Optimal replacement policies for two-unit machines with increasing running costs 1

Research output: Contribution to journalArticlepeer-review


A machine consists of two stochastically failing units. Failure of either of the units causes a failure of the machine and the failed unit has to be replaced immediately. Associated with the units are running costs which increase with the age of the unit because of increasing maintenance costs, decreasing output, etc. A preventive replacement policy is proposed under which, at failure points, we also replace the second unit if its age exceeds a predetermined control limit. It is proved that, for two identical units with exponential life-time distributions and linear running costs, this policy is optimal and the optimal control limit is calculated. In an additional model we take into consideration the length of time it takes to replace one unit or both units. The method of solution is a variation of dynamic semi-Markov programming. Analytical results are obtained and the influence of the various parameters on them is investigated. Finally, we study the saving due to our policy in comparison with a policy in which only failed units are replaced.

Original languageEnglish
Pages (from-to)89-106
Number of pages18
JournalStochastic Processes and their Applications
Issue number1
StatePublished - Jan 1976
Externally publishedYes


  • dynamic programming
  • optimal preventive maintenance
  • running costs
  • semi-Markov decision processes
  • two-unit systems

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics


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