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Fuzzy optimization approach to component selection of fault-tolerant software system

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Abstract

In developing software systems, a manager’s goal is to design software using limited resources and meet the user requirements. One of the important user requirements concerns the reliability of the software. The decision to choose the right software modules (components) becomes extremely difficult because of the number of parameters to be considered while making the decision. If suitable components are not available, then the decision process is further complicated with build versus buy decisions. In this paper, we have formulated a fuzzy multi-objective approach to optimal decision “build-or-buy” for component selection for a fault-tolerant modular software system under the consensus recovery block scheme. A joint optimization model is formulated where the two objectives are maximization of system reliability and minimization of the system cost with a constraint on delivery time. An example of developing a retail system for small-and-medium-size enterprises is used to illustrate the proposed methodology.

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Abbreviations

\(R\) :

System quality measure

\(C\) :

Overall system cost

\(f_l\) :

Frequency of use, of function \(l\)

\(s_l\) :

Set of modules required for function \(l\)

\(R_i\) :

Reliability of module \(i\)

\(L\) :

Number of functions, the software is required to perform

\(n\) :

Number of modules in the software

\(m_i\) :

Number of alternatives available for module \(i\)

\(V_{ij}\) :

Number of versions available for alternative \(j\) of module \(i\)

\(t_1\) :

Probability that next alternative is not invoked upon failure of the current alternative

\(t_2\) :

Probability that the correct result is judged wrong

\(t_3\) :

Probability that an incorrect result is accepted as correct

\(Y_{ij}\) :

Event that correct result of alternative \(j\) of module \(i\) is accepted

\(X_{ij}\) :

Event that output of alternative \(j\) of module \(i\)is rejected

\(r_{ij}\) :

Reliability of alternative \(j\) of module \(i\)

\(C_{ijk}\) :

Cost of version \(k\) of alternative \(j\) of module \(i\)

\(s_{ijk}\) :

Reliability of version \(k\) of alternative \(j\) of module \(i\)

\(d_{ijk}\) :

Delivery time of version \(k\) of alternative \(j\) of module \(i\)

\(c_{ij}\) :

Unitary development cost for alternative \(j\) of module \(i\)

\(t_{ij}\) :

Estimated development time for alternative \(j\) of module \(i\)

\(\tau _{ij}\) :

Average time required to perform a test case for alternative \(j\) of module \(i\)

\(\pi _{ij}\) :

Probability that a single execution of software fails on a test case chosen from a certain input distribution

\(x_{ijk}\) :

\(\left\{ {\begin{array}{l@{\quad }l} 1,&{} \text{ if } \text{ the }\, k\mathrm{th}\, \mathrm{version}\, \text{ of }\, j\mathrm{th}\, \text{ COTS } \text{ alternative }\\ &{} \text{ of } \text{ the }\, i\mathrm{th}\,\text{ module } \text{ is } \text{ chosen } \\ 0,&{} \text{ otherwise } \\ \end{array}} \right. \)

\(y_{ij}\) :

\(\left\{ {\begin{array}{l@{\quad }l} 1, &{}\text{ if } \text{ the }\,j\mathrm{th}\, \text{ alternative } \text{ of }\,i\mathrm{th}\,\text{ module } \text{ is }\\ &{} \mathrm{in}\text{- }\mathrm{house} \ \mathrm{developed} \\ 0,&{} \text{ otherwise } \\ \end{array}} \right. \)

\(z_{ij}\) :

\(\left\{ {\begin{array}{l@{\quad }l} 1, &{} \text{ if } \text{ alternative }\,j\,\text{ is } \text{ present } \text{ in } \text{ module }\,i \\ 0, &{} \text{ otherwise } \\ \end{array}} \right. \)

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Authors and Affiliations

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

    P. C. Jha

  2. Lal Bahadur Shastri Institute of Management, Delhi, India

    Shivani Bali

  3. Indian Institute of Management, Bangalore, India

    U. Dinesh Kumar

  4. Department of Industrial and System Engineering, Rutgers University, New Jersey, USA

    Hoang Pham

Authors
  1. P. C. Jha
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  2. Shivani Bali
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  3. U. Dinesh Kumar
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  4. Hoang Pham
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Correspondence to P. C. Jha.

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Jha, P.C., Bali, S., Kumar, U.D. et al. Fuzzy optimization approach to component selection of fault-tolerant software system. Memetic Comp. 6, 49–59 (2014). https://doi.org/10.1007/s12293-013-0116-4

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