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Reliability Growth Model

Usually based on data from the formal testing phases

( and especially when the testing is customer

oriented) .

Defect arrival or failure pattern are good indicatorsof the products reliability when it is used by

customer.

During such post development testing, when failures

occurs and defects are identified and fixed, the

software become more stable, and reliability grows

over time.

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Therefore models that address such a process are called

reliability growth models.

Example of reliability growth model is The

Exponential Model.

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The Exponential Model

The exponential model is another special case of

weibull family with shape parameter m=1.

It is best used for statistical process that decline

monotonically to an asymptote.

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Reliability Growth Models

Reliability growth model can be classified into two

classes.

Time between failure model.

Fault count model.

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Time between failure model The random variable under study is time between

failure.

For this model it is expected that the failure time willget longer as defects are remove from the software

product.

This model is based on the criteria that the (i-1)th

and ith failure follows a distribution whoseparameters are related to the product after the (i-1)th

failure.

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Fault count model

The random variable for this model is the number of

faults or failures in a specified time interval.

The time can be CPU execution time or calendar

time( such as hour, week or month).

As defects are detected and removed from the

software, it is expected that the observed number of

failure per unit time will decrease.

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Example ofTime between failure model

Jelinski- Moranda Model(J-M Model).

This model assumes N software fault at the start of

the testing.

Failure occurs purely at random, and all faultscontribute equally to cause a failure during testing.

It also assumes that the fixed time is negligible and

that the fix for each failure is perfect.

The software products failure rate improves by thesame amount at each fix.

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The instantaneous failure rate function at time ti, thetime between (i-1)th and ith failure is,

Z(ti) [N-(i-1)]Or Z(ti) = [N-(i-1)]

Where N= Number of software defects at the beginning

of testing.

= The proportionality constant.

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The failure rate function is constant between failure

but decreases monotonically after removal of each

fault.

As fault is removed the time between failure is

expected to be longer.

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Littlewood Model

This model assumes that different faults havedifferent sizes, so all faults contributes unequally to

failures.

Large sized faults tend to be detected and fixed

earlier.

As the number of errors is driven down with theprogress in test, so the average error size decreases.

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Goel Okumoto Imperfect Debugging

Model

The J-M model assumes that the fix time is

negligible and the fixed for each failure is perfect.

In the process of fixing a defect, new defects may be

injected.

During testing phase the number of defective fixes in

large commercial software development organization

may vary from 1% to 10%.

So the instantaneous failure rate function for this

model between (i-1)th and ith failure is

Z(ti) = [N-p(i-1)]

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Where N= Number of faults at the start of testing.

p= probability of imperfect debugging. = Failure rate per fault.

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Goel-Okumoto Nonhomogeneous

Poisson Process Model(NHPP Model)

This model concern with modeling the number of

failures observed in given testing interval.

Goel and Okumoto proposes that the cumulative

number of failures observed at time t, N(t) can be

modeled as a non-homogenous Poisson process.

Non- homogenous means a Poisson process with a

time dependent failure rate.

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They proposed that the time-dependent failure ratefollows an exponential distribution.

The instantaneous failure rate function is given by

Where y = 0, 1, 2, 3,..m(t)= expected number of failure observed by time

t.