Efficient Product Support—Optimum and Realistic Spare Parts Forecasting

  • Behzad Ghodrati
Part of the Springer Series in Reliability Engineering book series (RELIABILITY)


The required spare parts planning for a system/machine is an integral part of the product support strategy. The number of required spare parts can be effectively estimated on the basis of the product reliability characteristics. The reliability characteristics of an existing machine/system are influenced not only by the operating time, but also by factors such as the environmental parameters (e.g. dust, humidity, temperature, moisture, etc.), which can degrade or improve the reliability. In the product life cycle, for determining the accurate spare parts needs and for minimizing the machine life cycle cost, consideration of these factors are useful. Identification of the effects of operating environment factors (as covariates) on the reliability may facilitate more accurate prediction and calculation of the required spare parts for a system under given operating conditions. The Proportional Hazards Model (PHM) method is used for estimation of the hazard (failure) rate of components under the effect of covariates. The existing method for calculating the number of spare parts on the basis of the reliability characteristics, without consideration of covariates, is studied, modified and improved to arrive at the optimum spare parts requirement. In this chapter, an approach has been developed to forecast and estimate accurately the spare parts requirements considering operating environment and to create rational part ordering strategies. Subsequently, two methods of Poisson process and renewal process are introduced and discussed. The renewal process model uses a multiple regression type of analysis based on Cox’s proportional hazards modeling (PHM). The parametric approaches with baseline Weibull hazard functions and time independent covariates are considered, and the influence of operating environment factors on this model is analyzed. Only non-repairable components (changeable/service parts) which must be replaced upon failure are discussed.


Hazard Rate Planning Horizon Spare Part Life Cycle Cost Weibull Model 
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.
    Ansell JI, Philips MJ (1997) Practical aspects of modeling of repairable systems data using proportional hazards models. Reliab Eng Syst Saf 58:165–171CrossRefGoogle Scholar
  2. 2.
    Armistead CG, Clark G (1992) Customer service and support. Pitman, LondonGoogle Scholar
  3. 3.
    Aronis KP, Magou I, Dekker R, Tagaras G (2004) Inventory control of spare parts using a Bayesian approach: a case study. Eur J Oper Res 154:730–739CrossRefMATHGoogle Scholar
  4. 4.
    Billinton R, Allan RN (1983) Reliability evaluation of engineering systems: concepts and techniques. Pitman Books Limited, BostonCrossRefMATHGoogle Scholar
  5. 5.
    Birolini A (2004) Reliability engineering theory and practice, 4th edn. Springer, New YorkGoogle Scholar
  6. 6.
    Blanchard BS (2001) Maintenance and support: a critical element in the system life cycle. In: Proceedings of the International Conference of Maintenance Societies, MelbourneGoogle Scholar
  7. 7.
    Blanchard BS, Fabrycky WJ (1998) Systems engineering and analysis, 3rd edn. Prentice-Hall, Upper Saddle RiverGoogle Scholar
  8. 8.
    Blischke WR, Murthy DNP (1994) Warranty cost analysis. Marcel Dekker Inc., New YorkGoogle Scholar
  9. 9.
    Blischke WR, Murthy DNP (2000) Reliability: modeling, prediction, and optimization. Wiley, New YorkCrossRefGoogle Scholar
  10. 10.
    Cassady CR, Pohl EA, Jin S (2004) Managing availability improvement efforts with importance measures and optimization. IMA J Manage Math 15:161–174MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Chelbi A, Ait-Kadi D (2001) Spare provisioning strategy for preventively replaced systems subjected to random failure. Int J Prod Econ 74:183–189CrossRefGoogle Scholar
  12. 12.
    Cooper RG, Kleinschmidt EJ (1993) Major new products: What distinguishes the winners in the chemical industry. J Prod Innov Manage 10:90–111CrossRefGoogle Scholar
  13. 13.
    Cox DR (1972) Regression models and life-tables. J R Stat Soc B 34:187–220MATHGoogle Scholar
  14. 14.
    Cox DR, Oakes D (1984) Analysis of survival data. Chapman and Hall, LondonGoogle Scholar
  15. 15.
    Cui LR, Xie M (2003) Some numerical approximations for renewal function of large Weibull shape parameter, Communications in Statistics: B: Simulation and Computation, 32(1):1–16Google Scholar
  16. 16.
    Darko ML (2007) Optimization of critical spare parts inventories: a reliability perspective. Ph.D. thesis, University of Toronto, CanadaGoogle Scholar
  17. 17.
    Dekker R (1996) Applications of maintenance optimization models: A review and analysis. Reliab Eng Syst Saf 51:229–240CrossRefGoogle Scholar
  18. 18.
    Dhakar TS, Schmidt CP, Miller DM (1994) Base stock level determination for high cost low demand critical repairable spares. Comput Oper Res 21:411–420CrossRefMATHGoogle Scholar
  19. 19.
    Drenick RF (1960) The failure law of complex equipment. J Soc Ind Appl Math 8:680–690MathSciNetCrossRefGoogle Scholar
  20. 20.
    Fortuin L, Martin H (1999) Control of service parts. Int J Oper Prod Manage 19:950–971CrossRefGoogle Scholar
  21. 21.
    Ghodrati B (2005) Reliability and operating environment based spare parts planning. Ph.D. thesis, Luleå University of Technology, Sweden ISSN: 1402–1544Google Scholar
  22. 22.
    Ghodrati B, Kumar U (2005) Reliability and operating environment based spare parts estimation approach: a case study in Kiruna Mine, Sweden. J Qual Main Eng 11:169–184CrossRefGoogle Scholar
  23. 23.
    Gnedenko BV, Belyayev YK, Solovyev AD (1969) Mathematical methods of reliability theory. Academic Press, New YorkMATHGoogle Scholar
  24. 24.
    Goffin K (1998) Evaluating customer support during new product development: an exploratory study. J Prod Innov Manage 15:42–56CrossRefGoogle Scholar
  25. 25.
    Goffin K (2000) Design for supportability: Essential component of new product development. Res Technol Manage 43:40–47Google Scholar
  26. 26.
    Høyland A, Rausand M (1994) System reliability theory: models and statistical methods. John Wiley and Sons, New YorkGoogle Scholar
  27. 27.
    Huiskonen J (2001) Maintenance spare parts logistics: special characteristics and strategic choices. Int J Prod Econ 71:125–133CrossRefGoogle Scholar
  28. 28.
    IAEA (International Atomic Energy Agency) (2001) Reliability assurance programme guidebook for advanced light water reactors. IAEA-TECDOC-1264, ViennaGoogle Scholar
  29. 29.
    Intellect (2003) Reliability: a practitioner’s guide. The Information Technology Telecommunications and Electronics Association, Relex Software CorporationGoogle Scholar
  30. 30.
    Jardine AKS, Tsang AHC (2006) Maintenance, replacement and reliability: theory and application. CRC, Taylor and Francis, Boca RatonGoogle Scholar
  31. 31.
    Jardine AKS, Joseph T, Banjevic D (1999) Optimizing condition-based maintenance decisions for equipment subject to vibration monitoring. J Qual Main Eng 5:192–202CrossRefGoogle Scholar
  32. 32.
    Jardine AKS, Banjevic D, Wiseman M, Buck S, Joseph T (2001) Optimizing mine haul truck wheel motors’ condition monitoring program: use of proportional hazards modeling. J Qual Main 7:286–301CrossRefGoogle Scholar
  33. 33.
    Kales P (1998) Reliability: for technology, engineering, and management. Prentice-Hall Inc., USAGoogle Scholar
  34. 34.
    Kaplan EL, Meier P (1958) Non-parametric estimation from incomplete observations. J Am Stat Assoc 53:457–481MathSciNetCrossRefMATHGoogle Scholar
  35. 35.
    Kennedy WJ, Patterson JW, Fredendall LD (2002) An overview of recent literature on spare parts inventories. Int J Prod Econ 76:201–215CrossRefGoogle Scholar
  36. 36.
    Krajewski LJ, Ritzman LR (2005) Operations management: processes and value chains, 7th edn. Pearson Prentice Hall, New JerseyGoogle Scholar
  37. 37.
    Kumar D (1996) Reliability analysis and maintenance scheduling considering operating conditions. Ph.D. Thesis, Luleå University of Technology, SwedenGoogle Scholar
  38. 38.
    Kumar D, Klefsjö B (1994) Proportional hazards model: an application to power supply cables of electric mine loaders. Int J Reliab Qual Saf Eng 1:337–352CrossRefGoogle Scholar
  39. 39.
    Kumar D, Klefsjö B (1994) Proportional hazards model: a review. Reliab Eng Syst Saf 44:177–188CrossRefGoogle Scholar
  40. 40.
    Kumar D, Klefsjö B, Kumar U (1992) Reliability analysis of power transmission cables of electric mine loaders using the proportional hazard model. Reliab Eng Syst Saf 37:217–222CrossRefGoogle Scholar
  41. 41.
    Kumar KR, Loomba APS, Hadjinicola GC (2000) Theory and methodology: marketing-production coordination in channels of distribution. Eur J Oper Res 126:189–217MathSciNetCrossRefMATHGoogle Scholar
  42. 42.
    Kumar UD, Crocker J, Knezevic J, El-Haram M (2000) Reliability, maintenance and logistic support: a life cycle approach. Kluwer Academic Publishers, USACrossRefGoogle Scholar
  43. 43.
    Kuo W, Zuo MJ (2003) Optimal reliability modeling. John Wiley and Sons, New JerseyGoogle Scholar
  44. 44.
    Langford JW (1995) Logistics: principles and applications. McGraw-Hill Inc, New YorkGoogle Scholar
  45. 45.
    Lawless JF (1982) Statistical models and methods for lifetime data. John Wiley and Sons, New YorkMATHGoogle Scholar
  46. 46.
    Lawless JF (1983) Statistical methods in reliability (with discussion). Technometrics 25:305–335MathSciNetCrossRefMATHGoogle Scholar
  47. 47.
    Lewis EE (1996) Introduction to reliability engineering. John Wiley and Sons, New YorkGoogle Scholar
  48. 48.
    Markeset T (2003) Dimensioning of product support: issues, challenges, and opportunities. Ph.D. thesis, Stavanger University College, Norway, ISBN 82-7644-197-1Google Scholar
  49. 49.
    Markeset T, Kumar U (2003) Design and development of product support and maintenance concepts for industrial systems. J Qual Main Eng 9:376–392CrossRefGoogle Scholar
  50. 50.
    Markeset T, Kumar U (2003) Integration of RAMS and risk analysis in product design and development work processes: a case study. J Qual Maint Eng 9:393–410CrossRefGoogle Scholar
  51. 51.
    Nelson W (1969) Hazard plotting for incomplete failure data. J Qual Tech 1:27–52Google Scholar
  52. 52.
    NTNU (2005) Calculation of renewal function in the Weibull distribution. accessed on September 20, 2005
  53. 53.
    O’Connor PDT (1991) Practical reliability engineering, 3rd edn. John Wiley and Sons, West SussexGoogle Scholar
  54. 54.
    Orsburn DK (1991) Spares management handbook. McGraw-Hill, USAGoogle Scholar
  55. 55.
    Palm C (1938) Analysis of the Erlang traffic formula for busy-signal arrangements. Ericsson Tech 5:39–58Google Scholar
  56. 56.
    Ramakumar R (1993) Engineering reliability: fundamentals and applications. Prentice Hall, Eaglewood CliffsGoogle Scholar
  57. 57.
    Rigdon SE, Basu AP (2000) Statistical methods for the reliability of repairable systems. John Wiley and Sons, New YorkMATHGoogle Scholar
  58. 58.
    Sheikh AK, Younas M, Raouf A (2000) Reliability based spare parts forecasting and procurement strategies. In: Ben-Daya M, Duffuaa SO, Raouf A (eds) Maintenance, modeling and optimization. Kluwer Academic Publishers, BostonGoogle Scholar
  59. 59.
    Smeitink E, Dekker R (1990) A simple approximation to the renewal function. IEEE Transaction on Reliability, 39(1):71–75CrossRefMATHGoogle Scholar
  60. 60.
    Spearman ML (1989) A simple approximation for IFR Weibull renewal function. Microelectron Reliability 29(1):73–80MathSciNetCrossRefGoogle Scholar
  61. 61.
    Wååk O, Alfredsson P (2001) Constant vs. non-constant failure rates: some misconceptions with respect to practical applications. Systecon Publications, SwedenGoogle Scholar
  62. 62.
    Wong JYF, Chung DWC, Ngai BMT, Banjevic D, Jardine AKS (1997) Evaluation of spares requirements using statistical and probability analysis techniques. Trans Mech Eng IEAust 22:77–84Google Scholar

Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.Division of Operation and Maintenance EngineeringLuleå University of TechnologyLuleåSweden

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