Incorporating S-shaped testing-effort functions into NHPP software reliability model with imperfect debugging

Testing-effort（TE） and imperfect debugging（ID） in the reliability modeling process may further improve the fitting and prediction results of software reliability growth models（SRGMs）. For describing the S-shaped varying trend of TE increasing rate more accurately, first, two S-shaped testing-effort functions（TEFs）, i.e.,delayed S-shaped TEF（DS-TEF） and inflected S-shaped TEF（IS-TEF）, are proposed. Then these two TEFs are incorporated into various types（exponential-type, delayed S-shaped and inflected S-shaped） of non-homogeneous Poisson process（NHPP）SRGMs with two forms of ID respectively for obtaining a series of new NHPP SRGMs which consider S-shaped TEFs as well as ID. Finally these new SRGMs and several comparison NHPP SRGMs are applied into four real failure data-sets respectively for investigating the fitting and prediction power of these new SRGMs.The experimental results show that：（i） the proposed IS-TEF is more suitable and flexible for describing the consumption of TE than the previous TEFs;（ii） incorporating TEFs into the inflected S-shaped NHPP SRGM may be more effective and appropriate compared with the exponential-type and the delayed S-shaped NHPP SRGMs;（iii） the inflected S-shaped NHPP SRGM considering both IS-TEF and ID yields the most accurate fitting and prediction results than the other comparison NHPP SRGMs.

Extended research on software hybrid testing combining reliability and directed testing

The software reliability testing has many disadvantages in practice, such as high complexity of constructing operational profiles and poor fault detection efficiency. Oppositely, the directed testing with a high fault detection rate is incapable of estimating reliability quantificationally. To solve this problem, a hybrid testing combining reliability and directed testing as well as a reliability model based on the order statistic （OS） model were presented by Mitchell. An extended research on Mitchell＇s work is proposed. Firstly, the most proper distribution of the fault＇s failure rate which tends to be Iognormal is suggested, and a detailed form of the OS model based on Iognormal and the corresponding parameter estimation method are proposed, respectively. Secondly, an im- plementing framework for the hybrid testing is proposed. Finally, the hybrid testing and the OS model are applied on a real website system. The experimental results indicate： the hybrid testing has more efficient fault detection power and lower testing cost than the reliability testing; compared with three traditional software reliabil ity growth models, the OS model has a best or pretty estimation or prediction power for each data set; and for the failure data set collected from hybrid testing, the OS model also achieves an ac- ceptable estimation result.