A general imperfect-software-debugging model with s-shaped fault-detection rate

Hoang Pham, Lars Nordmann, Xueniei Zhang

Research output: Contribution to journalArticlepeer-review

184 Scopus citations


A general software reliability model based on the nonhomogeneous Poisson process (NHPP) is used to derive a model that integrates imperfect debugging with the learning phenomenon. Learning occurs if testing appears to improve dynamically in efficiency as one progresses through a testing phase. Learning usually manifests itself as a changing fault-detection rate. Published models and empirical data suggest that efficiency growth due to learning can follow many growth-curves, from linear to that described by the lo" gistic function. On the other hand, some recent work indicates that in a real industrial resource-constrained environment, very little actual learning might occur because non-operational profiles used to generate test & business models can prevent the learning. When that happens, the testing efficiency can still change when an explicit change in testing strategy occurs, or it can change as a result of the structural profile of the code under test and test-case ordering. Either way, software reliability engineering researchers agree that: • changes in the fault-detection rate are common during the testing process; • in most realistic situations, fault repair has associated with it a fault re-introduction rate due to imperfect debugging. We compare descriptive and predictive ability of a set of classical NHPP reliability models with the one we developed using 4 sets of software-failure data. The results show that inclusion of both imperfect debugging and a time-dependent fault-detection rate into an NHPP software reliability growth model (SRGM): • improve both the descriptive and the predictive properties of a model, • is worth the extra model-complexity and the increased number of parameters required for a better relative fit. We use the sum of squared error to compare relative goodnessof-fit of the models within a data set; and use the Akaike information criterion as an indicator of the overall relative goodness of a model after compensation for its complexity, viz, number of parameters it has. More application is needed to validate fully this model for descriptive & predictive software reliability modeling in a general industrial setting.

Original languageEnglish (US)
Pages (from-to)169-175
Number of pages7
JournalIEEE Transactions on Reliability
Issue number2
StatePublished - 1999

All Science Journal Classification (ASJC) codes

  • Safety, Risk, Reliability and Quality
  • Electrical and Electronic Engineering


  • Akaike's information criterion
  • Imperfect debugging
  • Learning model
  • Nonhomogeneous poisson process
  • Software reliability


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