Reliability Growth Models

Software Quality Management Unit – 3 G. Roy Antony Arnold Asst Prof /CSE Asst. Prof./GRAAI t tt R l i h hi h d l th d f t tt f • In contrast to Rayleigh, which models the defect pattern of the entire development process, reliability growth models are usually based on data from the formal testing phases. • Indeed it makes more sense to apply these models during the final testing phase when development is virtually complete especially when the testing is customer complete, oriented. • During such post‐development testing, when defects are id tifi d d fi d th ft b t bl identified and fixed, the software becomes more stable, and reliability grows over time. Therefore models that address such a process are called . GRAAh l ifi di l h • They are classified into two classes. They are, – Time between Failure Model • the variable under study is the time between failures • Mean time to next failure is usually the parameter to b i df h d l be estimated for the model. – Fault Count Model h i bl i i i h b f f l • the variable criterion is the number of faults or failures (or normalized rate) in a specified time interval. • The number of remaining defects or failures is the key parameter to be estimated from this class of models. GRAA• There are N unknown software faults at the start of testing • Failures occur randomly Allf l ib ll f il • All faults contribute equally to failure • Fix time is negligibly small g g y • Fix is perfect for each fault GRAAJ li kiM d (J M) M d l • Jelinski‐Moranda J‐Model – Assumes random failures, perfect zero time fixes, all f l ll b d faults equally bad • Littlewood Models – Like J‐M model, but assumes bigger faults found first • Goel‐Okumoto Imperfect Debugging Model – Like J‐M model, but with bad fixes possible J GRAA• One of the earliest model. ( 1972) ) • The software product’s failure rate improves by the same amount at each fix. • The hazard function at time ti, the time between the (i‐1)st and ith failures, is given • Where N is the number of software defects at the beginning of testing and φis a proportionality constant. N t Note: Hazard function is constant between failures but decreases in steps of φfollowing the removal of each fault. Therefore, as each fault is removed, the time between failures is expected to be longer. GRAA• Similar to J‐M Model, except it assumes that different faults have different sizes, thereby contributing unequally to failures. (1981) • Larger sized be Larger‐faults tend to detected and fixed earlier. • This concept makes the model assumption more realistic. GRAAJ MM d l f td b i B tthi i t • J‐M Model assumes perfect debugging. But this is not possible always. • In the process of a defect new defects may be fixing defect, injected. Indeed, defect fix activities are known to be error‐prone. • Hazard function is, • Where N is the number of software defects at the beginning of testing, φis a proportionality constant, p is the probability of imperfect debugging and λis the failure rate per fault. GRAA• Testing intervals are independent of each other • Testing during intervals is reasonably homogeneous • Number of defects detected is independent of each other GRAAG lOk t N h P i P • Goel‐Okumoto Non‐homogeneous Poisson Process Model (NHPP) – # failures exponential failure rate (i.e. of in a time period, the exponential model!) • Musa‐Okumoto Logarithmic Poisson Execution Time M d l Model – Like NHPP, but later fixes have less effect on reliability • The Delayed S and Inflection S Models – Delayed S: Recognizes time between failure detection and fix – Inflection S: As failures are detected, they reveal more failures GRAA• This model is concerned with modelling the number of failures observed in given testing intervals. (1979) • They proposed that the time‐dependent failure rate follows an exponential distribution. • The model is, e ode s, P{N(t)=y}= ... 2 , 1 , 0 , !)] ( [ ) ( = − y e yt m t m y GRAA