Cost Models for One-Dimensional Warranties

  • Wallace R. Blischke
  • M. Rezaul Karim
  • D. N. Prabhakar Murthy
Part of the Springer Series in Reliability Engineering book series (RELIABILITY)


When a manufacturer offers a warranty, all legitimate claims under warranty must be serviced. The number of claims that might be expected depends on the reliability of the product. Servicing of the claims results in additional costs to the manufacturer. There are several notions of warranty costs, each of which leads to a distinct cost model. In this chapter we focus on models for prediction of warranty costs as a function of product reliability for various one-dimensional warranties. These models play a critical role in warranty management.


Cost Model Product Life Cycle Life Cycle Cost Warranty Period Cost Element 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Bass FW (1969) A new product growth model for consumer durables. Manag Sci 15:215ᾢ227MATHCrossRefGoogle Scholar
  2. 2.
    Blischke WR, Murthy DNP (1994) Warranty cost analysis. Marcel Dekker, New YorkGoogle Scholar
  3. 3.
    Blischke WR, Murthy DNP (eds) (1996) Product warranty handbook. Marcel Dekker, New YorkGoogle Scholar
  4. 4.
    Chukova S, Arnold R, Wang D (2004) Warranty analysis: an approach to modeling imperfect repairs. Int J Prod Econ 89:57ᾢ68CrossRefGoogle Scholar
  5. 5.
    Doyen L, Gaudoin O (2004) Classes of imperfect repair models based on reduction of failure intensity or virtual age. Reliab Eng Sys Saf 84:45ᾢ56CrossRefGoogle Scholar
  6. 6.
    Henderson JM, Quandt RE (1958) Microeconomics theory. McGraw-Hill Inc., New YorkGoogle Scholar
  7. 7.
    Hill VL, Beall CW, Blischke WR (1991) A simulation model for warranty analysis. Int J Prod Econ 22:131ᾢ140CrossRefGoogle Scholar
  8. 8.
    Jack N, Murthy DNP (2001) A servicing strategy for items sold under warranty. J Oper Res Soc 52:1284ᾢ1288MATHCrossRefGoogle Scholar
  9. 9.
    Jack N, van der Duyn Schouten F (2000) Optimal repair-replace strategies for a warranted product. Int J Prod Econ 67:95ᾢ100CrossRefGoogle Scholar
  10. 10.
    Jiang X, Jardine AKS, Lugitigheid D (2006) On a conjecture of optimal repair-replacement strategies for warranted products. Math Comput Model 44:963ᾢ972MathSciNetMATHCrossRefGoogle Scholar
  11. 11.
    Kim CS, Djamaludin I, Murthy DNP (2001) Warranty cost analysis with heterogeneous usage intensity. Int Trans Oper Res 8:337ᾢ347MathSciNetMATHCrossRefGoogle Scholar
  12. 12.
    Kline MB (1984) Suitability of lognormal distribution for corrective maintenance repair times. Reliab Eng 9:65ᾢ80CrossRefGoogle Scholar
  13. 13.
    Mahajan V, Wind Y (1986) Innovation diffusion models of new product acceptance. Ballinger Publishing Company Cambridge, MassGoogle Scholar
  14. 14.
    Mahon BH, Bailey RJM (1975) A proposed improvement replacement policy for army vehicles. Oper Res Q 26:477ᾢ494CrossRefGoogle Scholar
  15. 15.
    Murthy DNP, Djamaludin I (2001) Warranty and quality. In: Rahim MA, Ben-Daya M (eds) Integrated optimal modelling in PIQM: production planning, inventory, quality and maintenance. Kluwer Academic Publishers, New YorkGoogle Scholar
  16. 16.
    Murthy DNP, Nguyen DG (1988) An optimal repair cost limit policy for servicing warranty. Math Model 11:595ᾢ599MathSciNetCrossRefGoogle Scholar
  17. 17.
    Nguyen DG, Murthy DNP (1986) An optimal policy for servicing warranty. J Oper Res 37:1081ᾢ1088MATHGoogle Scholar
  18. 18.
    Nguyen DG, Murthy DNP (1989) Optimal replace-repair strategy for servicing items sold with warranty. Eur J Oper Res 39:206ᾢ212MathSciNetMATHCrossRefGoogle Scholar
  19. 19.
    Padmanabhan V (1996) Marketing and warranty. In: Blischke WR, Murthy DNP (eds) Product warranty handbook. Marcel Dekker, New YorkGoogle Scholar
  20. 20.
    Patankar JG, Mitra A (1996) Warranty and consumer behavior: warranty execution. In: Blischke WR, Murthy DNP (eds) Product warranty handbook. Marcel Dekker, New YorkGoogle Scholar
  21. 21.
    Sahin I, Polatogu H (1998) Quality, warranty and preventive maintenance. Kluwer Academic Publishers, BostonCrossRefGoogle Scholar
  22. 22.
    Sheu SH, Yu SL (2005) Warranty strategy accounts for bathtub failure rate and random minimal repair cost. Comput Math Appl 49:1233ᾢ1242MathSciNetMATHCrossRefGoogle Scholar
  23. 23.
    Yun WY, Murthy DNP, Jack N (2008) Warranty servicing with imperfect repair. Int J Prod Econ 111:156ᾢ169CrossRefGoogle Scholar
  24. 24.
    Zuo MJ, Liu B, Murthy DN (2000) Replacementᾢrepair policy for multi-state deteriorating products under warranty. Eur J Oper Res 123:519ᾢ530MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  • Wallace R. Blischke
    • 1
  • M. Rezaul Karim
    • 2
  • D. N. Prabhakar Murthy
    • 3
  1. 1.Sherman Oaks, Los AngelesUSA
  2. 2.Department of StatisticsRajshahi UniversityRajshahiBangladesh
  3. 3.School of Mechanical and Mining EngineeringThe University of QueenslandBrisbaneAustralia

Personalised recommendations