Software Quality ManagementUnit – 3 

G. Roy Antony ArnoldAsst Prof /CSEAsst. Prof./CSE

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I t t t R l i h hi h d l th d f t tt f• In contrast to Rayleigh, which models the defect pattern ofthe entire development process, reliability growth modelsare usually based on data from the formal testing phases.

• Indeed it makes more sense to apply these models duringthe final testing phase when development is virtuallycomplete especially when the testing is customercomplete, especially when the testing is customeroriented.

• During such post‐development testing, when defects areid tifi d d fi d th ft b t blidentified and fixed, the software becomes more stable,and reliability grows over time. Therefore models thataddress such a process are called

.

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h l ifi d i l h• They are classified into two classes. They are,–– TimeTime betweenbetween FailureFailure ModelModel

• the variable under study is the time between failures• Mean time to next failure is usually the parameter tob i d f h d lbe estimated for the model.

–– FaultFault CountCount ModelModelh i bl i i i h b f f l• the variable criterion is the number of faults orfailures (or normalized rate) in a specified timeinterval.

• The number of remaining defects or failures is the key parameter to be estimated from this class of models.

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• There are N unknown software faultsat the start of testingg

• Failures occur randomlyAll f l ib ll f il• All faults contribute equally to failure

• Fix time is negligibly smallg g y• Fix is perfect for each fault

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J li ki M d (J M) M d l• Jelinski‐Moranda (J‐M) Model– Assumes random failures, perfect zero time fixes, all f l ll b dfaults equally bad

• Littlewood Models– Like J‐M model, but assumes bigger faults found first

• Goel‐Okumoto Imperfect Debugging Model– Like J‐Mmodel, but with bad fixes possibleLike J M model, but with bad fixes possible

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• 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 beginningWhere N is the number of software defects at the beginningof testing and φ is a proportionality constant.

N tNote:Hazard function is constant between failures but decreases in

steps of φ following the removal of each fault. Therefore, as each fault isremoved, the time between failures is expected to be longer.

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• Similar to J‐M Model, except it assumes that different faults have different sizes, thereby ycontributing 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.

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J M M d l f t d b i B t thi i t• J‐M Model assumes perfect debugging. But this is not possible always.

• In the process of fixing a defect new defects may beIn 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 thebeginning of testing, φ is a proportionality constant, pis the probability of imperfect debugging andλ is theis the probability of imperfect debugging andλ is thefailure rate per fault.

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• Testing intervals are independent of eachother

• Testing during intervals is reasonablyhomogeneoushomogeneous

• Number of defects detected is independentof each other

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G l Ok t N h P i P• Goel‐Okumoto Non‐homogeneous Poisson Process 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 M d lModel– 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 fixfix

– Inflection S: As failures are detected, they reveal more failures

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• 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,

!)]([ )( =− ye

ytm tm

y

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