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Optimal price and testing time of a software under warranty and two types of imperfect debugging

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Abstract

When a product is purchased and used by a customer then it might be possible that a difference between the product performance and customer expectation crops in. A warranty is simply a formal promise by a vendor that the product is defect free, meaning that it will do what it promises to do and that if it fails to do so, then how the vendor will go about rectifying defects. Warranties are also an effective means of promoting a product in the market when the company or product is not well known. Or in other words warranty serves as a source for spread of an innovation in the market. But servicing a warranty engages additional costs to the manufacturer and this has an effect on the profit levels. Warranty cost may be reduced by providing higher reliable product. The conflict existing in the context of software reliability, warranty period and selling price need to be considered jointly. In this paper, we formulate an optimization problem that determines the optimal testing time and price under two types of imperfect debugging of software product with warrant. The factors like fixed cost of testing and debugging during testing phase and warranty period, cost of testing up to the release time are considered in order to maximize profit. Results are illustrated in the numerical example.

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Abbreviations

a :

Expected number of faults in the software

b :

Proportionality constant

m f (t):

Expected number of faults detected in the interval (0, t]

m r (t):

Expected number of faults removed in the interval (0, t]

T :

Total testing time

W :

Warranty period

p :

Probability of perfect debugging of a fault (0 < p < 1)

ɛ :

Rate at which faults are introduced during the debugging process(0 < ɛ < 1)

C 0 :

Set-up cost for software development

C 1(C 1′):

Cost incurred on a perfect (Imperfect) debugging of fault during testing

C 2(C 2′):

Cost incurred on a perfect (Imperfect) debugging of fault during warranty period(C 2 > C 1, C 2′ > C 1′)

C 3 :

Software testing cost per unit testing time

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Authors and Affiliations

  1. AIBS, Amity University, Noida, UP, India

    P. K. Kapur

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

    Ompal Singh & A. K. Shrivastava

Authors
  1. P. K. Kapur
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  2. Ompal Singh
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  3. A. K. Shrivastava
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Correspondence to P. K. Kapur.

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Kapur, P.K., Singh, O. & Shrivastava, A.K. Optimal price and testing time of a software under warranty and two types of imperfect debugging. Int J Syst Assur Eng Manag 5, 120–126 (2014). https://doi.org/10.1007/s13198-014-0221-x

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  • DOI: https://doi.org/10.1007/s13198-014-0221-x

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