Journal of Systems Engineering and Electronics ›› 2022, Vol. 33 ›› Issue (2): 360-369.doi: 10.23919/JSEE.2022.000038

• SYSTEMS ENGINEERING • Previous Articles     Next Articles

Grey-based approach for estimating software reliability under nonhomogeneous Poisson process

Xiaomei LIU1,2(), Naiming XIE1,*()   

  1. 1 College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China
    2 College of Science, Jiujiang University, Jiujiang 332005, China
  • Received:2020-12-28 Online:2022-05-06 Published:2022-05-06
  • Contact: Naiming XIE;
  • About author:|LIU Xiaomei was born in 1981. She received her B.S. and M.S. degrees from Nanchang University in 2003 and 2006, respectively. Now, she is a lecturer at Jiujiang University. She has been pursuing her Ph.D. degree in Nanjing University of Aeronautics and Astronautics since 2018. Her research interests include grey information modeling and reliability system modeling. E-mail:||XIE Naiming was born in 1981. He received his B.S., M.S., and PH.D. degrees from Nanjing University of Aeronautics and Astronautics in 2002, 2005 and 2008, respectively. Now, he is a full professor from Institute of Grey System Studies, and serves as Vice-Dean of College of Economics and Management at Nanjing University of Aeronautics and Astronautics. His major research interests include grey information modelling, dynamic system modelling and data analytics in smart manufacturing. E-mail:
  • Supported by:
    This work was supported by the National Natural Science Foundation of China (71671090), the Fundamental Research Funds for the Central Universities (NP2020022), the Qinglan Project of Excellent Youth or Middle-Aged Academic Leaders in Jiangsu Province.


Due to the randomness and time dependence of the factors affecting software reliability, most software reliability models are treated as stochastic processes, and the non-homogeneous Poisson process (NHPP) is the most used one. However, the failure behavior of software does not follow the NHPP in a statistically rigorous manner, and the pure random method might be not enough to describe the software failure behavior. To solve these problems, this paper proposes a new integrated approach that combines stochastic process and grey system theory to describe the failure behavior of software. A grey NHPP software reliability model is put forward in a discrete form, and a grey-based approach for estimating software reliability under the NHPP is proposed as a nonlinear multi-objective programming problem. Finally, four grey NHPP software reliability models are applied to four real datasets, the dynamic R-square and predictive relative error are calculated. Comparing with the original single NHPP software reliability model, it is found that the modeling using the integrated approach has a higher prediction accuracy of software reliability. Therefore, there is the characteristics of grey uncertain information in the NHPP software reliability models, and exploiting the latent grey uncertain information might lead to more accurate software reliability estimation.

Key words: software reliability model, stochastic process, uncertainty system, non-homogeneous Poisson process, grey system theory