Regression Approach to Parameter Estimation of an Exponential Software Reliability Model

Albert Orwa Akuno; Timothy Mutunga Ndonye; Janiffer Mwende Nthiwa; Luke Akong’o Orawo

doi:doi:10.11648/j.ajtas.20160503.11

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Regression Approach to Parameter Estimation of an Exponential Software Reliability Model

Albert Orwa Akuno, Timothy Mutunga Ndonye, Janiffer Mwende Nthiwa, Luke Akong’o Orawo

Published in American Journal of Theoretical and Applied Statistics (Volume 5, Issue 3)

Received: 10 March 2016 Accepted: 5 April 2016 Published: 21 April 2016

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Abstract

Mathematical studies about the likelihood of failures of software systems have been advanced by various researchers. These studies have modeled the behavior of software systems by using failure times and time between failures in the past. The Goel-Okumoto software reliability model is amongst the many software reliability models proposed to model the failure behavior of software systems. To be able to use the model in software reliability assessment, it is important to estimate its parameters α and β and the intensity function λ(t). In this paper, classical parametric regression methods have been utilized in the estimation of the parameters α and β, the intensity function and the mean time between failures of the Goel-Okumoto software reliability model. The parameters α and β and the mean time between failures (MTBF) of the Goel-Okumoto software model have been estimated using the maximum likelihood estimation (MLE) method, regression approach applied to the model and simple linear regression model without assuming the Goel-Okumoto model. When these three estimation methods were validated using root mean squared error (RMSE) and mean absolute value difference (MAVD), which are the common error measurement criteria, regression approach applied to the Goel-Okumoto model outperformed MLE and simple linear regression estimation methods.

Published in	American Journal of Theoretical and Applied Statistics (Volume 5, Issue 3)
DOI	10.11648/j.ajtas.20160503.11
Page(s)	80-86
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2016. Published by Science Publishing Group

Keywords

Goel-Okumoto model, Regression Approach, Maximum Likelihood Estimation

References

[1]	Goel, A. L. and Okumoto, K., (1979). Time-dependent error detection rate model for software reliability and other performance measures. IEEE Trans. Reliability, 28: 206–211.
[2]	Stringfellow, C. and Amschler, A. A., (2002). An Empirical Method for Selecting Software Reliability Growth Models. Empirical Software Engineering, 7: 319-343.
[3]	Meyfroyt, P. H. A., (2012). Parameter Estimation for Software Reliability Models. Masters Thesis, Eindhoven University of Technology, Eindhoven, Netherlands.
[4]	Xie, M., Goh, T. N and Ranjan, P., (2002). Some effective control chart procedures for reliability monitoring. Elsevier, Reliability engineering and System safety.
[5]	Akuno, A. O., Orawo, L. A. andIslam, A. S. (2014) One-Sample Bayesian Predictive Analyses for an Exponential Non-Homogeneous Poisson Process in Software Reliability. Open Journal of Statistics, 4, 402-411.
[6]	Akuno, A. O., Orawo, L. A. and Islam, A. S. (2014) Two-Sample Bayesian Predictive Analyses for an Exponential Non-Homogeneous Poisson Process in Software Reliability. Open Journal of Statistics, 4, 742-750.
[7]	Satya, P., Bandla, S. R. and Kantham, R. R. L., (2011). Assessing Software Reliability using Inter Failures Time Data. International Journal of Computer Applications, 18: 975-978.
[8]	Abdelah, M. M., (2006). Regression Approach to Software Reliability Models. Graduate Theses and Dissertations, University of South Florida, USA.
[9]	Rigdon, S. E. and Basu, A. P., (2000). The Power Law Process: a Model for the Reliability of Repairable systems. Journal of Quality Technology, 21: 251-260.
[10]	Hossain, S. A. and Dahiya, R. C., (1993). Estimating the Parameters of a Non- homogenous Poisson-Process Model for Software Reliability. IEEE Tranis- actions on Reliability, 42:604-612.
[11]	Ascher, H. and Feingold, H., (1984). Repairable Systems Reliability, Inference, Misconceptions and their Causes. Marcel Dekker, New York.
[12]	Cox, D. R. and Lewis, P. A., (1996). The Statistical Analysis of Series of Events. Chapman and Hall, London.
[13]	Roberts, H., (2000). Predicting the Performance of Software Systems via the Power Law Process. Ph.D. thesis, University of South Florida, Tampa, FL.
[14]	Suresh, N., (1992). Modeling and Analysis of Software Reliability. Ph.D. thesis, University of South Florida, Tampa, FL.
[15]	Karambir, B. and Adima. A., (2014). A review on Parameter Estimation Techniques of Software Reliability Growth Models. International Journal of Computer Applications Technology and Research, 4: 267-272, ISSN: 2319-8656.
[16]	Latha, S. and Lilly, F., (2012). A Comparison of Parameter Best Estimation Method for Software Reliability Models. International Journal of Software Engineering & Applications (IJSEA), Vol. 3, No. 5.
[17]	Xie, M., Hong, G. Y. and Wohlin, C., (1997). A Practical Method of the Estimation of Software Reliability Growth in the Early Stages of Testing. Proceedings IEEE 7^th International Symposium on Software Reliability Engineering. pp. 116-123, Albuquerque, USA.

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APA Style

Albert Orwa Akuno, Timothy Mutunga Ndonye, Janiffer Mwende Nthiwa, Luke Akong’o Orawo. (2016). Regression Approach to Parameter Estimation of an Exponential Software Reliability Model. American Journal of Theoretical and Applied Statistics, 5(3), 80-86. https://doi.org/10.11648/j.ajtas.20160503.11

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ACS Style

Albert Orwa Akuno; Timothy Mutunga Ndonye; Janiffer Mwende Nthiwa; Luke Akong’o Orawo. Regression Approach to Parameter Estimation of an Exponential Software Reliability Model. Am. J. Theor. Appl. Stat. 2016, 5(3), 80-86. doi: 10.11648/j.ajtas.20160503.11

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AMA Style

Albert Orwa Akuno, Timothy Mutunga Ndonye, Janiffer Mwende Nthiwa, Luke Akong’o Orawo. Regression Approach to Parameter Estimation of an Exponential Software Reliability Model. Am J Theor Appl Stat. 2016;5(3):80-86. doi: 10.11648/j.ajtas.20160503.11

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@article{10.11648/j.ajtas.20160503.11,
  author = {Albert Orwa Akuno and Timothy Mutunga Ndonye and Janiffer Mwende Nthiwa and Luke Akong’o Orawo},
  title = {Regression Approach to Parameter Estimation of an Exponential Software Reliability Model},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {5},
  number = {3},
  pages = {80-86},
  doi = {10.11648/j.ajtas.20160503.11},
  url = {https://doi.org/10.11648/j.ajtas.20160503.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20160503.11},
  abstract = {Mathematical studies about the likelihood of failures of software systems have been advanced by various researchers. These studies have modeled the behavior of software systems by using failure times and time between failures in the past. The Goel-Okumoto software reliability model is amongst the many software reliability models proposed to model the failure behavior of software systems. To be able to use the model in software reliability assessment, it is important to estimate its parameters α and β and the intensity function λ(t). In this paper, classical parametric regression methods have been utilized in the estimation of the parameters α and β, the intensity function and the mean time between failures of the Goel-Okumoto software reliability model. The parameters α and β and the mean time between failures (MTBF) of the Goel-Okumoto software model have been estimated using the maximum likelihood estimation (MLE) method, regression approach applied to the model and simple linear regression model without assuming the Goel-Okumoto model. When these three estimation methods were validated using root mean squared error (RMSE) and mean absolute value difference (MAVD), which are the common error measurement criteria, regression approach applied to the Goel-Okumoto model outperformed MLE and simple linear regression estimation methods.},
 year = {2016}
}

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TY  - JOUR
T1  - Regression Approach to Parameter Estimation of an Exponential Software Reliability Model
AU  - Albert Orwa Akuno
AU  - Timothy Mutunga Ndonye
AU  - Janiffer Mwende Nthiwa
AU  - Luke Akong’o Orawo
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PY  - 2016
N1  - https://doi.org/10.11648/j.ajtas.20160503.11
DO  - 10.11648/j.ajtas.20160503.11
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
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EP  - 86
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20160503.11
AB  - Mathematical studies about the likelihood of failures of software systems have been advanced by various researchers. These studies have modeled the behavior of software systems by using failure times and time between failures in the past. The Goel-Okumoto software reliability model is amongst the many software reliability models proposed to model the failure behavior of software systems. To be able to use the model in software reliability assessment, it is important to estimate its parameters α and β and the intensity function λ(t). In this paper, classical parametric regression methods have been utilized in the estimation of the parameters α and β, the intensity function and the mean time between failures of the Goel-Okumoto software reliability model. The parameters α and β and the mean time between failures (MTBF) of the Goel-Okumoto software model have been estimated using the maximum likelihood estimation (MLE) method, regression approach applied to the model and simple linear regression model without assuming the Goel-Okumoto model. When these three estimation methods were validated using root mean squared error (RMSE) and mean absolute value difference (MAVD), which are the common error measurement criteria, regression approach applied to the Goel-Okumoto model outperformed MLE and simple linear regression estimation methods.
VL  - 5
IS  - 3
ER  -

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Author Information

Albert Orwa Akuno

Department of Mathematics, Egerton University, Egerton, Kenya
Timothy Mutunga Ndonye

Department of Mathematics, Egerton University, Egerton, Kenya
Janiffer Mwende Nthiwa

Department of Mathematics, Egerton University, Egerton, Kenya
Luke Akong’o Orawo

Department of Mathematics, Egerton University, Egerton, Kenya

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APA Style

Albert Orwa Akuno, Timothy Mutunga Ndonye, Janiffer Mwende Nthiwa, Luke Akong’o Orawo. (2016). Regression Approach to Parameter Estimation of an Exponential Software Reliability Model. American Journal of Theoretical and Applied Statistics, 5(3), 80-86. https://doi.org/10.11648/j.ajtas.20160503.11

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ACS Style

Albert Orwa Akuno; Timothy Mutunga Ndonye; Janiffer Mwende Nthiwa; Luke Akong’o Orawo. Regression Approach to Parameter Estimation of an Exponential Software Reliability Model. Am. J. Theor. Appl. Stat. 2016, 5(3), 80-86. doi: 10.11648/j.ajtas.20160503.11

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AMA Style

Albert Orwa Akuno, Timothy Mutunga Ndonye, Janiffer Mwende Nthiwa, Luke Akong’o Orawo. Regression Approach to Parameter Estimation of an Exponential Software Reliability Model. Am J Theor Appl Stat. 2016;5(3):80-86. doi: 10.11648/j.ajtas.20160503.11

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@article{10.11648/j.ajtas.20160503.11,
  author = {Albert Orwa Akuno and Timothy Mutunga Ndonye and Janiffer Mwende Nthiwa and Luke Akong’o Orawo},
  title = {Regression Approach to Parameter Estimation of an Exponential Software Reliability Model},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {5},
  number = {3},
  pages = {80-86},
  doi = {10.11648/j.ajtas.20160503.11},
  url = {https://doi.org/10.11648/j.ajtas.20160503.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20160503.11},
  abstract = {Mathematical studies about the likelihood of failures of software systems have been advanced by various researchers. These studies have modeled the behavior of software systems by using failure times and time between failures in the past. The Goel-Okumoto software reliability model is amongst the many software reliability models proposed to model the failure behavior of software systems. To be able to use the model in software reliability assessment, it is important to estimate its parameters α and β and the intensity function λ(t). In this paper, classical parametric regression methods have been utilized in the estimation of the parameters α and β, the intensity function and the mean time between failures of the Goel-Okumoto software reliability model. The parameters α and β and the mean time between failures (MTBF) of the Goel-Okumoto software model have been estimated using the maximum likelihood estimation (MLE) method, regression approach applied to the model and simple linear regression model without assuming the Goel-Okumoto model. When these three estimation methods were validated using root mean squared error (RMSE) and mean absolute value difference (MAVD), which are the common error measurement criteria, regression approach applied to the Goel-Okumoto model outperformed MLE and simple linear regression estimation methods.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - Regression Approach to Parameter Estimation of an Exponential Software Reliability Model
AU  - Albert Orwa Akuno
AU  - Timothy Mutunga Ndonye
AU  - Janiffer Mwende Nthiwa
AU  - Luke Akong’o Orawo
Y1  - 2016/04/21
PY  - 2016
N1  - https://doi.org/10.11648/j.ajtas.20160503.11
DO  - 10.11648/j.ajtas.20160503.11
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 80
EP  - 86
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20160503.11
AB  - Mathematical studies about the likelihood of failures of software systems have been advanced by various researchers. These studies have modeled the behavior of software systems by using failure times and time between failures in the past. The Goel-Okumoto software reliability model is amongst the many software reliability models proposed to model the failure behavior of software systems. To be able to use the model in software reliability assessment, it is important to estimate its parameters α and β and the intensity function λ(t). In this paper, classical parametric regression methods have been utilized in the estimation of the parameters α and β, the intensity function and the mean time between failures of the Goel-Okumoto software reliability model. The parameters α and β and the mean time between failures (MTBF) of the Goel-Okumoto software model have been estimated using the maximum likelihood estimation (MLE) method, regression approach applied to the model and simple linear regression model without assuming the Goel-Okumoto model. When these three estimation methods were validated using root mean squared error (RMSE) and mean absolute value difference (MAVD), which are the common error measurement criteria, regression approach applied to the Goel-Okumoto model outperformed MLE and simple linear regression estimation methods.
VL  - 5
IS  - 3
ER  -

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