Warranty cost analysis for k-out-of-n systems with 2-D warranty

Minjae Park, Hoang Pham

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


This paper presents new warranty cost models subject to two types of warranty periods (warranty and postwarranty periods), minimal repairs, and various types of warranty policies including free repair/replacement warranty and prorata warranty for k-out-of-n systems. Two-dimensional warranty is applied to investigate the warranty cost using repair times and failure times. We obtain the long-run expected cost functions per unit time with respect to both the warranty and postwarranty periods by considering the aspects of both the manufacturer and the customer. This paper considers a periodic preventive maintenance (PM) policy with both corrective maintenance and PM and also determines three decision variables including warranty period, repair time limit, and periodical maintenance cycles, which minimize the long-run expected cost. Numerical examples are discussed to demonstrate the applicability of the methodologies, and results including the three optimum decision-variable solution and their corresponding long-run expected cost per unit are derived.

Original languageEnglish (US)
Article number6178809
Pages (from-to)947-957
Number of pages11
JournalIEEE Transactions on Systems, Man, and Cybernetics Part A:Systems and Humans
Issue number4
StatePublished - Jul 2012

All Science Journal Classification (ASJC) codes

  • Software
  • Control and Systems Engineering
  • Human-Computer Interaction
  • Computer Science Applications
  • Electrical and Electronic Engineering


  • 2-D
  • k-out-of-n system
  • postwarranty period
  • preventive maintenance (PM)
  • warranty cost

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