Reliability growth models


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Anna University, Final CSE, Software Quality Management

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Reliability growth models

  1. 1. Software Quality Management Unit – 3  G. Roy Antony Arnold Asst. Prof./CSE Asst Prof /CSEGRAA
  2. 2. • I contrast t R l i h which models th d f t pattern of In t t to Rayleigh, hi h d l the defect tt f 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, complete especially when the testing is customer oriented.• During such post‐development testing, when defects are identified d fixed, the ft id tifi d and fi d th software b becomes more stable, t bl and reliability grows over time. Therefore models that address such a process are called . GRAA
  3. 3. • They are classified i h l ifi d into two classes. They are, l h – Time between Failure Model • the variable under study is the time between failures • Mean time to next failure is usually the parameter to be i b estimated f the model. d for h d l – Fault Count Model • the variable criterion i the number of f l or h i bl i i is h b f faults 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
  4. 4. • There are N unknown software faults g at the start of testing• Failures occur randomly• All f l contribute equally to f il faults ib ll failure• Fix time is negligibly small g g y• Fix is perfect for each fault GRAA
  5. 5. • J li ki M Jelinski‐Moranda (J M) M d l d (J‐M) Model – Assumes random failures, perfect zero time fixes, all  faults equally bad f l ll b d• 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 Like J M model, but with bad fixes possible GRAA
  6. 6. ( )• 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 φ is a proportionality constant.Note:N t Hazard function is constant between failures but decreases insteps of φ following the removal of each fault. Therefore, as each fault isremoved, the time between failures is expected to be longer. GRAA
  7. 7. • Similar to J‐M Model, except it assumes that  y different faults have different sizes, thereby  contributing unequally to failures. (1981)• Larger sized faults tend to be detected and Larger‐sized faults tend to be detected and  fixed earlier.• This concept makes the model assumption  more realistic. more realistic. GRAA
  8. 8. • J MM d l J‐M Model assumes perfect debugging. But this is not  f t d b i B t thi i t possible always.• In the process of fixing a defect new defects may be In the process of fixing a defect, new defects may be  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, φ is a proportionality constant, p is the probability of imperfect debugging andλ is the failure rate per fault. GRAA
  9. 9. • Testing intervals are independent of each other• Testing during intervals is reasonably homogeneous• Number of defects detected is independent of each other GRAA
  10. 10. • G l Ok Goel‐Okumoto N h t Non‐homogeneous Poisson Process  P i P Model (NHPP) – # of failures in a time period, exponential failure rate (i.e. # of failures in a time period, exponential failure rate (i.e.  the exponential model!)• Musa‐Okumoto Logarithmic Poisson Execution Time  Model M d l – Like NHPP, but later fixes have less effect on reliability• The Delayed S and Inflection S Models 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
  11. 11. • 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. e ode s,• The model is, [m(t )] y − m (t ) P{N(t)=y}= e , y = 0,1,2... y! GRAA