 2%, 5%, 10% and 20% level of significance. On the basis of these tests best distribution which is accepted on the basis of these tests and at maximum number of level of significance is selected for reliability model construction.

     On the basis of goodness fit test result following is the list of distributions which are suitable for time to failure data of Mysql 5.1 sample.

   • Beta Distribution

     1.2

     1

     0.8

     0.6

     0.4

     0.2

     0

   • Gen. Gamma Distribution(4 Parameters)

Reliability

RELIABILITY

Among these two distributions on the basis of their test statistic ranking and detail result of goodness of fit test Beta distribution is identified as best distribution to be fitted. In probability theory and statistics, the beta distribution [67],

0 200 400

WEEK

[68] is a family of continuous probability distributions defined on the interval (a, b) parameterized by two positive shape parameters, typically denoted by 1 and 2. This distribution is widely used in life data analysis.

Pdf of this distribution is as given by

0.08

0.07

0.06

0.05

0.04

0.03

0.02

0.01

0

FAILURE RATE

f (t)

1 (t

a) 1 1 (b

t) 2 1

( 1 , 2 )

Hazard

(b a)( 1

2 1)

(5)

0 100 200 300

WEEK

Function

Where 1 = continuous shape parameter 1 >0, 2 = continuous shape parameter, 2 >0 and a, b is continuous boundary parameter (a<=b). Domain of this distribution is given by a t b.

Here

Mysql 5.1

This version of Mysql came into existence in November 2008.Total of 898 preprocessed failure records related to this version of Mysql is extracted. Goodness of fit test is

(1, 2 )

1

t1 1 (1

0

t)2 1 dt

1,

2 0

(6)

applied on time to failure data of these records and on the basis of goodness of fit test best distribution is identified and model is constructed.

Incomplete Beta function is given by

x

Goodness of Fit Test [36]

x ( 1, 2 )

t 1 1(1

0

1. 2 1 dt

   1, 2

   0 , 0 x 1

   (7)

   Table 4:Weekly Reliability Measures Mysql 5.1
   TTFWEEK	PDF	RELIBILITY	HAZARD FUNCTION
   4	0.005192	0.986336	0.005263475
   8	0.006141	0.963464	0.00637401
   12	0.00672	0.937672	0.007166416
   16	0.007144	0.909907	0.007851518
   20	0.007481	0.880634	0.008494879
   24	0.00776	0.850137	0.009127831
   28	0.007997	0.81861	0.009769565
   32	0.008203	0.786199	0.010434251
   36	0.008384	0.753016	0.011134038
   40	0.008544	0.719154	0.01188064
   44	0.008686	0.684688	0.012686371
   48	0.008813	0.649685	0.013565001
   52	0.008926	0.614202	0.01453264
   56	0.009026	0.578294	0.015608769
   60	0.009115	0.542006	0.016817597
   64	0.009193	0.505386	0.018189928
   68	0.00926	0.468477	0.019765864
   72	0.009316	0.431322	0.021598845
   76	0.009361	0.393963	0.023761927
   80	0.009395	0.356446	0.02635789
   84	0.009417	0.318818	0.029536268
   88	0.009425	0.281131	0.033523532
   92	0.009416	0.243443	0.038680077
   96	0.009389	0.205825	0.04561662
   100	0.009337	0.168364	0.055457443
   104	0.009251	0.131174	0.070524275
   108	0.009113	0.094425	0.096509563
   Average	0.005511	0.507482	0.266878032

   CDF of this distribution is given by F (t) =

   I z ( 1,

   2 ) where z

   t – a

   b – a

   (8)

   Here Iz is regularized incomplete beta function. (1,2 is beta function given by

   IZ(1,2)=

   z ( 1 , 2 )

   (9)

   ( 1 , 2 )

   Likelihood function is given by

   n

   L= f (t; 1,

   i 1

   2, a, b) .

   To estimate parameters following equations are used

   ln(L) 1

   0; ln(L)

   2

   0; ln(L)

   a

   0; ln(L) 0

   b

   (10)

   By using method of Maximum Likelihood [69] these parameters are estimated as 1=1.2095, 2=1.0743, a=0.81959 and b=119.02.

   Thus we have

   Reliability Model

   R (t) =1-F(t) = 1-

   z (1.2095,1.0743)

   (1.2095,1.0743)

   (11)

   Hazard function which is defined as failure rate is given by

   f (t)

   H (t) =

   R(t)

   (12)

   PDF

   Figure 4 :Graphical representation of Pdf,Reliability and Hazard Function MYSQL 5.1
   		0.01
   		0.009
   		0.008
   		0.007
   		0.006
   Pdf		0.005 0.004
   		0.003
   		0.002
   		0.001
   		0
   			0	50 100	150
   				WEEK

   By using above equations value of pdf, reliability and hazard function (failure rate) is estimated. Weekly value of these estimates after every 4 weeks are shown in following Table 4 and its graphical representation is shown in Figure 4.

   RELIABILITY

   Reliability

   1.2

   1

   0.8

   0.6

   0.4

   0.2

   0

   0

   50

   100

   150

   WEEK

   Hazard Function

   0.4

   0.35

   0.3

   0.25

   0.2

   0.15

   0.1

   0.05

   0

   0

   50

   100

   150

   Table 5:Reliability Measures of Mysql 5.5 after every 4 Weeks
   TTF	PDF	RELIABILIT Y	HAZARD FUNCTION
   4	0.002092795	0.97965587	0.002136255
   8	0.002883681	0.9697674	0.00297358
   12	0.003884927	0.95630608	0.004062431
   16	0.005132388	0.93835983	0.005469531
   20	0.006665067	0.91486683	0.007285287
   24	0.008525176	0.88460287	0.009637291
   28	0.010758175	0.84616839	0.012713988
   32	0.013412825	0.79797542	0.016808569
   36	0.016541228	0.73823427	0.022406475
   40	0.020198872	0.66494009	0.03037698
   44	0.024444669	0.57585924	0.042449035
   48	0.029340999	0.46851552	0.062625459
   52	0.034953654	0.34017624	0.102751601
   56	0.041302458	0.18786991	0.219846055
   61	0.00741434	0.00193903	3.823728088
   Aver age	0.016163601	0.69888002	0.139064222

   Mysql 5.5

   All data related to Mysql5.5 is extracted .By using appropriate sql query Time to Failure in terms of week is calculated and stored. For Mysql5.5 we have total of 164 preprocessed failure records.

   Goodness of Fit Test (36)

   As in previous case Goodness of Fit Test is performed on data related to this version of Mysql. On the basis of goodness fit test result attached following is the list of distributions which are suitable for time to failure data of Mysql 5.5:

   • Gen. Gamma Distribution and

   • Gen. Extreme Value Distribution.

   Among these two distributions on the basis of their test statistic ranking and detail result of goodness of fit test Gen. Gamma Distribution is identified as best distribution to be fitted. This distribution is accepted at all level of significance by Kolmogorov-Smirnov and Anderson- Darling test and at 1% and 2% level of significance by Chi Squared Test.

   Reliability Model Construction and Model Fitting

   Same model as in case of Mysql 5.0 is used here. All parameters are estimated by using Method of Maximum Likelihood and is given by K=155.47, =0.03372, =107.51 and =-46.962.

   Thus using these parameters in Equation (1) to Equation (4) Reliability measures is estimated and its value after every 4 week is shown in Table 5 and graphically it is shown in Figure 5.

   FIGURE 5:GRAPHICAL REPRESENTATION OF RELIABILITY ESTIMATES OF MYSQL 5.5

   Table 6: Average Reliability Estimates for Mysql5 series.
   MYSQL VERSION	Averag e Pdf	Average Reliability	Average Failure Rate
   5.0	0.0035 57009	0.45704778	0.0176602 22
   5.1	0.0055 10869	0.50748216 9	0.2668780 32
   5.5	0.0161 63601	0.69888002	0.1390642 22
   OVERALL AVERAGEMYS QL5	0.0084 10493	0.55446999	0.1412008 25
   	VERSION WISE AVERAGE
   	0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1	RELIABILITY ESTIMATES
   		5.0 5.1 5.5
   	0 Average Pdf Average Average Reliability Failure Rate

   0.05

   0.04

   PDF

   0.03

   PDF

   0.02

   0.01

   0

   RELIABILIT

   Y

   1.2

   1

   0.8

   0.6

   0.4

   0.2

   0

   HAZARD

   0 20 40 60 80

   RELIABILITY

   WEEK

   0

   20 40 60 80

   WEEK

   On the basis of above table it is clear that from all three prospects Mysql 5.1 is found to most reliable. The research of this type will be very useful for researchers in Open Source and Reliability.

   FUNCTION

   0

   50

   WEEK

   100

   4.5

   4

   3.5

   3

   2.5

   2

   1.5

   1

   0.5

   0

   PDF

   Section IV: Conclusion

   In above study a detail methodology to estimate reliability is discussed and it has been analyzed that mere calculating reliability one cannot judge whether the product is reliable or not. The average value of three estimates for each of these sub versions are calculted and is shown here:

   References:

   1. Ying ZHOU, Joseph DAVIS Open source software reliability model: an empirical approach

   2. IEEE Reliability Society, IEEE recommended practice on softwarereliability, IEEE Std 1633-2008, June 2008.

   3. MySQL Server:www.Mysql.com

   4. J.D. Musa and K. Okumoto, A logarithmic poisson execution time model for software reliability measurement, 7th Intl Conference on Software Engineering (ICSE), 1984, pp. 230-238.

[5]H. Pham, Software Reliability. Springer Verlag, 2000.

1. J.De.S Coutinho, Software reliability growth. IEEE Symposium onComputer Software Reliability, 1973, pp. 58- 64.

2. Z. Jelinski and P.B. Moranda,Software reliability research, inStatistical Computer Performance Evaluation,

W. Freiberger, Ed.,New York: Academic Press, 1972, pp. 465-484.

[8]H.S. Kan, Metrics and Models in Software Quality Engineering, 2Ed., Addison-Wesley, 2003.

1. I. Koren and C.M. Krishna, Fault-Tolerant Systems, MorganKaufmann, 2007.

2. A. Mockus, T.R. Fielding, and J.D. Herbsleb, Two case studies of open source software development: Apache and Mozilla, ACM Transactions on Software Engineering and Methodology, vol. 11, no. 3, July 2002, pp. 309-346.

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4. E.W.STACY and G.A.MIHRAM Parameter Estimation for a Generalized Gamma Distribution

5. Gamma Distribution: Pham, T. Almhana, J. Fac. of Sci. & Eng., Moncton Univ., NB The generalized Gamma distribution: its hazard rate and stress-strength model Reliability, IEEE Transactions

6. H. Leon Harter, Maximum Likelihood Estimation of Parameters of Four Parameter Generalized Gamma population from Complete and Censored Samples.

7. Dean G. Boerrigter Captain, USAF Parameter Estimation of the Mixed Generalized Gamma Distribution using Maximum likelihood Estimation and Minimum Distance Estimation

8. Beta Distribution:

   http://en.wikipedia.org/wiki/Beta_distribution

9. Beta Distribution: http://itl.nist.gov/div898/handbook/eda/section3/eda366h.ht m.

10. Gnanadeshikaran, Pinkham and Hughes Maximum Likelihood estimation Beta Distribution

    :http://www.jstor.org/pss/1266199

11. W.L. Wang, Y. Wu and M.H. Chen, An architecture- based software reliability model, Proceedings of Pacific Rim Intl Symposium on Dependable Computing, 1999.

12. S. Yacoub, B. Cukic and H.H. Ammar, A software- based reliability analysis approach for component-based software, IEEE Transactions on Reliability, vol. 53, no. 4, Dec 2004.

13. Sanjeev Kumar Jha, Dr. A.K.D. Dwivedi and Dr. Amod Tiwari Necessity of Goodness of Fit Tests in Research and Developmentwww.ijcst.com/vol22/1/sanjeev.pdf

14. An Experimental Analysis of Open Source Software ReliabilityCobra Rahmani, Harvey Siy, Azad Azadmanesh

Biography:

Sanjeev Kumar Jha, Senior Systems Analyst, NIELIT Chandigarh, Ministry of C&IT Government of India. Bachelors and Masters Degree in Statistics [Honors] from Patna University and presently doing his PhD in Computer Science from Singhania University, Rajasthan. He has attended 2 international Conferences. Area of research interest is Reliability and Open Source Software.

Shivlok Singh , Programmer NIELIT is presently doing his PhD in Computer Science from Singhania University, Rajasthan. He has attended 2 international Conferences. Area of research interest is Reliability and Open Source Software

Dr. Amod Tiwari, Associate Professor, PSIT Kanpur. PhD from IIT Kanpur. Attended many international and national Conferences. Published many papers in international and national journals. Area of research interest is Image Processing, Reliability and Open Source Software.