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Software Reliability Assessment with OR Applications pp 97–130Cite as

Imperfect Debugging/Testing Efficiency Software Reliability Growth Models

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Part of the book series: Springer Series in Reliability Engineering ((RELIABILITY))

Abstract

Software systems are the means developed and designed by humans for automated operation of several types of real operating systems meant for human kind. Even though the creator of software systems is the universe most dominant and intelligent creature in the universe we cannot deny the possibility of software failures during their operation period. These failures are mainly due to faults manifested in them by their designers. Primarily testing of software is performed with a goal to detect and remove most of the underlying faults. Even though the software testing and debugging team put its best efforts, uses distinct methods and techniques or the developers makes heavy expenditure on testing and debugging latest, well planed and controlled strategies, we cannot be sure that the software can be made free of all type of faults at the time of its launch.

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Authors and Affiliations

  1. Department of Operational Research, University of Delhi, Delhi, 110007, India

    Prof. P. K. Kapur (Faculty of Mathematical Sciences), Dr. A. Gupta (Faculty of Mathematical Sciences) & Dr. P. C. Jha (Faculty of Mathematical Sciences)

  2. Department of Industrial and Systems Engineering, Rutgers University, Frelinghuysen Road 96, Piscataway, NJ, 08854-8018, USA

    Prof. H. Pham

Authors
  1. Prof. P. K. Kapur
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  2. Prof. H. Pham
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  3. Dr. A. Gupta
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  4. Dr. P. C. Jha
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Corresponding author

Correspondence to H. Pham .

Additional information

Exercises

  1. 1.

    What is imperfect debugging? What types of imperfect debugging can be occur while testing the software?

  2. 2.

    A test case is executed during the testing of software in the testing phase. The execution of test case resulted in a failure, indicating the presence of some fault on some path of the module which is executed on the test run. The software debuggers identified the fault and attempted to correct it. What would be the fault count of the software after the fault correction attempt?

  3. 3.

    The failure phenomenon of a pure error generation type SRGM is described as

$$ {\frac{{\rm d}m(t)}{{\rm d}t}} = b(t)[a(t) - m(t)] $$

If the failure rate b(t) = b and a(t) = a + K(1 − e−θt), obtain the mean value function of the SRGM.

  1. 4.

    The mean value function of the removal phenomenon of integrated imperfect debugging SRGM is given by

$$ m_{r} (t) = {e}^{{ - p\int {(1 - \alpha (u))b(u)\,du} }} \left[ {ap\int_{0}^{t} {b(x){e}^{{ - p\int {(1 - \alpha (x))b(x)\,dx} }} \,} dx} \right] $$

If \( b(t) = \left({\frac{{b^{2} t}}{1 + bt}}\right) \) and \( \alpha (t) = \alpha \) then

$$ m_{r} (t) = {\frac{a}{1 - \alpha }}[1 - (1 + bt)^{p(1 - \alpha )} {e}^{ - bp(1 - \alpha )t} ] $$
  1. 5.

    Show that \( m_{r} (t) = pm_{f} (t) \) if \( \frac{\rm d}{{\rm d}t}m_{r} (t) = pb(t)[a(t) - m_{r} (t)] \) and \( \frac{\rm d}{{\rm d}t}m_{f} (t) = b(t)[a(t) - pm_{f} (t)] \).

  2. 6.

    Obtain the mean value function of the exponential test effort based integrated imperfect debugging SRGM if the fault content function is given as a(t) = a + αm r (t).

  3. 7.

    A model developed to describe the reliability growth of software during testing phase, fails in adequately describing the reliability growth during the field usage. Comment.

  4. 8.

    Suppose the usage function of project type software can also be described by W(t) = r + st k, where r, s and k are constant. Determine the unknown parameters of the SRGM for project type software in operational phase using usage function specified above and compare the result on mean square error with the results of Sect. 3.8.3.

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Kapur, P.K., Pham, H., Gupta, A., Jha, P.C. (2011). Imperfect Debugging/Testing Efficiency Software Reliability Growth Models. In: Software Reliability Assessment with OR Applications. Springer Series in Reliability Engineering. Springer, London. https://doi.org/10.1007/978-0-85729-204-9_3

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  • DOI: https://doi.org/10.1007/978-0-85729-204-9_3

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  • Publisher Name: Springer, London

  • Print ISBN: 978-0-85729-203-2

  • Online ISBN: 978-0-85729-204-9

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