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Optimization problems of replacement first or last in reliability theory


  • Zhao, Xufeng
  • Nakagawa, Toshio


This paper takes up age and periodic replacement last models with working cycles, where the unit is replaced before failure at a total operating time T or at a random working cycle Y, whichever occurs last, which is called replacement last. Expected cost rates are formulated, and optimal replacement policies which minimize them are discussed analytically. Comparisons between such a replacement last and the conventional replacement first are made in detail. It is determined theoretically and numerically which policy is better than the other according to the ratios of replacement costs and how the mean time of working cycles affects the comparison results. It is also shown that the unit can be operating for a longer time and avoid unnecessary replacements when replacement last is done. For further studies, expected cost rates of modified models and their applications in a standard cumulative damage model with working cycles are obtained and computed numerically. Finally, case studies on replacement last and first in maintaining electronic systems of naval ships under battle and non-battle statuses are given.

Suggested Citation

  • Zhao, Xufeng & Nakagawa, Toshio, 2012. "Optimization problems of replacement first or last in reliability theory," European Journal of Operational Research, Elsevier, vol. 223(1), pages 141-149.
  • Handle: RePEc:eee:ejores:v:223:y:2012:i:1:p:141-149
    DOI: 10.1016/j.ejor.2012.05.035

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    References listed on IDEAS

    1. Montoro-Cazorla, Delia & Pérez-Ocón, Rafael, 2011. "Two shock and wear systems under repair standing a finite number of shocks," European Journal of Operational Research, Elsevier, vol. 214(2), pages 298-307, October.
    2. repec:eee:reensy:v:93:y:2008:i:3:p:433-446 is not listed on IDEAS
    3. Berrade, M.D. & Cavalcante, Cristiano A.V. & Scarf, Philip A., 2012. "Maintenance scheduling of a protection system subject to imperfect inspection and replacement," European Journal of Operational Research, Elsevier, vol. 218(3), pages 716-725.
    4. Sheu, Shey-Huei & Griffith, William S., 2002. "Extended block replacement policy with shock models and used items," European Journal of Operational Research, Elsevier, vol. 140(1), pages 50-60, July.
    5. Sheu, Shey-Huei & Chang, Chin-Chih & Zhang, Zhe George & Chien, Yu-Hung, 2012. "A note on replacement policy for a system subject to non-homogeneous pure birth shocks," European Journal of Operational Research, Elsevier, vol. 216(2), pages 503-508.
    6. Sheu, Shey-Huei & Chien, Yu-Hung, 2004. "Optimal age-replacement policy of a system subject to shocks with random lead-time," European Journal of Operational Research, Elsevier, vol. 159(1), pages 132-144, November.
    7. Deris, Safaai & Omatu, Sigeru & Ohta, Hiroshi & Shaharudin Kutar, Lt. Cdr & Abd Samat, Pathiah, 1999. "Ship maintenance scheduling by genetic algorithm and constraint-based reasoning," European Journal of Operational Research, Elsevier, vol. 112(3), pages 489-502, February.
    8. Taghipour, Sharareh & Banjevic, Dragan, 2012. "Optimal inspection of a complex system subject to periodic and opportunistic inspections and preventive replacements," European Journal of Operational Research, Elsevier, vol. 220(3), pages 649-660.
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    5. repec:eee:reensy:v:142:y:2015:i:c:p:203-211 is not listed on IDEAS
    6. Zhao, Xufeng & Mizutani, Satoshi & Nakagawa, Toshio, 2015. "Which is better for replacement policies with continuous or discrete scheduled times?," European Journal of Operational Research, Elsevier, vol. 242(2), pages 477-486.
    7. repec:eee:reensy:v:110:y:2013:i:c:p:50-59 is not listed on IDEAS
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    12. repec:eee:reensy:v:154:y:2016:i:c:p:42-48 is not listed on IDEAS


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