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Software Testing and Quality Assurance

Lecture 36 – Software Quality Assurance

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Lecture Objectives Markov Models Software Reliability Growth

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Markov Models Reliability block diagrams are

Useful for analyzing failure probabilities and reliability over fixed time intervals

We also need to understand How reliability changes over time; Especially in the presence of hardware.

Markov Chain can provide extra information abouthow a system’s reliability changes over time.

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Markov Models – stochastic process Random variable are functions that

Assign a number to each outcome in the sample space of an experiment.

In Reliability Models The number of failures at time T which is

discrete, or an integer-valued; OR The time at which the first failure occurs,

which is a continuous, real-valued, random variable.

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Markov Models – Example We are interested in Markov systems

We want to explore how the reliability of systems evolves over time.

Finite State Automaton (FSA)

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Markov Models – Example There are two states of interest in the

automation Functioning state; and Failed state.

The transitions in the automation are not labeled with events Labeled with probabilities.

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Markov Models – Example Each λ is the probability of making a

transition from one state to the next Within a specified time interval.

For the simple model of failure processes, we can interpret the states and probabilities over a time interval T

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Markov Models – Example

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Transition Matrix for the two State Model

We can represent the probabilities for the simple two model as a matrix.

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Transition Matrix for the two State Model

Transition Matrix for the Markov Chain

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Software Reliability Growth Collection of techniques for estimating

reliability as a program is being developed and tested. Components/modules are tested and their

failure rates are measured.

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Software Reliability Growth Failure rate of a component is the

number of failures observed per unit time. Failure rates are plotted against reliability

models to determine How much more development time is

required to reach acceptable levels of reliability.

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Software Reliability Growth Measure Reliability

Through random testing. Not specifically aimed at uncovering faults

in a program, although it will certainly help to uncover any faults.

It aims at providing a random sample of inputs for the purpose of estimating a program’s reliability.

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Software Reliability Growth Reliability Growth Models

Assumes that as development and testing continues

The failure rates experienced should decrease.

If failure rates are decreasing then the reliability should be increasing.

If the failure rates are not decreasing then there may Be something wrong with our testing and development process

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Software Reliability Growth – Basic Execution Time Model

Reliability depends on: The failure intensity λ(T) at time T and The execution time itself.

Failure intensity is defined as The failures experienced per unit time.

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Software Reliability Growth – Basic Execution Time Model

Relation between failure rates and reliability is given by:

Where e is Euler’s number (the base of the natural logarithm).

Reliability is approximated by an inverse exponential Function of time and failure intensity.

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Software Reliability Growth – Basic Execution Time Model

As the failure intensity λ approaches 0 Then R(T) approaches 1; and

As the failure intensity approaches ∞ Then R(T) approaches 0.

Even if we reached a low reliability estimate, the longerthat a system is required toe execute without

Failure, the lower the reliability R (T) becomes.

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Software Reliability Growth – Basic Execution Time Model

Obtaining Failure Data Test cases are selected randomly We can not predict what the next test case

selected will be. In reliability measurement, to get

meaningful results, test cases are selected according to the patterns of usage of the program.

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Software Reliability Growth – Basic Execution Time Model

Four ways of estimating failure intensity The time of the failure; The failures experienced in a specified

time interval; The time interval between failures; The cumulative failures experienced up to

a specified time.

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Key points Markov Models – stochastic process

Transition Matrix for the two State Model Software Reliability Growth

Basic Execution Time Model